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\refsection{0}
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      \field{abstract}{Strut-braced wing (SBW) is considered in the ongoing ONERA research project ALBATROS as one of a potential fuel-saving transport aircraft configuration. Although not a new concept [1] (several aircraft such as the Hurel-Dubois HD-34, 1956, have used this concept), it has recently received renewed interest since [2][3][4][5][6][7][8][9]. Indeed, the structural strut enables a reduction of the wing weight thanks to the reduction of the bending moment to be sustained by the wing box. The presence of the strut therefore enables to increase the wing aspect ratio, which results in direct aerodynamic performance gains, without considerable weight penalty as it is the case with conventional cantilever wings. The ALBATROS project aims at evaluating the potential of a strut-braced wing concept to improve the aero-structural efficiency of transonic transport aircraft. For that, specific studies are carried out to investigate the potential gains and possible problems of the concept in term of aerodynamics, structures and flight mechanics.}
      \field{title}{Investigation of a {Strut}-{Braced} {Wing} {Configuration} for {Future} {Commercial} {Transport}}
      \field{year}{2012}
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      \field{booktitle}{{AIAA} {SCITECH} 2022 {Forum}}
      \field{month}{12}
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      \field{title}{Multidisciplinary analysis and design of strut-braced wing concept for medium range aircraft}
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      \field{urlyear}{2024}
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      \keyw{Aerodynamic Coefficients,Aerodynamic Performance,Aircraft Conceptual Design,Aircraft Configurations,Aircraft Design,Cantilever,High Aspect Ratio,Structural Analysis,Transport Aircraft,Wing Configurations}
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      \field{abstract}{Airbus has revealed three concepts for the world’s first zero-emission commercial aircraft which could enter service by 2035. These concepts each represent a different approach to achieving zero-emission flight, exploring various technology pathways and aerodynamic configurations in order to support the Company’s ambition of leading the way in the decarbonisation of the entire aviation industry.}
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    \entry{belvin_space_2016}{inproceedings}{}
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      \field{booktitle}{3rd {AIAA} {Spacecraft} {Structures} {Conference}}
      \field{month}{1}
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      \field{shorttitle}{In-{Space} {Structural} {Assembly}}
      \field{title}{In-{Space} {Structural} {Assembly}: {Applications} and {Technology}}
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      \keyw{High Definition Space Telescope,Human Exploration Destination Systems,Infrared Telescopes,International Space Station,Planar Truss,Planets,Robotics,Solar Electric Propulsion,Spacecraft System,Structural Technology}
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      \field{issn}{0036-8075, 1095-9203}
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      \field{title}{Reversibly {Assembled} {Cellular} {Composite} {Materials}}
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      \field{title}{Algorithmic {Approaches} to {Reconfigurable} {Assembly} {Systems}}
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      \field{title}{Topology {Optimization}}
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      \field{year}{2004}
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      \field{abstract}{The paper presents a uniform method of treating a variety of problems of optimal design of sandwich structures. The design procedure consists of two steps: The integration of an optimality condition, which is a differential equation for the optimal displacement field that does not involve any design parameters, and the subsequent determination of the optimal distribution of elastic stiffness or plastic resistance from the usual differential equations of the structure. Optimal elastic design for maximum stiffness, maximum fundamental frequency, or maximum buckling load, and optimal plastic design for maximum safety are treated as examples.}
      \field{issn}{0021-8936}
      \field{journaltitle}{Journal of Applied Mechanics}
      \field{month}{3}
      \field{number}{1}
      \field{title}{Problems of {Optimal} {Structural} {Design}}
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      \field{issn}{0027-8424}
      \field{journaltitle}{Proceedings of the National Academy of Sciences of the United States of America}
      \field{number}{3}
      \field{title}{Optimality {Criteria} in {Structural} {Design}}
      \field{urlday}{9}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{61}
      \field{year}{1968}
      \field{urldateera}{ce}
      \field{pages}{794\bibrangedash 796}
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           family={Kikuchi},
           familyi={K\bibinitperiod},
           given={Noboru},
           giveni={N\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{97a2ed0b27e78a3a4c50980973627aae}
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      \field{issn}{0045-7825}
      \field{journaltitle}{Computer Methods in Applied Mechanics and Engineering}
      \field{month}{11}
      \field{number}{2}
      \field{title}{Generating optimal topologies in structural design using a homogenization method}
      \field{urlday}{13}
      \field{urlmonth}{10}
      \field{urlyear}{2020}
      \field{volume}{71}
      \field{year}{1988}
      \field{urldateera}{ce}
      \field{pages}{197\bibrangedash 224}
      \range{pages}{28}
      \verb{doi}
      \verb 10.1016/0045-7825(88)90086-2
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      \verb http://www.sciencedirect.com/science/article/pii/0045782588900862
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      \verb{url}
      \verb http://www.sciencedirect.com/science/article/pii/0045782588900862
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    \entry{bendsoe_optimization_1995}{book}{}
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           given={Martin\bibnamedelima P.},
           giveni={M\bibinitperiod\bibinitdelim P\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \list{location}{1}{%
        {Berlin, Heidelberg}%
      }
      \list{publisher}{1}{%
        {Springer Berlin Heidelberg}%
      }
      \strng{namehash}{066757951bb74a0ccbc836e088427aea}
      \strng{fullhash}{066757951bb74a0ccbc836e088427aea}
      \strng{bibnamehash}{066757951bb74a0ccbc836e088427aea}
      \strng{authorbibnamehash}{066757951bb74a0ccbc836e088427aea}
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      \field{isbn}{978-3-662-03117-9 978-3-662-03115-5}
      \field{title}{Optimization of {Structural} {Topology}, {Shape}, and {Material}}
      \field{year}{1995}
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      \verb 10.1007/978-3-662-03115-5
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    \endentry
    \entry{sigmund_99_2001}{article}{}
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           family={Sigmund},
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           given={O.},
           giveni={O\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{8e39f252b54fbee1f97675ee90b87f23}
      \strng{fullhash}{8e39f252b54fbee1f97675ee90b87f23}
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      \field{labeltitlesource}{title}
      \field{issn}{1615-147X, 1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{4}
      \field{number}{2}
      \field{title}{A 99 line topology optimization code written in {Matlab}}
      \field{urlday}{9}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{21}
      \field{year}{2001}
      \field{urldateera}{ce}
      \field{pages}{120\bibrangedash 127}
      \range{pages}{8}
      \verb{doi}
      \verb 10.1007/s001580050176
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      \verb{file}
      \verb Full Text:D\:\\estragio\\Zotero\\storage\\IGHV78QG\\Sigmund - 2001 - A 99 line topology optimization code written in Ma.pdf:application/pdf
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      \verb{urlraw}
      \verb http://link.springer.com/10.1007/s001580050176
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      \verb http://link.springer.com/10.1007/s001580050176
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    \endentry
    \entry{allaire_homogenization_1996}{article}{}
      \name{author}{3}{}{%
        {{hash=e689b43ac5d3242f4613a353518abfb7}{%
           family={Allaire},
           familyi={A\bibinitperiod},
           given={Grégoire},
           giveni={G\bibinitperiod}}}%
        {{hash=9b2489461a2e707ed8e2220ecf5fb5c9}{%
           family={Belhachmi},
           familyi={B\bibinitperiod},
           given={Zakaria},
           giveni={Z\bibinitperiod}}}%
        {{hash=71dd35ee6f0ac1ffa65812bb0ea5c7e8}{%
           family={Jouve},
           familyi={J\bibinitperiod},
           given={François},
           giveni={F\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{0f594d449ee7d56313be907c3c0e2b0a}
      \strng{fullhash}{0f594d449ee7d56313be907c3c0e2b0a}
      \strng{bibnamehash}{0f594d449ee7d56313be907c3c0e2b0a}
      \strng{authorbibnamehash}{0f594d449ee7d56313be907c3c0e2b0a}
      \strng{authornamehash}{0f594d449ee7d56313be907c3c0e2b0a}
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      \field{labeltitlesource}{title}
      \field{abstract}{This paper is devoted to an elementary introduction to the homogenization method applied to topology and shape optimization of elastic structures under single and multiple external loads. The single load case, in the context of minimum compliance and weight design of elastic structures, has been fully described in its theoretical as well as its numerical aspects in [4]. It is here brieﬂy recalled. In the more realistic context of “multiple loads”, i.e. when the structure is optimized with respect to more than one set of external forces, most of the obtained theoretical results remain true. However, the parameters that deﬁne optimal composite materials cannot be computed explicitly. In this paper, a method to treat numerically the multiple loads case is proposed.}
      \field{issn}{1250-6559}
      \field{journaltitle}{Revue Européenne des Éléments Finis}
      \field{month}{1}
      \field{number}{5-6}
      \field{title}{The homogenization method for topology and shape optimization. {Single} and multiple loads case}
      \field{urlday}{9}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{5}
      \field{year}{1996}
      \field{urldateera}{ce}
      \field{pages}{649\bibrangedash 672}
      \range{pages}{24}
      \verb{doi}
      \verb 10.1080/12506559.1996.10511241
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      \verb{file}
      \verb Allaire et al. - 1996 - The homogenization method for topology and shape o.pdf:D\:\\estragio\\Zotero\\storage\\F7S628NX\\Allaire et al. - 1996 - The homogenization method for topology and shape o.pdf:application/pdf
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      \verb{url}
      \verb https://www.tandfonline.com/doi/full/10.1080/12506559.1996.10511241
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    \endentry
    \entry{li_accelerated_2020}{article}{}
      \name{author}{3}{}{%
        {{hash=ebf6a7335f287cd5be3f31fef0909fc0}{%
           family={Li},
           familyi={L\bibinitperiod},
           given={Weichen},
           giveni={W\bibinitperiod}}}%
        {{hash=65eddc3eafad476927e069af7723e43a}{%
           family={Suryanarayana},
           familyi={S\bibinitperiod},
           given={Phanish},
           giveni={P\bibinitperiod}}}%
        {{hash=d23667ac0203644c62a6179e0cd9673d}{%
           family={Paulino},
           familyi={P\bibinitperiod},
           given={Glaucio\bibnamedelima H.},
           giveni={G\bibinitperiod\bibinitdelim H\bibinitperiod}}}%
      }
      \strng{namehash}{7cbf2855bceed845e99b15a1fa0ffed6}
      \strng{fullhash}{7cbf2855bceed845e99b15a1fa0ffed6}
      \strng{bibnamehash}{7cbf2855bceed845e99b15a1fa0ffed6}
      \strng{authorbibnamehash}{7cbf2855bceed845e99b15a1fa0ffed6}
      \strng{authornamehash}{7cbf2855bceed845e99b15a1fa0ffed6}
      \strng{authorfullhash}{7cbf2855bceed845e99b15a1fa0ffed6}
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      \field{sortinithash}{108d0be1b1bee9773a1173443802c0a3}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{shorttitle}
      \field{abstract}{We present a simple, effective, and scalable approach for significantly accelerating the convergence in Topology Optimization simulations. Specifically, treating the design process as a fixed-point iteration, we propose employing a recently developed acceleration technique in which Anderson extrapolation is applied periodically, with simple weighted relaxation used for the remaining steps. Through selected examples in compliance minimization, we show that the proposed approach is able to accelerate the overall simulation several fold, while maintaining the quality of the solution.}
      \field{issn}{0093-6413}
      \field{journaltitle}{Mechanics Research Communications}
      \field{month}{1}
      \field{shorttitle}{Accelerated fixed-point formulation of topology optimization}
      \field{title}{Accelerated fixed-point formulation of topology optimization: {Application} to compliance minimization problems}
      \field{urlday}{11}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{103}
      \field{year}{2020}
      \field{urldateera}{ce}
      \field{pages}{103469}
      \range{pages}{1}
      \verb{doi}
      \verb 10.1016/j.mechrescom.2019.103469
      \endverb
      \verb{urlraw}
      \verb https://www.sciencedirect.com/science/article/pii/S0093641319305051
      \endverb
      \verb{url}
      \verb https://www.sciencedirect.com/science/article/pii/S0093641319305051
      \endverb
      \keyw{Anderson extrapolation,Compliance minimization,Fixed-point iteration,Optimality criteria,Topology optimization}
    \endentry
    \entry{ferrari_new_2020}{article}{}
      \name{author}{2}{}{%
        {{hash=8ea05860eca5cf81174a397fc54c388e}{%
           family={Ferrari},
           familyi={F\bibinitperiod},
           given={Federico},
           giveni={F\bibinitperiod}}}%
        {{hash=d76f1c09e8d8d06e1b7c3c254efeae1a}{%
           family={Sigmund},
           familyi={S\bibinitperiod},
           given={Ole},
           giveni={O\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{42e939677318d23dc9868cc4c55ec42e}
      \strng{fullhash}{42e939677318d23dc9868cc4c55ec42e}
      \strng{bibnamehash}{42e939677318d23dc9868cc4c55ec42e}
      \strng{authorbibnamehash}{42e939677318d23dc9868cc4c55ec42e}
      \strng{authornamehash}{42e939677318d23dc9868cc4c55ec42e}
      \strng{authorfullhash}{42e939677318d23dc9868cc4c55ec42e}
      \field{sortinit}{7}
      \field{sortinithash}{108d0be1b1bee9773a1173443802c0a3}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Compact and efficient Matlab implementations of compliance topology optimization (TO) for 2D and 3D continua are given, consisting of 99 and 125 lines respectively. On discretizations ranging from 3 ⋅ 104 to 4.8 ⋅ 105 elements, the 2D version, named top99neo, shows speedups from 2.55 to 5.5 times compared to the well-known top88 code of Andreassen et al. (Struct Multidiscip Optim 43(1):1–16, 2011). The 3D version, named top3D125, is the most compact and efficient Matlab implementation for 3D TO to date, showing a speedup of 1.9 times compared to the code of Amir et al. (Struct Multidiscip Optim 49(5):815–829, 2014), on a discretization with 2.2 ⋅ 105 elements. For both codes, improvements are due to much more efficient procedures for the assembly and implementation of filters and shortcuts in the design update step. The use of an acceleration strategy, yielding major cuts in the overall computational time, is also discussed, stressing its easy integration within the basic codes.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{10}
      \field{number}{4}
      \field{title}{A new generation 99 line {Matlab} code for compliance topology optimization and its extension to {3D}}
      \field{urlday}{29}
      \field{urlmonth}{8}
      \field{urlyear}{2023}
      \field{volume}{62}
      \field{year}{2020}
      \field{urldateera}{ce}
      \field{pages}{2211\bibrangedash 2228}
      \range{pages}{18}
      \verb{doi}
      \verb 10.1007/s00158-020-02629-w
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\V33SC4NV\\Ferrari and Sigmund - 2020 - A new generation 99 line Matlab code for complianc.pdf:application/pdf
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      \verb{urlraw}
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      \verb{url}
      \verb https://doi.org/10.1007/s00158-020-02629-w
      \endverb
      \keyw{Acceleration methods,Computational efficiency,Matlab,Topology optimization}
    \endentry
    \entry{anderson_iterative_1965}{article}{}
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        {{hash=7e126090ab137d73927b5fc2e57c9628}{%
           family={Anderson},
           familyi={A\bibinitperiod},
           given={Donald\bibnamedelima G.},
           giveni={D\bibinitperiod\bibinitdelim G\bibinitperiod}}}%
      }
      \strng{namehash}{7e126090ab137d73927b5fc2e57c9628}
      \strng{fullhash}{7e126090ab137d73927b5fc2e57c9628}
      \strng{bibnamehash}{7e126090ab137d73927b5fc2e57c9628}
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      \strng{authornamehash}{7e126090ab137d73927b5fc2e57c9628}
      \strng{authorfullhash}{7e126090ab137d73927b5fc2e57c9628}
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      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{issn}{0004-5411}
      \field{journaltitle}{Journal of the ACM}
      \field{month}{10}
      \field{number}{4}
      \field{title}{Iterative {Procedures} for {Nonlinear} {Integral} {Equations}}
      \field{urlday}{11}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{12}
      \field{year}{1965}
      \field{urldateera}{ce}
      \field{pages}{547\bibrangedash 560}
      \range{pages}{14}
      \verb{doi}
      \verb 10.1145/321296.321305
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      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\RK394ISY\\Anderson - 1965 - Iterative Procedures for Nonlinear Integral Equati.pdf:application/pdf
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      \verb https://dl.acm.org/doi/10.1145/321296.321305
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      \verb{url}
      \verb https://dl.acm.org/doi/10.1145/321296.321305
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    \entry{conn_introduction_2009}{book}{}
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        {{hash=c58a1dee7a9c46aa0891197fce7bdd88}{%
           family={Conn},
           familyi={C\bibinitperiod},
           given={Andrew\bibnamedelima R.},
           giveni={A\bibinitperiod\bibinitdelim R\bibinitperiod}}}%
        {{hash=227fd756890273896e67d801c215790f}{%
           family={Scheinberg},
           familyi={S\bibinitperiod},
           given={Katya},
           giveni={K\bibinitperiod}}}%
        {{hash=c6e8d6bbfdfa70386adea45b40083afb}{%
           family={Vicente},
           familyi={V\bibinitperiod},
           given={Luis\bibnamedelima N.},
           giveni={L\bibinitperiod\bibinitdelim N\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \list{publisher}{2}{%
        {Society for Industrial}%
        {Applied Mathematics}%
      }
      \strng{namehash}{b22601daa4b8425395199ff4496a433a}
      \strng{fullhash}{b22601daa4b8425395199ff4496a433a}
      \strng{bibnamehash}{b22601daa4b8425395199ff4496a433a}
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      \strng{authornamehash}{b22601daa4b8425395199ff4496a433a}
      \strng{authorfullhash}{b22601daa4b8425395199ff4496a433a}
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      \field{labeltitlesource}{title}
      \field{isbn}{978-0-89871-668-9 978-0-89871-876-8}
      \field{month}{1}
      \field{title}{Introduction to {Derivative}-{Free} {Optimization}}
      \field{urlday}{9}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{year}{2009}
      \field{urldateera}{ce}
      \verb{doi}
      \verb 10.1137/1.9780898718768
      \endverb
      \verb{urlraw}
      \verb http://epubs.siam.org/doi/book/10.1137/1.9780898718768
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      \verb{url}
      \verb http://epubs.siam.org/doi/book/10.1137/1.9780898718768
      \endverb
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    \entry{audet_derivative-free_2017}{book}{}
      \name{author}{2}{}{%
        {{hash=ed0b747bdbc1c890273435f38ee58f68}{%
           family={Audet},
           familyi={A\bibinitperiod},
           given={Charles},
           giveni={C\bibinitperiod}}}%
        {{hash=a89f482f852c8a0cdaf391220173ff9f}{%
           family={Hare},
           familyi={H\bibinitperiod},
           given={Warren},
           giveni={W\bibinitperiod}}}%
      }
      \list{location}{1}{%
        {Cham}%
      }
      \list{publisher}{1}{%
        {Springer International Publishing}%
      }
      \strng{namehash}{b0ea96677380aa959961b1b7f1eb72b4}
      \strng{fullhash}{b0ea96677380aa959961b1b7f1eb72b4}
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      \field{isbn}{978-3-319-68912-8 978-3-319-68913-5}
      \field{series}{Springer {Series} in {Operations} {Research} and {Financial} {Engineering}}
      \field{title}{Derivative-{Free} and {Blackbox} {Optimization}}
      \field{urlday}{9}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{year}{2017}
      \field{urldateera}{ce}
      \verb{doi}
      \verb 10.1007/978-3-319-68913-5
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      \verb{file}
      \verb Submitted Version:D\:\\estragio\\Zotero\\storage\\NDDKUXFP\\Audet and Hare - 2017 - Derivative-Free and Blackbox Optimization.pdf:application/pdf
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      \verb{urlraw}
      \verb http://link.springer.com/10.1007/978-3-319-68913-5
      \endverb
      \verb{url}
      \verb http://link.springer.com/10.1007/978-3-319-68913-5
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    \endentry
    \entry{simon_evolutionary_2013}{book}{}
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        {{hash=d2075620d3db6f848d4904775355e936}{%
           family={Simon},
           familyi={S\bibinitperiod},
           given={Dan},
           giveni={D\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {eng}%
      }
      \list{location}{1}{%
        {Hoboken, NJ}%
      }
      \list{publisher}{1}{%
        {Wiley}%
      }
      \strng{namehash}{d2075620d3db6f848d4904775355e936}
      \strng{fullhash}{d2075620d3db6f848d4904775355e936}
      \strng{bibnamehash}{d2075620d3db6f848d4904775355e936}
      \strng{authorbibnamehash}{d2075620d3db6f848d4904775355e936}
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      \field{labeltitlesource}{shorttitle}
      \field{edition}{1. ed}
      \field{isbn}{978-1-118-65950-2 978-0-470-93741-9}
      \field{shorttitle}{Evolutionary optimization algorithms}
      \field{title}{Evolutionary optimization algorithms: biologically-inspired and population-based approaches to computer intelligence}
      \field{year}{2013}
      \verb{file}
      \verb Table of Contents PDF:D\:\\estragio\\Zotero\\storage\\UD9458J9\\Simon - 2013 - Evolutionary optimization algorithms biologically.pdf:application/pdf
      \endverb
    \endentry
    \entry{balamurugan_two_2011}{article}{}
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           family={Balamurugan},
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           given={R.},
           giveni={R\bibinitperiod}}}%
        {{hash=1886efc85417d01066a3d0749fb4cb01}{%
           family={Ramakrishnan},
           familyi={R\bibinitperiod},
           given={C.\bibnamedelimi V.},
           giveni={C\bibinitperiod\bibinitdelim V\bibinitperiod}}}%
        {{hash=e036b92e0d080682c84949cef65d1de8}{%
           family={Swaminathan},
           familyi={S\bibinitperiod},
           given={N.},
           giveni={N\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{8c4d4919ff7527a5def5d6aa95158c4e}
      \strng{fullhash}{8c4d4919ff7527a5def5d6aa95158c4e}
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      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{issn}{1615-147X, 1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{3}
      \field{number}{3}
      \field{title}{A two phase approach based on skeleton convergence and geometric variables for topology optimization using genetic algorithm}
      \field{urlday}{9}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{43}
      \field{year}{2011}
      \field{urldateera}{ce}
      \field{pages}{381\bibrangedash 404}
      \range{pages}{24}
      \verb{doi}
      \verb 10.1007/s00158-010-0560-4
      \endverb
      \verb{urlraw}
      \verb http://link.springer.com/10.1007/s00158-010-0560-4
      \endverb
      \verb{url}
      \verb http://link.springer.com/10.1007/s00158-010-0560-4
      \endverb
    \endentry
    \entry{sigmund_usefulness_2011}{article}{}
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        {{hash=d76f1c09e8d8d06e1b7c3c254efeae1a}{%
           family={Sigmund},
           familyi={S\bibinitperiod},
           given={Ole},
           giveni={O\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{fullhash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
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      \field{issn}{1615-147X, 1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{5}
      \field{number}{5}
      \field{title}{On the usefulness of non-gradient approaches in topology optimization}
      \field{urlday}{21}
      \field{urlmonth}{10}
      \field{urlyear}{2020}
      \field{volume}{43}
      \field{year}{2011}
      \field{urldateera}{ce}
      \field{pages}{589\bibrangedash 596}
      \range{pages}{8}
      \verb{doi}
      \verb 10.1007/s00158-011-0638-7
      \endverb
      \verb{urlraw}
      \verb http://link.springer.com/10.1007/s00158-011-0638-7
      \endverb
      \verb{url}
      \verb http://link.springer.com/10.1007/s00158-011-0638-7
      \endverb
    \endentry
    \entry{luh_structural_2009}{article}{}
      \name{author}{2}{}{%
        {{hash=2adb7ba20295d7137b3979fe1fdbd753}{%
           family={Luh},
           familyi={L\bibinitperiod},
           given={Guan-Chun},
           giveni={G\bibinithyphendelim C\bibinitperiod}}}%
        {{hash=7f9b5c9dd3dc44d1d55de069b29ffd88}{%
           family={Lin},
           familyi={L\bibinitperiod},
           given={Chun-Yi},
           giveni={C\bibinithyphendelim Y\bibinitperiod}}}%
      }
      \strng{namehash}{8483bd04bdd70a2ff4c5dcdcfbfe8d6c}
      \strng{fullhash}{8483bd04bdd70a2ff4c5dcdcfbfe8d6c}
      \strng{bibnamehash}{8483bd04bdd70a2ff4c5dcdcfbfe8d6c}
      \strng{authorbibnamehash}{8483bd04bdd70a2ff4c5dcdcfbfe8d6c}
      \strng{authornamehash}{8483bd04bdd70a2ff4c5dcdcfbfe8d6c}
      \strng{authorfullhash}{8483bd04bdd70a2ff4c5dcdcfbfe8d6c}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{The ant colony optimization (ACO) algorithm, a relatively recent bio-inspired approach to solve combinatorial optimization problems mimicking the behavior of real ant colonies, is applied to problems of continuum structural topology design. An overview of the ACO algorithm is first described. A discretized topology design representation and the method for mapping ant's trail into this representation are then detailed. Subsequently, a modified ACO algorithm with elitist ants, niche strategy and memory of multiple colonies is illustrated. Several well-studied examples from structural topology optimization problems of minimum weight and minimum compliance are used to demonstrate its efficiency and versatility. The results indicate the effectiveness of the proposed algorithm and its ability to find families of multi-modal optimal design.}
      \field{issn}{1568-4946}
      \field{journaltitle}{Applied Soft Computing}
      \field{month}{9}
      \field{number}{4}
      \field{title}{Structural topology optimization using ant colony optimization algorithm}
      \field{urlday}{9}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{9}
      \field{year}{2009}
      \field{urldateera}{ce}
      \field{pages}{1343\bibrangedash 1353}
      \range{pages}{11}
      \verb{doi}
      \verb 10.1016/j.asoc.2009.06.001
      \endverb
      \verb{urlraw}
      \verb https://www.sciencedirect.com/science/article/pii/S1568494609000672
      \endverb
      \verb{url}
      \verb https://www.sciencedirect.com/science/article/pii/S1568494609000672
      \endverb
      \keyw{Ant colony optimization algorithm,Continuum structural topology optimization,Elitist ants,Multiple colonies,Niche strategy}
    \endentry
    \entry{luh_binary_2011}{article}{}
      \name{author}{3}{}{%
        {{hash=2adb7ba20295d7137b3979fe1fdbd753}{%
           family={Luh},
           familyi={L\bibinitperiod},
           given={Guan-Chun},
           giveni={G\bibinithyphendelim C\bibinitperiod}}}%
        {{hash=7f9b5c9dd3dc44d1d55de069b29ffd88}{%
           family={Lin},
           familyi={L\bibinitperiod},
           given={Chun-Yi},
           giveni={C\bibinithyphendelim Y\bibinitperiod}}}%
        {{hash=5791bf33a24574a7151f7f0d6b1eaa4d}{%
           family={Lin},
           familyi={L\bibinitperiod},
           given={Yu-Shu},
           giveni={Y\bibinithyphendelim S\bibinitperiod}}}%
      }
      \strng{namehash}{1a1a6551dc456b807b36965112d2cb0b}
      \strng{fullhash}{1a1a6551dc456b807b36965112d2cb0b}
      \strng{bibnamehash}{1a1a6551dc456b807b36965112d2cb0b}
      \strng{authorbibnamehash}{1a1a6551dc456b807b36965112d2cb0b}
      \strng{authornamehash}{1a1a6551dc456b807b36965112d2cb0b}
      \strng{authorfullhash}{1a1a6551dc456b807b36965112d2cb0b}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{The particle swarm optimization (PSO) algorithm, a relatively recent bio-inspired approach to solve combinatorial optimization problems mimicking the social behavior of birds flocking, is applied to problems of continuum structural topology design for the purpose of investigating optimal topologies and automatically creating innovative solutions. An overview of the PSO and binary PSO algorithms are first described. A discretized topology design representation and the method for mapping binary particle into this representation are then detailed. Subsequently, a modified binary PSO algorithm that adopts the concept of genotype–phenotype representation is illustrated. Several well-studied examples from structural topology optimization problems of minimum weight and minimum compliance are used to demonstrate its efficiency and versatility. The results indicate the effectiveness of the proposed algorithm and its ability to find families of structural topologies.}
      \field{issn}{1568-4946}
      \field{journaltitle}{Applied Soft Computing}
      \field{month}{3}
      \field{number}{2}
      \field{series}{The {Impact} of {Soft} {Computing} for the {Progress} of {Artificial} {Intelligence}}
      \field{title}{A binary particle swarm optimization for continuum structural topology optimization}
      \field{urlday}{9}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{11}
      \field{year}{2011}
      \field{urldateera}{ce}
      \field{pages}{2833\bibrangedash 2844}
      \range{pages}{12}
      \verb{doi}
      \verb 10.1016/j.asoc.2010.11.013
      \endverb
      \verb{urlraw}
      \verb https://www.sciencedirect.com/science/article/pii/S1568494610002905
      \endverb
      \verb{url}
      \verb https://www.sciencedirect.com/science/article/pii/S1568494610002905
      \endverb
      \keyw{Binary particle swarm optimization,Continuum structural topology optimization,Genotype–phenotype representation}
    \endentry
    \entry{stolpe_global_2004}{article}{}
      \name{author}{1}{}{%
        {{hash=9bad1d1c66b6ba268b1b0102bf0ab5ad}{%
           family={Stolpe},
           familyi={S\bibinitperiod},
           given={M.},
           giveni={M\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{9bad1d1c66b6ba268b1b0102bf0ab5ad}
      \strng{fullhash}{9bad1d1c66b6ba268b1b0102bf0ab5ad}
      \strng{bibnamehash}{9bad1d1c66b6ba268b1b0102bf0ab5ad}
      \strng{authorbibnamehash}{9bad1d1c66b6ba268b1b0102bf0ab5ad}
      \strng{authornamehash}{9bad1d1c66b6ba268b1b0102bf0ab5ad}
      \strng{authorfullhash}{9bad1d1c66b6ba268b1b0102bf0ab5ad}
      \field{extraname}{1}
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      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{issn}{1097-0207}
      \field{journaltitle}{International Journal for Numerical Methods in Engineering}
      \field{number}{8}
      \field{title}{Global optimization of minimum weight truss topology problems with stress, displacement, and local buckling constraints using branch-and-bound}
      \field{urlday}{25}
      \field{urlmonth}{3}
      \field{urlyear}{2021}
      \field{volume}{61}
      \field{year}{2004}
      \field{urldateera}{ce}
      \field{pages}{1270\bibrangedash 1309}
      \range{pages}{40}
      \verb{doi}
      \verb https://doi.org/10.1002/nme.1112
      \endverb
      \keyw{topology optimization,global optimization,stress constraints}
    \endentry
    \entry{mattheck_new_1990}{article}{}
      \name{author}{2}{}{%
        {{hash=7227e1ee8bb2d1215d2c6ecb68589c6a}{%
           family={Mattheck},
           familyi={M\bibinitperiod},
           given={C.},
           giveni={C\bibinitperiod}}}%
        {{hash=d988865193b5b073d8be7ce6e9a4b7ab}{%
           family={Burkhardt},
           familyi={B\bibinitperiod},
           given={S.},
           giveni={S\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{5123ddfe30000b4dbd8685f5be63f190}
      \strng{fullhash}{5123ddfe30000b4dbd8685f5be63f190}
      \strng{bibnamehash}{5123ddfe30000b4dbd8685f5be63f190}
      \strng{authorbibnamehash}{5123ddfe30000b4dbd8685f5be63f190}
      \strng{authornamehash}{5123ddfe30000b4dbd8685f5be63f190}
      \strng{authorfullhash}{5123ddfe30000b4dbd8685f5be63f190}
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      \field{labeltitlesource}{title}
      \field{abstract}{A new method has been developed which allows the reduction of localized notch stresses in two-dimensional (2D) and three-dimensional (3D) elastic structures in a very effective way, with only a commercial finite-element code (the authors used ABAQUS) required. The method simulates on a computer the mechanism of tree growth copying the self-optimization of living trees which always try to grow into a shape of constant surface stress. The success and efficiency of the method is demonstrated by 2D and 3D examples.}
      \field{issn}{0142-1123}
      \field{journaltitle}{International Journal of Fatigue}
      \field{month}{5}
      \field{number}{3}
      \field{title}{A new method of structural shape optimization based on biological growth}
      \field{urlday}{13}
      \field{urlmonth}{1}
      \field{urlyear}{2021}
      \field{volume}{12}
      \field{year}{1990}
      \field{urldateera}{ce}
      \field{pages}{185\bibrangedash 190}
      \range{pages}{6}
      \verb{doi}
      \verb 10.1016/0142-1123(90)90094-U
      \endverb
      \verb{file}
      \verb ScienceDirect Full Text PDF:D\:\\estragio\\Zotero\\storage\\CTWA3SM7\\Mattheck and Burkhardt - 1990 - A new method of structural shape optimization base.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb http://www.sciencedirect.com/science/article/pii/014211239090094U
      \endverb
      \verb{url}
      \verb http://www.sciencedirect.com/science/article/pii/014211239090094U
      \endverb
      \keyw{biological structures,elastic structures,finite-element code,notches,self-optimized shapes}
    \endentry
    \entry{xie_simple_1993}{article}{}
      \name{author}{2}{}{%
        {{hash=dfa4794abf731bd58660a4dae45c4dad}{%
           family={Xie},
           familyi={X\bibinitperiod},
           given={Y.\bibnamedelimi M.},
           giveni={Y\bibinitperiod\bibinitdelim M\bibinitperiod}}}%
        {{hash=71660560a4d13ee9a5b8a107628e1a6f}{%
           family={Steven},
           familyi={S\bibinitperiod},
           given={G.\bibnamedelimi P.},
           giveni={G\bibinitperiod\bibinitdelim P\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{1c5f72e963fbf01d149227877826e5f4}
      \strng{fullhash}{1c5f72e963fbf01d149227877826e5f4}
      \strng{bibnamehash}{1c5f72e963fbf01d149227877826e5f4}
      \strng{authorbibnamehash}{1c5f72e963fbf01d149227877826e5f4}
      \strng{authornamehash}{1c5f72e963fbf01d149227877826e5f4}
      \strng{authorfullhash}{1c5f72e963fbf01d149227877826e5f4}
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      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{A simple evolutionary procedure is proposed for shape and layout optimization of structures. During the evolution process low stressed material is progressively eliminated from the structure. Various examples are presented to illustrate the optimum structural shapes and layouts achieved by such a procedure.}
      \field{issn}{0045-7949}
      \field{journaltitle}{Computers \&amp; Structures}
      \field{month}{12}
      \field{number}{5}
      \field{title}{A simple evolutionary procedure for structural optimization}
      \field{urlday}{13}
      \field{urlmonth}{1}
      \field{urlyear}{2021}
      \field{volume}{49}
      \field{year}{1993}
      \field{urldateera}{ce}
      \field{pages}{885\bibrangedash 896}
      \range{pages}{12}
      \verb{doi}
      \verb 10.1016/0045-7949(93)90035-C
      \endverb
      \verb{file}
      \verb ScienceDirect Full Text PDF:D\:\\estragio\\Zotero\\storage\\S3KAJU7K\\Xie and Steven - 1993 - A simple evolutionary procedure for structural opt.pdf:application/pdf
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      \verb{urlraw}
      \verb http://www.sciencedirect.com/science/article/pii/004579499390035C
      \endverb
      \verb{url}
      \verb http://www.sciencedirect.com/science/article/pii/004579499390035C
      \endverb
    \endentry
    \entry{manickarajah_evolutionary_1998}{article}{}
      \name{author}{3}{}{%
        {{hash=43b45fac476a3da0a6b5047a28285674}{%
           family={Manickarajah},
           familyi={M\bibinitperiod},
           given={D},
           giveni={D\bibinitperiod}}}%
        {{hash=dfa4794abf731bd58660a4dae45c4dad}{%
           family={Xie},
           familyi={X\bibinitperiod},
           given={Y.\bibnamedelimi M},
           giveni={Y\bibinitperiod\bibinitdelim M\bibinitperiod}}}%
        {{hash=71660560a4d13ee9a5b8a107628e1a6f}{%
           family={Steven},
           familyi={S\bibinitperiod},
           given={G.\bibnamedelimi P},
           giveni={G\bibinitperiod\bibinitdelim P\bibinitperiod}}}%
      }
      \strng{namehash}{3c2dc37be324dd7e588a5fdda29ac1ba}
      \strng{fullhash}{3c2dc37be324dd7e588a5fdda29ac1ba}
      \strng{bibnamehash}{3c2dc37be324dd7e588a5fdda29ac1ba}
      \strng{authorbibnamehash}{3c2dc37be324dd7e588a5fdda29ac1ba}
      \strng{authornamehash}{3c2dc37be324dd7e588a5fdda29ac1ba}
      \strng{authorfullhash}{3c2dc37be324dd7e588a5fdda29ac1ba}
      \field{sortinit}{1}
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      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Optimization of plate buckling resistance is very complicated, because the in-plane stress resultants in the prebuckled state of a plate are functions of thickness distribution. This paper discusses the problem of finding the optimum thickness distribution of isotropic plate structures, with a given volume and layout, that would maximise the buckling load. A simple numerical method using the finite-element analysis is presented to obtain the optimum thickness distribution. Optimum designs of compression-loaded rectangular plates with different boundary conditions and plate aspect ratios are obtained by using the proposed method. Optimum designs from earlier studies and the methods of buckling analysis used to attain these results are discussed and compared with the designs from the proposed method. This paper also examines the reliability of the optimality criterion generally used for plate buckling optimization, which is based on the uniform strain energy density.}
      \field{issn}{0168-874X}
      \field{journaltitle}{Finite Elements in Analysis and Design}
      \field{month}{6}
      \field{number}{3}
      \field{title}{An evolutionary method for optimization of plate buckling resistance}
      \field{urlday}{9}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{29}
      \field{year}{1998}
      \field{urldateera}{ce}
      \field{pages}{205\bibrangedash 230}
      \range{pages}{26}
      \verb{doi}
      \verb 10.1016/S0168-874X(98)00012-2
      \endverb
      \verb{urlraw}
      \verb https://www.sciencedirect.com/science/article/pii/S0168874X98000122
      \endverb
      \verb{url}
      \verb https://www.sciencedirect.com/science/article/pii/S0168874X98000122
      \endverb
      \keyw{Bimodal,Buckling resistance,Eigenvalue,Multimodal,Optimum design,Plate structures,Sensitivity number}
    \endentry
    \entry{young_3d_1999}{article}{}
      \name{author}{4}{}{%
        {{hash=556d6e142593b52789dcf41d7fb835b9}{%
           family={Young},
           familyi={Y\bibinitperiod},
           given={V.},
           giveni={V\bibinitperiod}}}%
        {{hash=9508075703a4777bac90b5f3836f76cf}{%
           family={Querin},
           familyi={Q\bibinitperiod},
           given={O.\bibnamedelimi M.},
           giveni={O\bibinitperiod\bibinitdelim M\bibinitperiod}}}%
        {{hash=71660560a4d13ee9a5b8a107628e1a6f}{%
           family={Steven},
           familyi={S\bibinitperiod},
           given={G.\bibnamedelimi P.},
           giveni={G\bibinitperiod\bibinitdelim P\bibinitperiod}}}%
        {{hash=dfa4794abf731bd58660a4dae45c4dad}{%
           family={Xie},
           familyi={X\bibinitperiod},
           given={Y.\bibnamedelimi M.},
           giveni={Y\bibinitperiod\bibinitdelim M\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{c559f7a85ef08286dcccf4cd67a09582}
      \strng{fullhash}{f3b5c7c4ec60470a6888d006466ec4e3}
      \strng{bibnamehash}{f3b5c7c4ec60470a6888d006466ec4e3}
      \strng{authorbibnamehash}{f3b5c7c4ec60470a6888d006466ec4e3}
      \strng{authornamehash}{c559f7a85ef08286dcccf4cd67a09582}
      \strng{authorfullhash}{f3b5c7c4ec60470a6888d006466ec4e3}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Evolutionary Structural Optimization (ESO), is a numerical method of structural optimization that is integrated with finite element analysis (FEA). Bi-directional ESO (BESO) is an extension to this method and can begin with minimal amount of material (only that necessary to support the load and support cases) in contrast to ESO which uses an initially oversized structure. Using BESO the structure is then allowed to grow into the optimum design or shape by both adding elements where the stresses are the highest and taking elements away where stresses are the lowest. In conducting this research, a methodology was developed (and integrated into the ESO program EVOLVE) which produced the optimal 3D finite element models of a structure in a more reliable way than the traditional ESO method. Additionally, the BESO method was successfully extended to multiple load cases for both 2D and 3D. Two different algorithms were used to find the best structure experiencing more than one load case and the results of each are included.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural optimization}
      \field{month}{10}
      \field{number}{2}
      \field{title}{{3D} and multiple load case bi-directional evolutionary structural optimization ({BESO})}
      \field{urlday}{13}
      \field{urlmonth}{1}
      \field{urlyear}{2021}
      \field{volume}{18}
      \field{year}{1999}
      \field{urldateera}{ce}
      \field{pages}{183\bibrangedash 192}
      \range{pages}{10}
      \verb{doi}
      \verb 10.1007/BF01195993
      \endverb
      \verb{file}
      \verb Springer Full Text PDF:D\:\\estragio\\Zotero\\storage\\8MCBK36H\\Young et al. - 1999 - 3D and multiple load case bi-directional evolution.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/BF01195993
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/BF01195993
      \endverb
    \endentry
    \entry{kraft_software_1988}{article}{}
      \name{author}{1}{}{%
        {{hash=1b8969ea21b1ab928b992d82a573d33e}{%
           family={Kraft},
           familyi={K\bibinitperiod},
           given={Dieter},
           giveni={D\bibinitperiod}}}%
      }
      \strng{namehash}{1b8969ea21b1ab928b992d82a573d33e}
      \strng{fullhash}{1b8969ea21b1ab928b992d82a573d33e}
      \strng{bibnamehash}{1b8969ea21b1ab928b992d82a573d33e}
      \strng{authorbibnamehash}{1b8969ea21b1ab928b992d82a573d33e}
      \strng{authornamehash}{1b8969ea21b1ab928b992d82a573d33e}
      \strng{authorfullhash}{1b8969ea21b1ab928b992d82a573d33e}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{journaltitle}{Tech. Rep. DFVLR-FB 88-28, DLR German Aerospace Center — Institute for Flight Mechanics, Koln, Germany.}
      \field{title}{A software package for sequential quadratic programming}
      \field{year}{1988}
      \verb{file}
      \verb DFVLR_FB_88_28.pdf:D\:\\estragio\\Zotero\\storage\\UTWYP829\\DFVLR_FB_88_28.pdf:application/pdf
      \endverb
    \endentry
    \entry{fleury_structural_1986}{article}{}
      \name{author}{2}{}{%
        {{hash=3d372b1ad18602856ff4157efc35fa46}{%
           family={Fleury},
           familyi={F\bibinitperiod},
           given={Claude},
           giveni={C\bibinitperiod}}}%
        {{hash=1da4398df128d138da708f535b695220}{%
           family={Braibant},
           familyi={B\bibinitperiod},
           given={Vincent},
           giveni={V\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{3ca3a9f55bb2f57db527af76dfed464c}
      \strng{fullhash}{3ca3a9f55bb2f57db527af76dfed464c}
      \strng{bibnamehash}{3ca3a9f55bb2f57db527af76dfed464c}
      \strng{authorbibnamehash}{3ca3a9f55bb2f57db527af76dfed464c}
      \strng{authornamehash}{3ca3a9f55bb2f57db527af76dfed464c}
      \strng{authorfullhash}{3ca3a9f55bb2f57db527af76dfed464c}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{shorttitle}
      \field{abstract}{A new and powerful mathematical programming method is described, which is capable of solving a broad class of structural optimization problems. The method employs mixed direct/reciprocal design variables in order to get conservative, first-order approximations to the objective function and to the constraints. By this approach the primary optimization problem is replaced with a sequence of explicit subproblems. Each subproblem being convex and separable, it can be efficiently solved by using a dual formulation. An attractive feature of the new method lies in its inherent tendency to generate a sequence of steadily improving feasible designs. Examples of application to real-life aerospace structures are offered to demonstrate the power and generality of the approach presented.}
      \field{issn}{1097-0207}
      \field{journaltitle}{International Journal for Numerical Methods in Engineering}
      \field{number}{3}
      \field{shorttitle}{Structural optimization}
      \field{title}{Structural optimization: {A} new dual method using mixed variables}
      \field{urlday}{9}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{23}
      \field{year}{1986}
      \field{urldateera}{ce}
      \field{pages}{409\bibrangedash 428}
      \range{pages}{20}
      \verb{doi}
      \verb 10.1002/nme.1620230307
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\MLH9DCNH\\Fleury and Braibant - 1986 - Structural optimization A new dual method using m.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.1620230307
      \endverb
      \verb{url}
      \verb https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.1620230307
      \endverb
    \endentry
    \entry{svanberg_method_1987}{article}{}
      \name{author}{1}{}{%
        {{hash=4c3f01f4598088ac379577d4d80943b7}{%
           family={Svanberg},
           familyi={S\bibinitperiod},
           given={Krister},
           giveni={K\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{4c3f01f4598088ac379577d4d80943b7}
      \strng{fullhash}{4c3f01f4598088ac379577d4d80943b7}
      \strng{bibnamehash}{4c3f01f4598088ac379577d4d80943b7}
      \strng{authorbibnamehash}{4c3f01f4598088ac379577d4d80943b7}
      \strng{authornamehash}{4c3f01f4598088ac379577d4d80943b7}
      \strng{authorfullhash}{4c3f01f4598088ac379577d4d80943b7}
      \field{extraname}{1}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{journaltitle}{International Journal for Numerical Methods in Engineering}
      \field{number}{2}
      \field{title}{The method of moving asymptotes—a new method for structural optimization}
      \field{urlday}{13}
      \field{urlmonth}{1}
      \field{urlyear}{2021}
      \field{volume}{24}
      \field{year}{1987}
      \field{urldateera}{ce}
      \field{pages}{359\bibrangedash 373}
      \range{pages}{15}
      \verb{doi}
      \verb https://doi.org/10.1002/nme.1620240207
      \endverb
    \endentry
    \entry{svanberg_class_2002}{article}{}
      \name{author}{1}{}{%
        {{hash=4c3f01f4598088ac379577d4d80943b7}{%
           family={Svanberg},
           familyi={S\bibinitperiod},
           given={Krister},
           giveni={K\bibinitperiod}}}%
      }
      \strng{namehash}{4c3f01f4598088ac379577d4d80943b7}
      \strng{fullhash}{4c3f01f4598088ac379577d4d80943b7}
      \strng{bibnamehash}{4c3f01f4598088ac379577d4d80943b7}
      \strng{authorbibnamehash}{4c3f01f4598088ac379577d4d80943b7}
      \strng{authornamehash}{4c3f01f4598088ac379577d4d80943b7}
      \strng{authorfullhash}{4c3f01f4598088ac379577d4d80943b7}
      \field{extraname}{2}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This paper deals with a certain class of optimization methods, based on conservative convex separable approximations (CCSA), for solving inequality-constrained nonlinear programming problems. Each generated iteration point is a feasible solution with lower objective value than the previous one, and it is proved that the sequence of iteration points converges toward the set of Karush--Kuhn--Tucker points. A major advantage of CCSA methods is that they can be applied to problems with a very large number of variables (say 104--105) even if the Hessian matrices of the objective and constraint functions are dense.}
      \field{issn}{1052-6234}
      \field{journaltitle}{SIAM Journal on Optimization}
      \field{month}{1}
      \field{number}{2}
      \field{title}{A {Class} of {Globally} {Convergent} {Optimization} {Methods} {Based} on {Conservative} {Convex} {Separable} {Approximations}}
      \field{urlday}{13}
      \field{urlmonth}{1}
      \field{urlyear}{2021}
      \field{volume}{12}
      \field{year}{2002}
      \field{urldateera}{ce}
      \field{pages}{555\bibrangedash 573}
      \range{pages}{19}
      \verb{doi}
      \verb 10.1137/S1052623499362822
      \endverb
      \verb{file}
      \verb Submitted Version:D\:\\estragio\\Zotero\\storage\\R2MQYCZB\\Svanberg - 2002 - A Class of Globally Convergent Optimization Method.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://epubs.siam.org/doi/abs/10.1137/S1052623499362822
      \endverb
      \verb{url}
      \verb https://epubs.siam.org/doi/abs/10.1137/S1052623499362822
      \endverb
    \endentry
    \entry{bruyneel_family_2002}{article}{}
      \name{author}{3}{}{%
        {{hash=d49ff4b355bc7046bb07b2daca26f6f2}{%
           family={Bruyneel},
           familyi={B\bibinitperiod},
           given={M.},
           giveni={M\bibinitperiod}}}%
        {{hash=b1ed7d234fa596fdf5e7b44ba01e7c30}{%
           family={Duysinx},
           familyi={D\bibinitperiod},
           given={P.},
           giveni={P\bibinitperiod}}}%
        {{hash=8c7436572570f15ac71fbf05e4d47e47}{%
           family={Fleury},
           familyi={F\bibinitperiod},
           given={C.},
           giveni={C\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{0ead767fa319c43627801951f8311203}
      \strng{fullhash}{0ead767fa319c43627801951f8311203}
      \strng{bibnamehash}{0ead767fa319c43627801951f8311203}
      \strng{authorbibnamehash}{0ead767fa319c43627801951f8311203}
      \strng{authornamehash}{0ead767fa319c43627801951f8311203}
      \strng{authorfullhash}{0ead767fa319c43627801951f8311203}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This paper proposes a new first-order approximation scheme used for solving structural optimization problems. It is based on approximations of the MMA family (MMA and GCMMA), but it utilizes the gradients and/or the function values at two successive design points to improve the quality of the approximation. In addition, this scheme can consider simultaneously monotonous and nonmonotonous structural behaviour. According to the characteristics of the treated problem, one of the approximations or a mix of them is automatically selected. Based on this approach, the accuracy of the approximated subproblems is improved and the solution process can be sped up. Numerical results compare the effectiveness of the method with previously derived approximations of the MMA family for shape optimization of trusses and for composite design problems. The benefit of using mixed approximations is also discussed.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{10}
      \field{number}{4}
      \field{title}{A family of {MMA} approximations for structural optimization}
      \field{urlday}{9}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{24}
      \field{year}{2002}
      \field{urldateera}{ce}
      \field{pages}{263\bibrangedash 276}
      \range{pages}{14}
      \verb{doi}
      \verb 10.1007/s00158-002-0238-7
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\8XWATLVL\\Bruyneel et al. - 2002 - A family of MMA approximations for structural opti.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/s00158-002-0238-7
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s00158-002-0238-7
      \endverb
      \keyw{Key words: structural approximations,method of moving asymptotes}
    \endentry
    \entry{wachter_implementation_2006}{article}{}
      \name{author}{2}{}{%
        {{hash=dc724f071bd0fcc1e9eabf5f96209481}{%
           family={Wächter},
           familyi={W\bibinitperiod},
           given={Andreas},
           giveni={A\bibinitperiod}}}%
        {{hash=b4cf951e494c45f4de462df04ec3b5df}{%
           family={Biegler},
           familyi={B\bibinitperiod},
           given={Lorenz\bibnamedelima T.},
           giveni={L\bibinitperiod\bibinitdelim T\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{842d46b1a24346d113a0e8274fa09dd0}
      \strng{fullhash}{842d46b1a24346d113a0e8274fa09dd0}
      \strng{bibnamehash}{842d46b1a24346d113a0e8274fa09dd0}
      \strng{authorbibnamehash}{842d46b1a24346d113a0e8274fa09dd0}
      \strng{authornamehash}{842d46b1a24346d113a0e8274fa09dd0}
      \strng{authorfullhash}{842d46b1a24346d113a0e8274fa09dd0}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{We present a primal-dual interior-point algorithm with a filter line-search method for nonlinear programming. Local and global convergence properties of this method were analyzed in previous work. Here we provide a comprehensive description of the algorithm, including the feasibility restoration phase for the filter method, second-order corrections, and inertia correction of the KKT matrix. Heuristics are also considered that allow faster performance. This method has been implemented in the IPOPT code, which we demonstrate in a detailed numerical study based on 954 problems from the CUTEr test set. An evaluation is made of several line-search options, and a comparison is provided with two state-of-the-art interior-point codes for nonlinear programming.}
      \field{issn}{1436-4646}
      \field{journaltitle}{Mathematical Programming}
      \field{month}{3}
      \field{number}{1}
      \field{title}{On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming}
      \field{urlday}{29}
      \field{urlmonth}{11}
      \field{urlyear}{2021}
      \field{volume}{106}
      \field{year}{2006}
      \field{urldateera}{ce}
      \field{pages}{25\bibrangedash 57}
      \range{pages}{33}
      \verb{doi}
      \verb 10.1007/s10107-004-0559-y
      \endverb
    \endentry
    \entry{rojas_labanda_benchmarking_2015}{article}{}
      \name{author}{2}{}{%
        {{hash=71fafcd8e67251e0b048022599d2725a}{%
           family={Rojas\bibnamedelima Labanda},
           familyi={R\bibinitperiod\bibinitdelim L\bibinitperiod},
           given={Susana},
           giveni={S\bibinitperiod}}}%
        {{hash=2ac977bc03dde1f3d4061cda61ab9795}{%
           family={Stolpe},
           familyi={S\bibinitperiod},
           given={Mathias},
           giveni={M\bibinitperiod}}}%
      }
      \strng{namehash}{c1eb616e32b424da8b7b0b556afec6ab}
      \strng{fullhash}{c1eb616e32b424da8b7b0b556afec6ab}
      \strng{bibnamehash}{c1eb616e32b424da8b7b0b556afec6ab}
      \strng{authorbibnamehash}{c1eb616e32b424da8b7b0b556afec6ab}
      \strng{authornamehash}{c1eb616e32b424da8b7b0b556afec6ab}
      \strng{authorfullhash}{c1eb616e32b424da8b7b0b556afec6ab}
      \field{sortinit}{2}
      \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{The purpose of this article is to benchmark different optimization solvers when applied to various finite element based structural topology optimization problems. An extensive and representative library of minimum compliance, minimum volume, and mechanism design problem instances for different sizes is developed for this benchmarking. The problems are based on a material interpolation scheme combined with a density filter. Different optimization solvers including Optimality Criteria (OC), the Method of Moving Asymptotes (MMA) and its globally convergent version GCMMA, the interior point solvers in IPOPT and FMINCON, and the sequential quadratic programming method in SNOPT, are benchmarked on the library using performance profiles. Whenever possible the methods are applied to both the nested and the Simultaneous Analysis and Design (SAND) formulations of the problem. The performance profiles conclude that general solvers are as efficient and reliable as classical structural topology optimization solvers. Moreover, the use of the exact Hessians in SAND formulations, generally produce designs with better objective function values. However, with the benchmarked implementations solving SAND formulations consumes more computational time than solving the corresponding nested formulations.}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{9}
      \field{title}{Benchmarking optimization solvers for structural topology optimization}
      \field{volume}{52}
      \field{year}{2015}
      \verb{doi}
      \verb 10.1007/s00158-015-1250-z
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\7GQDA246\\Rojas Labanda and Stolpe - 2015 - Benchmarking optimization solvers for structural t.pdf:application/pdf
      \endverb
    \endentry
    \entry{dorn_automatic_1964}{article}{}
      \name{author}{3}{}{%
        {{hash=b376238ba054044a486754c2044d0e16}{%
           family={Dorn},
           familyi={D\bibinitperiod},
           given={W.\bibnamedelimi S.},
           giveni={W\bibinitperiod\bibinitdelim S\bibinitperiod}}}%
        {{hash=59a40b26652a8190fc919a256f13719b}{%
           family={Gomory},
           familyi={G\bibinitperiod},
           given={Ralph\bibnamedelima E.},
           giveni={R\bibinitperiod\bibinitdelim E\bibinitperiod}}}%
        {{hash=a8af5dcff31a4841021a638f0d608a1e}{%
           family={Greenberg},
           familyi={G\bibinitperiod},
           given={H.},
           giveni={H\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{cfb42fb5cc62cb831bec503f75cd4c6a}
      \strng{fullhash}{cfb42fb5cc62cb831bec503f75cd4c6a}
      \strng{bibnamehash}{cfb42fb5cc62cb831bec503f75cd4c6a}
      \strng{authorbibnamehash}{cfb42fb5cc62cb831bec503f75cd4c6a}
      \strng{authornamehash}{cfb42fb5cc62cb831bec503f75cd4c6a}
      \strng{authorfullhash}{cfb42fb5cc62cb831bec503f75cd4c6a}
      \field{sortinit}{2}
      \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{journaltitle}{J. Mécanique}
      \field{title}{Automatic design of optimal structures}
      \field{urlday}{14}
      \field{urlmonth}{1}
      \field{urlyear}{2021}
      \field{year}{1964}
      \field{urldateera}{ce}
    \endentry
    \entry{chan_optimum_1964}{article}{}
      \name{author}{1}{}{%
        {{hash=67486fcf525af448814c4c33547119d4}{%
           family={Chan},
           familyi={C\bibinitperiod},
           given={H.\bibnamedelimi S.\bibnamedelimi Y.},
           giveni={H\bibinitperiod\bibinitdelim S\bibinitperiod\bibinitdelim Y\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{67486fcf525af448814c4c33547119d4}
      \strng{fullhash}{67486fcf525af448814c4c33547119d4}
      \strng{bibnamehash}{67486fcf525af448814c4c33547119d4}
      \strng{authorbibnamehash}{67486fcf525af448814c4c33547119d4}
      \strng{authornamehash}{67486fcf525af448814c4c33547119d4}
      \strng{authorfullhash}{67486fcf525af448814c4c33547119d4}
      \field{sortinit}{2}
      \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{journaltitle}{College of Aeronautics Report Aero 175}
      \field{title}{Optimum structural design and linear programming}
      \field{urlday}{18}
      \field{urlmonth}{1}
      \field{urlyear}{2021}
      \field{year}{1964}
      \field{urldateera}{ce}
      \verb{urlraw}
      \verb https://repository.tudelft.nl/islandora/object/uuid%3Ae255d625-3602-4e2e-a486-debcb2447320
      \endverb
      \verb{url}
      \verb https://repository.tudelft.nl/islandora/object/uuid%3Ae255d625-3602-4e2e-a486-debcb2447320
      \endverb
    \endentry
    \entry{hemp_optimum_1973}{book}{}
      \name{author}{1}{}{%
        {{hash=2582d45fcb57e3014533a29b290a9394}{%
           family={Hemp},
           familyi={H\bibinitperiod},
           given={W.\bibnamedelimi S.},
           giveni={W\bibinitperiod\bibinitdelim S\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \list{publisher}{1}{%
        {Clarendon Press}%
      }
      \strng{namehash}{2582d45fcb57e3014533a29b290a9394}
      \strng{fullhash}{2582d45fcb57e3014533a29b290a9394}
      \strng{bibnamehash}{2582d45fcb57e3014533a29b290a9394}
      \strng{authorbibnamehash}{2582d45fcb57e3014533a29b290a9394}
      \strng{authornamehash}{2582d45fcb57e3014533a29b290a9394}
      \strng{authorfullhash}{2582d45fcb57e3014533a29b290a9394}
      \field{sortinit}{2}
      \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{isbn}{978-0-19-856110-1}
      \field{note}{Google-Books-ID: cJhpAAAAMAAJ}
      \field{title}{Optimum {Structures}}
      \field{year}{1973}
    \endentry
    \entry{sankaranarayanan_truss_1994}{article}{}
      \name{author}{3}{}{%
        {{hash=ec31ae80c65f63ba67850106aeb1a997}{%
           family={Sankaranarayanan},
           familyi={S\bibinitperiod},
           given={S.},
           giveni={S\bibinitperiod}}}%
        {{hash=13489fe106344e803b89af024b23b17a}{%
           family={Haftka},
           familyi={H\bibinitperiod},
           given={Raphael\bibnamedelima T.},
           giveni={R\bibinitperiod\bibinitdelim T\bibinitperiod}}}%
        {{hash=7c8d9c20cc9eb2768db7a7d9ae231c44}{%
           family={Kapania},
           familyi={K\bibinitperiod},
           given={Rakesh\bibnamedelima K.},
           giveni={R\bibinitperiod\bibinitdelim K\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{789c5bf21b94cacfbd1829ffab87efc9}
      \strng{fullhash}{789c5bf21b94cacfbd1829ffab87efc9}
      \strng{bibnamehash}{789c5bf21b94cacfbd1829ffab87efc9}
      \strng{authorbibnamehash}{789c5bf21b94cacfbd1829ffab87efc9}
      \strng{authornamehash}{789c5bf21b94cacfbd1829ffab87efc9}
      \strng{authorfullhash}{789c5bf21b94cacfbd1829ffab87efc9}
      \field{sortinit}{2}
      \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{issn}{0001-1452, 1533-385X}
      \field{journaltitle}{AIAA Journal}
      \field{month}{2}
      \field{number}{2}
      \field{title}{Truss topology optimization with simultaneous analysis and design}
      \field{urlday}{8}
      \field{urlmonth}{2}
      \field{urlyear}{2022}
      \field{volume}{32}
      \field{year}{1994}
      \field{urldateera}{ce}
      \field{pages}{420\bibrangedash 424}
      \range{pages}{5}
      \verb{doi}
      \verb 10.2514/3.12000
      \endverb
      \verb{file}
      \verb Sankaranarayanan et al. - 1994 - Truss topology optimization with simultaneous anal.pdf:D\:\\estragio\\Zotero\\storage\\XVREBJT5\\Sankaranarayanan et al. - 1994 - Truss topology optimization with simultaneous anal.pdf:application/pdf
      \endverb
    \endentry
    \entry{bendsoe_optimal_1989}{article}{}
      \name{author}{1}{}{%
        {{hash=193e92bb57a8aeb7a8a809f2e4f7221f}{%
           family={Bendsøe},
           familyi={B\bibinitperiod},
           given={M.\bibnamedelimi P.},
           giveni={M\bibinitperiod\bibinitdelim P\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{193e92bb57a8aeb7a8a809f2e4f7221f}
      \strng{fullhash}{193e92bb57a8aeb7a8a809f2e4f7221f}
      \strng{bibnamehash}{193e92bb57a8aeb7a8a809f2e4f7221f}
      \strng{authorbibnamehash}{193e92bb57a8aeb7a8a809f2e4f7221f}
      \strng{authornamehash}{193e92bb57a8aeb7a8a809f2e4f7221f}
      \strng{authorfullhash}{193e92bb57a8aeb7a8a809f2e4f7221f}
      \field{extraname}{2}
      \field{sortinit}{2}
      \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Shape optimization in a general setting requires the determination of the optimal spatial material distribution for given loads and boundary conditions. Every point in space is thus a material point or a void and the optimization problem is a discrete variable one. This paper describes various ways of removing this discrete nature of the problem by the introduction of a density function that is a continuous design variable. Domains of high density then define the shape of the mechanical element. For intermediate densities, material parameters given by an artificial material law can be used. Alternatively, the density can arise naturally through the introduction of periodically distributed, microscopic voids, so that effective material parameters for intermediate density values can be computed through homogenization. Several examples in two-dimensional elasticity illustrate that these methods allow a determination of the topology of a mechanical element, as required for a boundary variations shape optimization technique.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural optimization}
      \field{month}{12}
      \field{number}{4}
      \field{title}{Optimal shape design as a material distribution problem}
      \field{urlday}{13}
      \field{urlmonth}{10}
      \field{urlyear}{2020}
      \field{volume}{1}
      \field{year}{1989}
      \field{urldateera}{ce}
      \field{pages}{193\bibrangedash 202}
      \range{pages}{10}
      \verb{doi}
      \verb 10.1007/BF01650949
      \endverb
      \keyw{Topology optimisation,Otimization,Algorithm}
    \endentry
    \entry{sigmund_materials_1994}{article}{}
      \name{author}{1}{}{%
        {{hash=d76f1c09e8d8d06e1b7c3c254efeae1a}{%
           family={Sigmund},
           familyi={S\bibinitperiod},
           given={Ole},
           giveni={O\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{fullhash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{bibnamehash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{authorbibnamehash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{authornamehash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{authorfullhash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \field{extraname}{3}
      \field{sortinit}{2}
      \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{shorttitle}
      \field{abstract}{This paper deals with the construction of materials with arbitrary prescribed positive semi-definite constitutive tensors. The construction problem can be called an inverse problem of finding a material with given homogenized coefficients. The inverse problem is formulated as a topology optimization problem i.e. finding the interior topology of a base cell such that cost is minimized and the constraints are defined by the prescribed constitutive parameters. Numerical values of the constitutive parameters of a given material are found using a numerical homogenization method expressed in terms of element mutual energies. Numerical results show that arbitrary materials, including materials with Poisson's ratio −1.0 and other extreme materials, can be obtained by modelling the base cell as a truss structure. Furthermore, a wide spectrum of materials can be constructed from base cells modelled as continuous discs of varying thickness. Only the two-dimensional case is considered in this paper but formulation and numerical procedures can easily be extended to the three-dimensional case.}
      \field{issn}{0020-7683}
      \field{journaltitle}{International Journal of Solids and Structures}
      \field{month}{9}
      \field{number}{17}
      \field{shorttitle}{Materials with prescribed constitutive parameters}
      \field{title}{Materials with prescribed constitutive parameters: {An} inverse homogenization problem}
      \field{urlday}{19}
      \field{urlmonth}{1}
      \field{urlyear}{2021}
      \field{volume}{31}
      \field{year}{1994}
      \field{urldateera}{ce}
      \field{pages}{2313\bibrangedash 2329}
      \range{pages}{17}
      \verb{doi}
      \verb 10.1016/0020-7683(94)90154-6
      \endverb
      \verb{file}
      \verb ScienceDirect Full Text PDF:D\:\\estragio\\Zotero\\storage\\WQZ52QQK\\Sigmund - 1994 - Materials with prescribed constitutive parameters.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb http://www.sciencedirect.com/science/article/pii/0020768394901546
      \endverb
      \verb{url}
      \verb http://www.sciencedirect.com/science/article/pii/0020768394901546
      \endverb
    \endentry
    \entry{zhang_scale-related_2006}{article}{}
      \name{author}{2}{}{%
        {{hash=1703058ac1e82b63641879518d53a9de}{%
           family={Zhang},
           familyi={Z\bibinitperiod},
           given={Weihong},
           giveni={W\bibinitperiod}}}%
        {{hash=6cfd394df702d7f435362facc53d5b53}{%
           family={Sun},
           familyi={S\bibinitperiod},
           given={Shiping},
           giveni={S\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{ac463b22862efbb5f9082b51225c4519}
      \strng{fullhash}{ac463b22862efbb5f9082b51225c4519}
      \strng{bibnamehash}{ac463b22862efbb5f9082b51225c4519}
      \strng{authorbibnamehash}{ac463b22862efbb5f9082b51225c4519}
      \strng{authornamehash}{ac463b22862efbb5f9082b51225c4519}
      \strng{authorfullhash}{ac463b22862efbb5f9082b51225c4519}
      \field{sortinit}{2}
      \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{The integrated optimization of lightweight cellular materials and structures are discussed in this paper. By analysing the basic features of such a two-scale problem, it is shown that the optimal solution strongly depends upon the scale effect modelling of the periodic microstructure of material unit cell (MUC), i.e. the so-called representative volume element (RVE). However, with the asymptotic homogenization method used widely in actual topology optimization procedure, effective material properties predicted can give rise to limit values depending upon only volume fractions of solid phases, properties and spatial distribution of constituents in the microstructure regardless of scale effect. From this consideration, we propose the design element (DE) concept being able to deal with conventional designs of materials and structures in a unified way. By changing the scale and aspect ratio of the DE, scale-related effects of materials and structures are well revealed and distinguished in the final results of optimal design patterns. To illustrate the proposed approach, numerical design problems of 2D layered structures with cellular core are investigated. Copyright © 2006 John Wiley \&amp; Sons, Ltd.}
      \field{issn}{1097-0207}
      \field{journaltitle}{International Journal for Numerical Methods in Engineering}
      \field{number}{9}
      \field{title}{Scale-related topology optimization of cellular materials and structures}
      \field{urlday}{23}
      \field{urlmonth}{6}
      \field{urlyear}{2021}
      \field{volume}{68}
      \field{year}{2006}
      \field{urldateera}{ce}
      \field{pages}{993\bibrangedash 1011}
      \range{pages}{19}
      \verb{doi}
      \verb 10.1002/nme.1743
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\Z7G7EADZ\\Zhang and Sun - 2006 - Scale-related topology optimization of cellular ma.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.1743
      \endverb
      \verb{url}
      \verb https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.1743
      \endverb
      \keyw{topology optimization,cellular material design,homogenization method,scale effect,unit cell}
    \endentry
    \entry{collet_topology_2018}{article}{}
      \name{author}{4}{}{%
        {{hash=741463c587fb29799e8a149f6f2f68ef}{%
           family={Collet},
           familyi={C\bibinitperiod},
           given={Maxime},
           giveni={M\bibinitperiod}}}%
        {{hash=064db37370157c34c0de7f4def8afc10}{%
           family={Noël},
           familyi={N\bibinitperiod},
           given={Lise},
           giveni={L\bibinitperiod}}}%
        {{hash=a59dab04e567acdb5c9d56e5f573819f}{%
           family={Bruggi},
           familyi={B\bibinitperiod},
           given={Matteo},
           giveni={M\bibinitperiod}}}%
        {{hash=55bbf59917324962aed0534c9e5595b5}{%
           family={Duysinx},
           familyi={D\bibinitperiod},
           given={Pierre},
           giveni={P\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{436c629e0d99cdd93b9e11517736519f}
      \strng{fullhash}{83aa1cba5ea8f23b7ba75c0c30e426fd}
      \strng{bibnamehash}{83aa1cba5ea8f23b7ba75c0c30e426fd}
      \strng{authorbibnamehash}{83aa1cba5ea8f23b7ba75c0c30e426fd}
      \strng{authornamehash}{436c629e0d99cdd93b9e11517736519f}
      \strng{authorfullhash}{83aa1cba5ea8f23b7ba75c0c30e426fd}
      \field{sortinit}{2}
      \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This work aims at introducing stress responses within a topology optimization framework applied to the design of periodic microstructures. The emergence of novel additive manufacturing techniques fosters research towards new approaches to tailor materials properties. This paper derives a formulation to prevent the occurrence of high stress concentrations, often present in optimized microstructures. Applying macroscopic test strain fields to the material, microstructural layouts, reducing the stress level while exhibiting the best overall stiffness properties, are sought for. Equivalent stiffness properties of the designed material are predicted by numerical homogenization and considering a metallic base material for the microstructure, it is assumed that the classical Von Mises stress criterion remains valid to predict the material elastic allowable stress at the microscale. Stress constraints with arbitrary bounds are considered, assuming that a sizing optimization step could be applied to match the actual stress limits under realistic service loads. Density–based topology optimization, relying on the SIMP model, is used and the qp–approach is exploited to overcome the singularity phenomenon arising from the introduction of stress constraints with vanishing material. Optimization problems are solved using mathematical programming schemes, in particular MMA, so that a sensitivity analysis of stress responses at the microstructural level is required and performed considering the adjoint approach. Finally, the developed method is first validated with classical academic benchmarks and then illustrated with an original application: tailoring metamaterials for a museum anti–seismic stand.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{12}
      \field{number}{6}
      \field{title}{Topology optimization for microstructural design under stress constraints}
      \field{urlday}{9}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{58}
      \field{year}{2018}
      \field{urldateera}{ce}
      \field{pages}{2677\bibrangedash 2695}
      \range{pages}{19}
      \verb{doi}
      \verb 10.1007/s00158-018-2045-9
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\AUMDP8FH\\Collet et al. - 2018 - Topology optimization for microstructural design u.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/s00158-018-2045-9
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s00158-018-2045-9
      \endverb
      \keyw{Density–based topology optimization,Homogenization,Material design,Periodic microstructures,Stress constraints}
    \endentry
    \entry{borrvall_topology_2003}{article}{}
      \name{author}{2}{}{%
        {{hash=2f9cabd2d0018afb31cec964bde68c2e}{%
           family={Borrvall},
           familyi={B\bibinitperiod},
           given={Thomas},
           giveni={T\bibinitperiod}}}%
        {{hash=6f32b7d50b188dbda2f985ea10292506}{%
           family={Petersson},
           familyi={P\bibinitperiod},
           given={Joakim},
           giveni={J\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{609829a2bf2ed2d778a0a37df5898f67}
      \strng{fullhash}{609829a2bf2ed2d778a0a37df5898f67}
      \strng{bibnamehash}{609829a2bf2ed2d778a0a37df5898f67}
      \strng{authorbibnamehash}{609829a2bf2ed2d778a0a37df5898f67}
      \strng{authornamehash}{609829a2bf2ed2d778a0a37df5898f67}
      \strng{authorfullhash}{609829a2bf2ed2d778a0a37df5898f67}
      \field{sortinit}{2}
      \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{We consider topology optimization of fluids in Stokes flow. The design objective is to minimize a power function, which for the absence of body fluid forces is the dissipated power in the fluid, subject to a fluid volume constraint. A generalized Stokes problem is derived that is used as a base for introducing the design parameterization. Mathematical proofs of existence of optimal solutions and convergence of discretized solutions are given and it is concluded that no regularization of the optimization problem is needed. The discretized state problem is a mixed finite element problem that is solved by a preconditioned conjugate gradient method and the design optimization problem is solved using sequential separable and convex programming. Several numerical examples are presented that illustrate this new methodology and the results are compared to results obtained in the context of shape optimization of fluids. Copyright © 2003 John Wiley \&amp; Sons, Ltd.}
      \field{issn}{1097-0363}
      \field{journaltitle}{International Journal for Numerical Methods in Fluids}
      \field{number}{1}
      \field{title}{Topology optimization of fluids in {Stokes} flow}
      \field{urlday}{9}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{41}
      \field{year}{2003}
      \field{urldateera}{ce}
      \field{pages}{77\bibrangedash 107}
      \range{pages}{31}
      \verb{doi}
      \verb 10.1002/fld.426
      \endverb
      \verb{urlraw}
      \verb https://onlinelibrary.wiley.com/doi/abs/10.1002/fld.426
      \endverb
      \verb{url}
      \verb https://onlinelibrary.wiley.com/doi/abs/10.1002/fld.426
      \endverb
    \endentry
    \entry{bruyneel_note_2005}{article}{}
      \name{author}{2}{}{%
        {{hash=d49ff4b355bc7046bb07b2daca26f6f2}{%
           family={Bruyneel},
           familyi={B\bibinitperiod},
           given={M.},
           giveni={M\bibinitperiod}}}%
        {{hash=b1ed7d234fa596fdf5e7b44ba01e7c30}{%
           family={Duysinx},
           familyi={D\bibinitperiod},
           given={P.},
           giveni={P\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{79630ff0a4cb0291f44f089a72df5c92}
      \strng{fullhash}{79630ff0a4cb0291f44f089a72df5c92}
      \strng{bibnamehash}{79630ff0a4cb0291f44f089a72df5c92}
      \strng{authorbibnamehash}{79630ff0a4cb0291f44f089a72df5c92}
      \strng{authornamehash}{79630ff0a4cb0291f44f089a72df5c92}
      \strng{authorfullhash}{79630ff0a4cb0291f44f089a72df5c92}
      \field{sortinit}{2}
      \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This paper proposes to investigate topology optimization with density-dependent body forces and especially self-weight loading. Surprisingly the solution of such problems cannot be based on a direct extension of the solution procedure used for minimum-compliance topology optimization with fixed external loads. At first the particular difficulties arising in the considered topology problems are pointed out: non-monotonous behaviour of the compliance, possible unconstrained character of the optimum and the parasitic effect for low densities when using the power model (SIMP). To get rid of the last problem requires the modification of the power law model for low densities. The other problems require that the solution procedure and the selection of appropriate structural approximations be revisited. Numerical applications compare the efficiency of different approximation schemes of the MMA family. It is shown that important improvements are achieved when the solution is carried out using the gradient-based method of moving asymptotes (GBMMA) approximations. Criteria for selecting the approximations are suggested. In addition, the applications also provide the opportunity to illustrate the strong influence of the ratio between the applied loads and the structural weight on the optimal structural topology.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{4}
      \field{number}{4}
      \field{title}{Note on topology optimization of continuum structures including self-weight}
      \field{urlday}{9}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{29}
      \field{year}{2005}
      \field{urldateera}{ce}
      \field{pages}{245\bibrangedash 256}
      \range{pages}{12}
      \verb{doi}
      \verb 10.1007/s00158-004-0484-y
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\AMBJAHC6\\Bruyneel and Duysinx - 2005 - Note on topology optimization of continuum structu.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/s00158-004-0484-y
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s00158-004-0484-y
      \endverb
      \keyw{Convex approximations,MMA,Self-weight,Topology optimization}
    \endentry
    \entry{sigmund_manufacturing_2009}{article}{}
      \name{author}{1}{}{%
        {{hash=d76f1c09e8d8d06e1b7c3c254efeae1a}{%
           family={Sigmund},
           familyi={S\bibinitperiod},
           given={Ole},
           giveni={O\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{fullhash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{bibnamehash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{authorbibnamehash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{authornamehash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{authorfullhash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \field{extraname}{4}
      \field{sortinit}{2}
      \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{In this paper we present an extension of the topology optimization method to include uncertainties during the fabrication of macro, micro and nano structures. More specifically, we consider devices that are manufactured using processes which may result in (uniformly) too thin (eroded) or too thick (dilated) structures compared to the intended topology. Examples are MEMS devices manufactured using etching processes, nano-devices manufactured using e-beam lithography or laser micro-machining and macro structures manufactured using milling processes. In the suggested robust topology optimization approach, under- and over-etching is modelled by image processing-based “erode” and “dilate” operators and the optimization problem is formulated as a worst case design problem. Applications of the method to the design of macro structures for minimum compliance and micro compliant mechanisms show that the method provides manufacturing tolerant designs with little decrease in performance. As a positive side effect the robust design formulation also eliminates the longstanding problem of one-node connected hinges in compliant mechanism design using topology optimization.}
      \field{issn}{1614-3116}
      \field{journaltitle}{Acta Mechanica Sinica}
      \field{month}{4}
      \field{number}{2}
      \field{title}{Manufacturing tolerant topology optimization}
      \field{urlday}{26}
      \field{urlmonth}{9}
      \field{urlyear}{2021}
      \field{volume}{25}
      \field{year}{2009}
      \field{urldateera}{ce}
      \field{pages}{227\bibrangedash 239}
      \range{pages}{13}
      \verb{doi}
      \verb 10.1007/s10409-009-0240-z
      \endverb
      \verb{file}
      \verb Springer Full Text PDF:D\:\\estragio\\Zotero\\storage\\BUN2KRQV\\Sigmund - 2009 - Manufacturing tolerant topology optimization.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/s10409-009-0240-z
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s10409-009-0240-z
      \endverb
    \endentry
    \entry{brackett_topology_2011}{article}{}
      \name{author}{3}{}{%
        {{hash=4ea785be3aa8e5a093761d31edbb10c0}{%
           family={Brackett},
           familyi={B\bibinitperiod},
           given={D},
           giveni={D\bibinitperiod}}}%
        {{hash=be3bfc2b309000ad93704c31267c01d2}{%
           family={Ashcroft},
           familyi={A\bibinitperiod},
           given={I},
           giveni={I\bibinitperiod}}}%
        {{hash=1a7d6c61f0ef31bda5f94a4229f75581}{%
           family={Hague},
           familyi={H\bibinitperiod},
           given={R},
           giveni={R\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{698c0ef2721c89f69d528dc085af655b}
      \strng{fullhash}{698c0ef2721c89f69d528dc085af655b}
      \strng{bibnamehash}{698c0ef2721c89f69d528dc085af655b}
      \strng{authorbibnamehash}{698c0ef2721c89f69d528dc085af655b}
      \strng{authornamehash}{698c0ef2721c89f69d528dc085af655b}
      \strng{authorfullhash}{698c0ef2721c89f69d528dc085af655b}
      \field{sortinit}{2}
      \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This paper gives an overview of the issues and opportunities for the application of topology optimization methods for additive manufacturing (AM). The main analysis issues discussed are: how to achieve the maximum geometric resolution to allow the fine features easily manufacturable by AM to be represented in the optimization model; the manufacturing constraints to be considered, and the workflow modifications required to handle the geometric complexity in the post optimization stages. The main manufacturing issues discussed are the potential for realizing intermediate density regions, in the case of the solid isotropic material with penalization (SIMP) approach, the use of small scale lattice structures, the use of multiple material AM processes, and an approach to including support structure requirement as a manufacturing constraint.}
      \field{title}{Topology {Optimization} for {Additive} {Manufacturing}}
      \field{year}{2011}
      \field{pages}{15}
      \range{pages}{1}
      \verb{doi}
      \verb 10.26153/tsw/15300
      \endverb
      \verb{file}
      \verb Brackett et al. - TOPOLOGY OPTIMIZATION FOR ADDITIVE MANUFACTURING.pdf:D\:\\estragio\\Zotero\\storage\\WY259A29\\Brackett et al. - TOPOLOGY OPTIMIZATION FOR ADDITIVE MANUFACTURING.pdf:application/pdf
      \endverb
    \endentry
    \entry{sigmund_design_1997}{article}{}
      \name{author}{1}{}{%
        {{hash=d76f1c09e8d8d06e1b7c3c254efeae1a}{%
           family={Sigmund},
           familyi={S\bibinitperiod},
           given={Ole},
           giveni={O\bibinitperiod}}}%
      }
      \strng{namehash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{fullhash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{bibnamehash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{authorbibnamehash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{authornamehash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{authorfullhash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \field{extraname}{5}
      \field{sortinit}{2}
      \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This paper presents a method for optimal design of compliant mechanism topologies. The method is based on continuum-type topology optimization techniques and finds the optimal compliant mechanism topology within a given design domain and a given position and direction of input and output forces. By constraining the allowed displacement at the input port, it is possible to control the maximum stress level in the compliant mechanism. The ability of the design method to find a mechanism with complex output behavior is demonstrated by several examples. Some of the optimal mechanism topologies have been manufactured, both in macroscale (hand-size) made in Nylon, and in microscale ({&lt;}.5mm)) made of micromachined glass.}
      \field{issn}{0890-5452}
      \field{journaltitle}{Mechanics of Structures and Machines}
      \field{month}{1}
      \field{number}{4}
      \field{title}{On the {Design} of {Compliant} {Mechanisms} {Using} {Topology} {Optimization}*}
      \field{urlday}{9}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{25}
      \field{year}{1997}
      \field{urldateera}{ce}
      \field{pages}{493\bibrangedash 524}
      \range{pages}{32}
      \verb{doi}
      \verb 10.1080/08905459708945415
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\G38LET7Q\\Sigmund - 1997 - On the Design of Compliant Mechanisms Using Topolo.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1080/08905459708945415
      \endverb
      \verb{url}
      \verb https://doi.org/10.1080/08905459708945415
      \endverb
    \endentry
    \entry{bruns_topology_2001}{article}{}
      \name{author}{2}{}{%
        {{hash=81ef21b7ffc38af99e00c271ce1e64e5}{%
           family={Bruns},
           familyi={B\bibinitperiod},
           given={Tyler\bibnamedelima E.},
           giveni={T\bibinitperiod\bibinitdelim E\bibinitperiod}}}%
        {{hash=2dc94736fafc9292d9d5fe6bbacf2606}{%
           family={Tortorelli},
           familyi={T\bibinitperiod},
           given={Daniel\bibnamedelima A.},
           giveni={D\bibinitperiod\bibinitdelim A\bibinitperiod}}}%
      }
      \strng{namehash}{2de152a876fa591ad74f56a138e14203}
      \strng{fullhash}{2de152a876fa591ad74f56a138e14203}
      \strng{bibnamehash}{2de152a876fa591ad74f56a138e14203}
      \strng{authorbibnamehash}{2de152a876fa591ad74f56a138e14203}
      \strng{authornamehash}{2de152a876fa591ad74f56a138e14203}
      \strng{authorfullhash}{2de152a876fa591ad74f56a138e14203}
      \field{sortinit}{2}
      \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{A linear elastic response is assumed in most structural topology optimization problems. While this assumption is valid for a wide variety of problems, it is not valid for structures undergoing large displacements. The elastic structural analysis used here accommodates geometric and material non-linearities. The material density field is filtered to enforce a length scale on the field variation and is penalized to remove less effective intermediate densities. The filtering scheme is embedded in the structural analysis to resolve the non-existent solution to the solid-void topology problem. In this way, we know precisely what optimization problem is being solved. The structural topology optimization formulation is also used to design compliant mechanisms.}
      \field{issn}{0045-7825}
      \field{journaltitle}{Computer Methods in Applied Mechanics and Engineering}
      \field{month}{3}
      \field{number}{26}
      \field{title}{Topology optimization of non-linear elastic structures and compliant mechanisms}
      \field{urlday}{9}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{190}
      \field{year}{2001}
      \field{urldateera}{ce}
      \field{pages}{3443\bibrangedash 3459}
      \range{pages}{17}
      \verb{doi}
      \verb 10.1016/S0045-7825(00)00278-4
      \endverb
      \verb{urlraw}
      \verb https://www.sciencedirect.com/science/article/pii/S0045782500002784
      \endverb
      \verb{url}
      \verb https://www.sciencedirect.com/science/article/pii/S0045782500002784
      \endverb
    \endentry
    \entry{wang_space-time_2020}{article}{}
      \name{author}{5}{}{%
        {{hash=112adf0cbdda2b275ef5430c7499989c}{%
           family={Wang},
           familyi={W\bibinitperiod},
           given={Weiming},
           giveni={W\bibinitperiod}}}%
        {{hash=86d57f1424c871d9cee9a456c6cac101}{%
           family={Munro},
           familyi={M\bibinitperiod},
           given={Dirk},
           giveni={D\bibinitperiod}}}%
        {{hash=67857bd3a22d47754bccb05202b9067d}{%
           family={Wang},
           familyi={W\bibinitperiod},
           given={Charlie\bibnamedelimb C.\bibnamedelimi L.},
           giveni={C\bibinitperiod\bibinitdelim C\bibinitperiod\bibinitdelim L\bibinitperiod}}}%
        {{hash=fced7f35e3ed00611970d9aa7179fda2}{%
           family={Keulen},
           familyi={K\bibinitperiod},
           given={Fred},
           giveni={F\bibinitperiod},
           prefix={van},
           prefixi={v\bibinitperiod}}}%
        {{hash=aaf4818e3816b53809f264b2c1b2ecae}{%
           family={Wu},
           familyi={W\bibinitperiod},
           given={Jun},
           giveni={J\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{5a481f93661f05484f00e2e1dc4eeb75}
      \strng{fullhash}{60c3611290356b3264961ca57b7d0122}
      \strng{bibnamehash}{60c3611290356b3264961ca57b7d0122}
      \strng{authorbibnamehash}{60c3611290356b3264961ca57b7d0122}
      \strng{authornamehash}{5a481f93661f05484f00e2e1dc4eeb75}
      \strng{authorfullhash}{60c3611290356b3264961ca57b7d0122}
      \field{extraname}{1}
      \field{sortinit}{2}
      \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{The design of optimal structures and the planning of (additive manufacturing) fabrication sequences have been considered typically as two separate tasks that are performed consecutively. In the light of recent advances in robot-assisted (wire-arc) additive manufacturing which enable addition of material along curved surfaces, we present a novel topology optimization formulation which concurrently optimizes the structure and the fabrication sequence. For this, two sets of design variables, i.e., a density field for defining the structural layout, and a time field which determines the fabrication process order, are simultaneously optimized. These two fields allow to generate a sequence of intermediate structures, upon which manufacturing constraints (e.g., fabrication continuity and speed) are imposed. The proposed space-time formulation is general, and is demonstrated on three fabrication settings, considering self-weight of the intermediate structures, process-dependent critical loads, and time-dependent material properties.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{1}
      \field{number}{1}
      \field{title}{Space-time topology optimization for additive manufacturing}
      \field{urlday}{9}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{61}
      \field{year}{2020}
      \field{urldateera}{ce}
      \field{pages}{1\bibrangedash 18}
      \range{pages}{18}
      \verb{doi}
      \verb 10.1007/s00158-019-02420-6
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\DJ4PEXUR\\Wang et al. - 2020 - Space-time topology optimization for additive manu.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/s00158-019-02420-6
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s00158-019-02420-6
      \endverb
      \keyw{Additive manufacturing,Manufacturing process planning,Space-time optimization,Topology optimization}
    \endentry
    \entry{allaire_level-set_2002}{article}{}
      \name{author}{3}{}{%
        {{hash=e689b43ac5d3242f4613a353518abfb7}{%
           family={Allaire},
           familyi={A\bibinitperiod},
           given={Grégoire},
           giveni={G\bibinitperiod}}}%
        {{hash=71dd35ee6f0ac1ffa65812bb0ea5c7e8}{%
           family={Jouve},
           familyi={J\bibinitperiod},
           given={François},
           giveni={F\bibinitperiod}}}%
        {{hash=8c4eba1d6c2f7538225d3eac375ebaaf}{%
           family={Toader},
           familyi={T\bibinitperiod},
           given={Anca-Maria},
           giveni={A\bibinithyphendelim M\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{ceb78d584ee90d8f0724c5528bbc91ee}
      \strng{fullhash}{ceb78d584ee90d8f0724c5528bbc91ee}
      \strng{bibnamehash}{ceb78d584ee90d8f0724c5528bbc91ee}
      \strng{authorbibnamehash}{ceb78d584ee90d8f0724c5528bbc91ee}
      \strng{authornamehash}{ceb78d584ee90d8f0724c5528bbc91ee}
      \strng{authorfullhash}{ceb78d584ee90d8f0724c5528bbc91ee}
      \field{extraname}{1}
      \field{sortinit}{2}
      \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{We study a level-set method for numerical shape optimization of elastic structures. Our approach combines the level-set algorithm of Osher and Sethian with the classical shape gradient. Although this method is not specifically designed for topology optimization, it can easily handle topology changes for a very large class of objective functions. Its cost is moderate since the shape is captured on a fixed Eulerian mesh. To cite this article: G.&nbsp;Allaire et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 1125–1130. Résumé Nous proposons une méthode de lignes de niveaux pour l'optimisation de la forme de structures élastiques. Notre approche combine la méthode des lignes de niveaux d'Osher et Sethian et la dérivée classique de formes. Bien que cette méthode ne soit pas spécifiquement conçue pour faire de l'optimisation topologique, elle permet très facilement les changements de topologie de la forme d'une structure pour des fonctions objectifs très générales. Son coût en temps de calcul est modéré puisqu'il s'agit d'une méthode numérique de capture de formes sur un maillage eulérien fixe. Pour citer cet article : G.&nbsp;Allaire et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 1125–1130.}
      \field{issn}{1631-073X}
      \field{journaltitle}{Comptes Rendus Mathematique}
      \field{month}{1}
      \field{number}{12}
      \field{title}{A level-set method for shape optimization}
      \field{urlday}{13}
      \field{urlmonth}{1}
      \field{urlyear}{2021}
      \field{volume}{334}
      \field{year}{2002}
      \field{urldateera}{ce}
      \field{pages}{1125\bibrangedash 1130}
      \range{pages}{6}
      \verb{doi}
      \verb 10.1016/S1631-073X(02)02412-3
      \endverb
      \verb{file}
      \verb ScienceDirect Full Text PDF:D\:\\estragio\\Zotero\\storage\\YI6UXJA4\\Allaire et al. - 2002 - A level-set method for shape optimization.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb http://www.sciencedirect.com/science/article/pii/S1631073X02024123
      \endverb
      \verb{url}
      \verb http://www.sciencedirect.com/science/article/pii/S1631073X02024123
      \endverb
    \endentry
    \entry{wang_level_2003}{article}{}
      \name{author}{3}{}{%
        {{hash=219774870c8d1b82bd1df5d310461471}{%
           family={Wang},
           familyi={W\bibinitperiod},
           given={Michael\bibnamedelima Yu},
           giveni={M\bibinitperiod\bibinitdelim Y\bibinitperiod}}}%
        {{hash=3968616b3c918008452b8995ddb270e6}{%
           family={Wang},
           familyi={W\bibinitperiod},
           given={Xiaoming},
           giveni={X\bibinitperiod}}}%
        {{hash=01c4e3c0171db0e4b47bb1f5a9cbe0bd}{%
           family={Guo},
           familyi={G\bibinitperiod},
           given={Dongming},
           giveni={D\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{d2dd93a21e484910d25402115a0fb53d}
      \strng{fullhash}{d2dd93a21e484910d25402115a0fb53d}
      \strng{bibnamehash}{d2dd93a21e484910d25402115a0fb53d}
      \strng{authorbibnamehash}{d2dd93a21e484910d25402115a0fb53d}
      \strng{authornamehash}{d2dd93a21e484910d25402115a0fb53d}
      \strng{authorfullhash}{d2dd93a21e484910d25402115a0fb53d}
      \field{sortinit}{2}
      \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This paper presents a new approach to structural topology optimization. We represent the structural boundary by a level set model that is embedded in a scalar function of a higher dimension. Such level set models are flexible in handling complex topological changes and are concise in describing the boundary shape of the structure. Furthermore, a well-founded mathematical procedure leads to a numerical algorithm that describes a structural optimization as a sequence of motions of the implicit boundaries converging to an optimum solution and satisfying specified constraints. The result is a 3D topology optimization technique that demonstrates outstanding flexibility of handling topological changes, fidelity of boundary representation and degree of automation. We have implemented the algorithm with the use of several robust and efficient numerical techniques of level set methods. The benefit and the advantages of the proposed method are illustrated with several 2D examples that are widely used in the recent literature of topology optimization, especially in the homogenization based methods.}
      \field{issn}{0045-7825}
      \field{journaltitle}{Computer Methods in Applied Mechanics and Engineering}
      \field{month}{1}
      \field{number}{1}
      \field{title}{A level set method for structural topology optimization}
      \field{urlday}{13}
      \field{urlmonth}{1}
      \field{urlyear}{2021}
      \field{volume}{192}
      \field{year}{2003}
      \field{urldateera}{ce}
      \field{pages}{227\bibrangedash 246}
      \range{pages}{20}
      \verb{doi}
      \verb 10.1016/S0045-7825(02)00559-5
      \endverb
      \verb{file}
      \verb ScienceDirect Full Text PDF:D\:\\estragio\\Zotero\\storage\\7PK6LKHP\\Wang et al. - 2003 - A level set method for structural topology optimiz.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb http://www.sciencedirect.com/science/article/pii/S0045782502005595
      \endverb
      \verb{url}
      \verb http://www.sciencedirect.com/science/article/pii/S0045782502005595
      \endverb
      \keyw{Topology optimization,Structural optimization,Level set method,Shape optimization,Implicit moving boundary,Level set models}
    \endentry
    \entry{allaire_structural_2004}{article}{}
      \name{author}{3}{}{%
        {{hash=e689b43ac5d3242f4613a353518abfb7}{%
           family={Allaire},
           familyi={A\bibinitperiod},
           given={Grégoire},
           giveni={G\bibinitperiod}}}%
        {{hash=71dd35ee6f0ac1ffa65812bb0ea5c7e8}{%
           family={Jouve},
           familyi={J\bibinitperiod},
           given={François},
           giveni={F\bibinitperiod}}}%
        {{hash=8c4eba1d6c2f7538225d3eac375ebaaf}{%
           family={Toader},
           familyi={T\bibinitperiod},
           given={Anca-Maria},
           giveni={A\bibinithyphendelim M\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{ceb78d584ee90d8f0724c5528bbc91ee}
      \strng{fullhash}{ceb78d584ee90d8f0724c5528bbc91ee}
      \strng{bibnamehash}{ceb78d584ee90d8f0724c5528bbc91ee}
      \strng{authorbibnamehash}{ceb78d584ee90d8f0724c5528bbc91ee}
      \strng{authornamehash}{ceb78d584ee90d8f0724c5528bbc91ee}
      \strng{authorfullhash}{ceb78d584ee90d8f0724c5528bbc91ee}
      \field{extraname}{2}
      \field{sortinit}{2}
      \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{In the context of structural optimization we propose a new numerical method based on a combination of the classical shape derivative and of the level-set method for front propagation. We implement this method in two and three space dimensions for a model of linear or nonlinear elasticity. We consider various objective functions with weight and perimeter constraints. The shape derivative is computed by an adjoint method. The cost of our numerical algorithm is moderate since the shape is captured on a ﬁxed Eulerian mesh. Although this method is not speciﬁcally designed for topology optimization, it can easily handle topology changes. However, the resulting optimal shape is strongly dependent on the initial guess.}
      \field{issn}{00219991}
      \field{journaltitle}{Journal of Computational Physics}
      \field{month}{2}
      \field{number}{1}
      \field{title}{Structural optimization using sensitivity analysis and a level-set method}
      \field{urlday}{13}
      \field{urlmonth}{1}
      \field{urlyear}{2021}
      \field{volume}{194}
      \field{year}{2004}
      \field{urldateera}{ce}
      \field{pages}{363\bibrangedash 393}
      \range{pages}{31}
      \verb{doi}
      \verb 10.1016/j.jcp.2003.09.032
      \endverb
      \verb{file}
      \verb Allaire et al. - 2004 - Structural optimization using sensitivity analysis.pdf:D\:\\estragio\\Zotero\\storage\\QHT3ZQRP\\Allaire et al. - 2004 - Structural optimization using sensitivity analysis.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://linkinghub.elsevier.com/retrieve/pii/S002199910300487X
      \endverb
      \verb{url}
      \verb https://linkinghub.elsevier.com/retrieve/pii/S002199910300487X
      \endverb
    \endentry
    \entry{tortorelli_design_1994}{article}{}
      \name{author}{2}{}{%
        {{hash=4caf98a4b6b232023a7a520e17f32e2b}{%
           family={Tortorelli},
           familyi={T\bibinitperiod},
           given={D.\bibnamedelimi A.},
           giveni={D\bibinitperiod\bibinitdelim A\bibinitperiod}}}%
        {{hash=72089b361a5757cc32b5cdd0317cb22b}{%
           family={Michaleris},
           familyi={M\bibinitperiod},
           given={P.},
           giveni={P\bibinitperiod}}}%
      }
      \strng{namehash}{2cf20aff48376ea27ad947ecf7076adc}
      \strng{fullhash}{2cf20aff48376ea27ad947ecf7076adc}
      \strng{bibnamehash}{2cf20aff48376ea27ad947ecf7076adc}
      \strng{authorbibnamehash}{2cf20aff48376ea27ad947ecf7076adc}
      \strng{authornamehash}{2cf20aff48376ea27ad947ecf7076adc}
      \strng{authorfullhash}{2cf20aff48376ea27ad947ecf7076adc}
      \field{sortinit}{3}
      \field{sortinithash}{ad6fe7482ffbd7b9f99c9e8b5dccd3d7}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{shorttitle}
      \field{abstract}{Design sensitivity plays a critical role in inverse and identification studies, as well as numerical optimization, and reliability analysis. Herein, we review the state of design sensitivity analysis as it applies to linear elliptic systems. Both first- and second-order sensitivities are derived as well as first-order sensitivities for symmetric positive definite eigenvalue systems. Although these results are not new, some of the derivations offer a different perspective than those previously presented. This article is meant as a tutorial, and as such, a simple two-degree-of-freedom spring system is employed to exemplify the sensitivity analyses. However, the concepts presented in this trivial example may be readily extended to compute sensitivities for complex systems via numerical techniques such as the finite element, boundary element, and finite difference methods.}
      \field{issn}{1068-2767}
      \field{journaltitle}{Inverse Problems in Engineering}
      \field{month}{10}
      \field{number}{1}
      \field{shorttitle}{Design sensitivity analysis}
      \field{title}{Design sensitivity analysis: {Overview} and review}
      \field{urlday}{29}
      \field{urlmonth}{10}
      \field{urlyear}{2020}
      \field{volume}{1}
      \field{year}{1994}
      \field{urldateera}{ce}
      \field{pages}{71\bibrangedash 105}
      \range{pages}{35}
      \verb{doi}
      \verb 10.1080/174159794088027573
      \endverb
      \verb{file}
      \verb Tortorelli et Michaleris - 1994 - Design sensitivity analysis Overview and review.pdf:D\:\\estragio\\Zotero\\storage\\XWWML8II\\Tortorelli et Michaleris - 1994 - Design sensitivity analysis Overview and review.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1080/174159794088027573
      \endverb
      \verb{url}
      \verb https://doi.org/10.1080/174159794088027573
      \endverb
      \keyw{Sensitivity analysis}
    \endentry
    \entry{guest_achieving_2004}{article}{}
      \name{author}{3}{}{%
        {{hash=7e4617bddd3988bc08159a5390a3c4cd}{%
           family={Guest},
           familyi={G\bibinitperiod},
           given={J.\bibnamedelimi K.},
           giveni={J\bibinitperiod\bibinitdelim K\bibinitperiod}}}%
        {{hash=61de3c7ca9d8f804a3cdffc5313bb868}{%
           family={Prévost},
           familyi={P\bibinitperiod},
           given={J.\bibnamedelimi H.},
           giveni={J\bibinitperiod\bibinitdelim H\bibinitperiod}}}%
        {{hash=87de48ed585a7dc01f0a933d6a6c62b0}{%
           family={Belytschko},
           familyi={B\bibinitperiod},
           given={T.},
           giveni={T\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{cef2a8c3062b9244d7f72a47dce6c900}
      \strng{fullhash}{cef2a8c3062b9244d7f72a47dce6c900}
      \strng{bibnamehash}{cef2a8c3062b9244d7f72a47dce6c900}
      \strng{authorbibnamehash}{cef2a8c3062b9244d7f72a47dce6c900}
      \strng{authornamehash}{cef2a8c3062b9244d7f72a47dce6c900}
      \strng{authorfullhash}{cef2a8c3062b9244d7f72a47dce6c900}
      \field{sortinit}{3}
      \field{sortinithash}{ad6fe7482ffbd7b9f99c9e8b5dccd3d7}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{A methodology for imposing a minimum length scale on structural members in discretized topology optimization problems is described. Nodal variables are implemented as the design variables and are projected onto element space to determine the element volume fractions that traditionally define topology. The projection is made via mesh independent functions that are based upon the minimum length scale. A simple linear projection scheme and a non-linear scheme using a regularized Heaviside step function to achieve nearly 0–1 solutions are examined. The new approach is demonstrated on the minimum compliance problem and the popular SIMP method is used to penalize the stiffness of intermediate volume fraction elements. Solutions are shown to meet user-defined length scale criterion without additional constraints, penalty functions or sensitivity filters. No instances of mesh dependence or checkerboard patterns have been observed. Copyright © 2004 John Wiley \&amp; Sons, Ltd.}
      \field{issn}{1097-0207}
      \field{journaltitle}{International Journal for Numerical Methods in Engineering}
      \field{number}{2}
      \field{title}{Achieving minimum length scale in topology optimization using nodal design variables and projection functions}
      \field{urlday}{26}
      \field{urlmonth}{9}
      \field{urlyear}{2021}
      \field{volume}{61}
      \field{year}{2004}
      \field{urldateera}{ce}
      \field{pages}{238\bibrangedash 254}
      \range{pages}{17}
      \verb{doi}
      \verb 10.1002/nme.1064
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\RFNNMZJF\\Guest et al. - 2004 - Achieving minimum length scale in topology optimiz.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.1064
      \endverb
      \verb{url}
      \verb https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.1064
      \endverb
      \keyw{length scale,topology optimization}
    \endentry
    \entry{wang_projection_2011}{article}{}
      \name{author}{3}{}{%
        {{hash=86b2febfa07ec8c15dec84b145213356}{%
           family={Wang},
           familyi={W\bibinitperiod},
           given={Fengwen},
           giveni={F\bibinitperiod}}}%
        {{hash=5cd89b878d0caf28d27df664e57605fa}{%
           family={Lazarov},
           familyi={L\bibinitperiod},
           given={Boyan\bibnamedelima Stefanov},
           giveni={B\bibinitperiod\bibinitdelim S\bibinitperiod}}}%
        {{hash=d76f1c09e8d8d06e1b7c3c254efeae1a}{%
           family={Sigmund},
           familyi={S\bibinitperiod},
           given={Ole},
           giveni={O\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{ebb044e76181e7c827ba8e6a1a7af8df}
      \strng{fullhash}{ebb044e76181e7c827ba8e6a1a7af8df}
      \strng{bibnamehash}{ebb044e76181e7c827ba8e6a1a7af8df}
      \strng{authorbibnamehash}{ebb044e76181e7c827ba8e6a1a7af8df}
      \strng{authornamehash}{ebb044e76181e7c827ba8e6a1a7af8df}
      \strng{authorfullhash}{ebb044e76181e7c827ba8e6a1a7af8df}
      \field{sortinit}{3}
      \field{sortinithash}{ad6fe7482ffbd7b9f99c9e8b5dccd3d7}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{6}
      \field{number}{6}
      \field{title}{On projection methods, convergence and robust formulations in topology optimization}
      \field{urlday}{3}
      \field{urlmonth}{6}
      \field{urlyear}{2021}
      \field{volume}{43}
      \field{year}{2011}
      \field{urldateera}{ce}
      \field{pages}{767\bibrangedash 784}
      \range{pages}{18}
      \verb{doi}
      \verb 10.1007/s00158-010-0602-y
      \endverb
    \endentry
    \entry{bendsoe_material_1999}{article}{}
      \name{author}{2}{}{%
        {{hash=193e92bb57a8aeb7a8a809f2e4f7221f}{%
           family={Bendsøe},
           familyi={B\bibinitperiod},
           given={M.\bibnamedelimi P.},
           giveni={M\bibinitperiod\bibinitdelim P\bibinitperiod}}}%
        {{hash=8e39f252b54fbee1f97675ee90b87f23}{%
           family={Sigmund},
           familyi={S\bibinitperiod},
           given={O.},
           giveni={O\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{63e48d356179b176429df024638ee206}
      \strng{fullhash}{63e48d356179b176429df024638ee206}
      \strng{bibnamehash}{63e48d356179b176429df024638ee206}
      \strng{authorbibnamehash}{63e48d356179b176429df024638ee206}
      \strng{authornamehash}{63e48d356179b176429df024638ee206}
      \strng{authorfullhash}{63e48d356179b176429df024638ee206}
      \field{extraname}{2}
      \field{sortinit}{3}
      \field{sortinithash}{ad6fe7482ffbd7b9f99c9e8b5dccd3d7}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{journaltitle}{Archive of Applied Mechanics}
      \field{month}{11}
      \field{number}{9}
      \field{title}{Material interpolation schemes in topology optimization}
      \field{urlday}{22}
      \field{urlmonth}{6}
      \field{urlyear}{2021}
      \field{volume}{69}
      \field{year}{1999}
      \field{urldateera}{ce}
      \field{pages}{635\bibrangedash 654}
      \range{pages}{20}
      \verb{doi}
      \verb 10.1007/s004190050248
      \endverb
    \endentry
    \entry{stolpe_alternative_2001}{article}{}
      \name{author}{2}{}{%
        {{hash=9bad1d1c66b6ba268b1b0102bf0ab5ad}{%
           family={Stolpe},
           familyi={S\bibinitperiod},
           given={M.},
           giveni={M\bibinitperiod}}}%
        {{hash=350e8570c519473f8a9f62854e7ef0a1}{%
           family={Svanberg},
           familyi={S\bibinitperiod},
           given={K.},
           giveni={K\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{efe1cb231b5b208e463f0508f00cd1fc}
      \strng{fullhash}{efe1cb231b5b208e463f0508f00cd1fc}
      \strng{bibnamehash}{efe1cb231b5b208e463f0508f00cd1fc}
      \strng{authorbibnamehash}{efe1cb231b5b208e463f0508f00cd1fc}
      \strng{authornamehash}{efe1cb231b5b208e463f0508f00cd1fc}
      \strng{authorfullhash}{efe1cb231b5b208e463f0508f00cd1fc}
      \field{extraname}{1}
      \field{sortinit}{3}
      \field{sortinithash}{ad6fe7482ffbd7b9f99c9e8b5dccd3d7}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{We consider the discretized zero-one continuum topology optimization problem of finding the optimal distribution of two linearly elastic materials such that compliance is minimized. The geometric complexity of the design is limited using a constraint on the perimeter of the design. A common approach to solve these problems is to relax the zero-one constraints and model the material properties by a power law which gives noninteger solutions very little stiffness in comparison to the amount of material used.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{9}
      \field{number}{2}
      \field{title}{An alternative interpolation scheme for minimum compliance topology optimization}
      \field{urlday}{26}
      \field{urlmonth}{9}
      \field{urlyear}{2021}
      \field{volume}{22}
      \field{year}{2001}
      \field{urldateera}{ce}
      \field{pages}{116\bibrangedash 124}
      \range{pages}{9}
      \verb{doi}
      \verb 10.1007/s001580100129
      \endverb
      \verb{file}
      \verb Springer Full Text PDF:D\:\\estragio\\Zotero\\storage\\XWY9ZUUE\\Stolpe and Svanberg - 2001 - An alternative interpolation scheme for minimum co.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/s001580100129
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s001580100129
      \endverb
    \endentry
    \entry{hashin_variational_1963}{article}{}
      \name{author}{2}{}{%
        {{hash=49128c65725c63446a3855ec32504223}{%
           family={Hashin},
           familyi={H\bibinitperiod},
           given={Z.},
           giveni={Z\bibinitperiod}}}%
        {{hash=7937bab147e26e39eb341a832acbc619}{%
           family={Shtrikman},
           familyi={S\bibinitperiod},
           given={S.},
           giveni={S\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{00acd1f11ef1807e13aab32a65ed034d}
      \strng{fullhash}{00acd1f11ef1807e13aab32a65ed034d}
      \strng{bibnamehash}{00acd1f11ef1807e13aab32a65ed034d}
      \strng{authorbibnamehash}{00acd1f11ef1807e13aab32a65ed034d}
      \strng{authornamehash}{00acd1f11ef1807e13aab32a65ed034d}
      \strng{authorfullhash}{00acd1f11ef1807e13aab32a65ed034d}
      \field{sortinit}{3}
      \field{sortinithash}{ad6fe7482ffbd7b9f99c9e8b5dccd3d7}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{issn}{00225096}
      \field{journaltitle}{Journal of the Mechanics and Physics of Solids}
      \field{month}{3}
      \field{number}{2}
      \field{title}{A variational approach to the theory of the elastic behaviour of multiphase materials}
      \field{urlday}{6}
      \field{urlmonth}{10}
      \field{urlyear}{2020}
      \field{volume}{11}
      \field{year}{1963}
      \field{urldateera}{ce}
      \field{pages}{127\bibrangedash 140}
      \range{pages}{14}
      \verb{doi}
      \verb 10.1016/0022-5096(63)90060-7
      \endverb
      \verb{urlraw}
      \verb https://linkinghub.elsevier.com/retrieve/pii/0022509663900607
      \endverb
      \verb{url}
      \verb https://linkinghub.elsevier.com/retrieve/pii/0022509663900607
      \endverb
    \endentry
    \entry{diaz_checkerboard_1995}{article}{}
      \name{author}{2}{}{%
        {{hash=367c682bf7b28d48b2efc8fc8e8dde97}{%
           family={Díaz},
           familyi={D\bibinitperiod},
           given={A.},
           giveni={A\bibinitperiod}}}%
        {{hash=8e39f252b54fbee1f97675ee90b87f23}{%
           family={Sigmund},
           familyi={S\bibinitperiod},
           given={O.},
           giveni={O\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{6970cef30fa2958e8eae20c6a5b7b481}
      \strng{fullhash}{6970cef30fa2958e8eae20c6a5b7b481}
      \strng{bibnamehash}{6970cef30fa2958e8eae20c6a5b7b481}
      \strng{authorbibnamehash}{6970cef30fa2958e8eae20c6a5b7b481}
      \strng{authornamehash}{6970cef30fa2958e8eae20c6a5b7b481}
      \strng{authorfullhash}{6970cef30fa2958e8eae20c6a5b7b481}
      \field{sortinit}{3}
      \field{sortinithash}{ad6fe7482ffbd7b9f99c9e8b5dccd3d7}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Effective properties of arrangements of strong and weak materials in a checkerboard fashion are computed. Kinematic constraints are imposed so that the displacements are consistent with typical finite element approximations. It is shown that when four-node quatrilateral elements are involved, these constraints result in a numerically induced, artificially high stiffness. This can account for the formation of checkerboard patterns in continuous layout optimization problems of compliance minimization.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural optimization}
      \field{month}{8}
      \field{number}{1}
      \field{title}{Checkerboard patterns in layout optimization}
      \field{urlday}{29}
      \field{urlmonth}{8}
      \field{urlyear}{2023}
      \field{volume}{10}
      \field{year}{1995}
      \field{urldateera}{ce}
      \field{pages}{40\bibrangedash 45}
      \range{pages}{6}
      \verb{doi}
      \verb 10.1007/BF01743693
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\WWJLQ8Z4\\Díaz and Sigmund - 1995 - Checkerboard patterns in layout optimization.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/BF01743693
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/BF01743693
      \endverb
      \keyw{Civil Engineer,Effective Property,Element Approximation,High Stiffness,Kinematic Constraint}
    \endentry
    \entry{sigmund_design_1994}{thesis}{}
      \name{author}{1}{}{%
        {{hash=d76f1c09e8d8d06e1b7c3c254efeae1a}{%
           family={Sigmund},
           familyi={S\bibinitperiod},
           given={Ole},
           giveni={O\bibinitperiod}}}%
      }
      \list{institution}{1}{%
        {Technical University of Denmark, DK-2800 Lyngby}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{fullhash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{bibnamehash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{authorbibnamehash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{authornamehash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{authorfullhash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \field{extraname}{6}
      \field{sortinit}{3}
      \field{sortinithash}{ad6fe7482ffbd7b9f99c9e8b5dccd3d7}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{title}{Design of {Material} {Structures} using {Topology} {Optimization}}
      \field{type}{phdthesis}
      \field{year}{1994}
      \verb{file}
      \verb Sigmund - Design of Material Structures using Topology Optim.pdf:D\:\\estragio\\Zotero\\storage\\ZHN5QX3A\\Sigmund - Design of Material Structures using Topology Optim.pdf:application/pdf
      \endverb
    \endentry
    \entry{sigmund_morphology-based_2007}{article}{}
      \name{author}{1}{}{%
        {{hash=d76f1c09e8d8d06e1b7c3c254efeae1a}{%
           family={Sigmund},
           familyi={S\bibinitperiod},
           given={Ole},
           giveni={O\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{fullhash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{bibnamehash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{authorbibnamehash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{authornamehash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{authorfullhash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \field{extraname}{7}
      \field{sortinit}{3}
      \field{sortinithash}{ad6fe7482ffbd7b9f99c9e8b5dccd3d7}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{4}
      \field{number}{4}
      \field{title}{Morphology-based black and white filters for topology optimization}
      \field{urlday}{9}
      \field{urlmonth}{12}
      \field{urlyear}{2020}
      \field{volume}{33}
      \field{year}{2007}
      \field{urldateera}{ce}
      \field{pages}{401\bibrangedash 424}
      \range{pages}{24}
      \verb{doi}
      \verb 10.1007/s00158-006-0087-x
      \endverb
    \endentry
    \entry{allaire_numerical_1993}{incollection}{}
      \name{author}{2}{}{%
        {{hash=01ec1538b00db5bf5f81d6d2221f5693}{%
           family={Allaire},
           familyi={A\bibinitperiod},
           given={G.},
           giveni={G\bibinitperiod}}}%
        {{hash=2962f5df2868345eac7f3a5c9f41ef5a}{%
           family={Francfort},
           familyi={F\bibinitperiod},
           given={G.\bibnamedelimi A.},
           giveni={G\bibinitperiod\bibinitdelim A\bibinitperiod}}}%
      }
      \name{editor}{2}{}{%
        {{hash=98d3b25fbc7c0c4f72bc274f68c9a705}{%
           family={Bendsøe},
           familyi={B\bibinitperiod},
           given={Martin\bibnamedelima Philip},
           giveni={M\bibinitperiod\bibinitdelim P\bibinitperiod}}}%
        {{hash=ab521e277a18c537b5c248e3f17df8dc}{%
           family={Soares},
           familyi={S\bibinitperiod},
           given={Carlos\bibnamedelimb A.\bibnamedelimi Mota},
           giveni={C\bibinitperiod\bibinitdelim A\bibinitperiod\bibinitdelim M\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \list{location}{1}{%
        {Dordrecht}%
      }
      \list{publisher}{1}{%
        {Springer Netherlands}%
      }
      \strng{namehash}{c5bfe34eebcd36382ba11b42c670e0c2}
      \strng{fullhash}{c5bfe34eebcd36382ba11b42c670e0c2}
      \strng{bibnamehash}{c5bfe34eebcd36382ba11b42c670e0c2}
      \strng{authorbibnamehash}{c5bfe34eebcd36382ba11b42c670e0c2}
      \strng{authornamehash}{c5bfe34eebcd36382ba11b42c670e0c2}
      \strng{authorfullhash}{c5bfe34eebcd36382ba11b42c670e0c2}
      \strng{editorbibnamehash}{fe8c93327cd494fe2b95b40cbf253c42}
      \strng{editornamehash}{fe8c93327cd494fe2b95b40cbf253c42}
      \strng{editorfullhash}{fe8c93327cd494fe2b95b40cbf253c42}
      \field{sortinit}{3}
      \field{sortinithash}{ad6fe7482ffbd7b9f99c9e8b5dccd3d7}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{In the context of topology and shape optimization, we minimize the sum of the elastic compliance and of the weight of a two-dimensional structure under specified loading. A relaxed formulation of the original problem which uses composites obtained by microperforation is introduced. A new numerical algorithm is proposed ; it provides a natural link between the previously known method of Bendsoe, Kikuchi, and Suzuki, and that of Allaire and Kohn.}
      \field{booktitle}{Topology {Design} of {Structures}}
      \field{isbn}{978-94-011-1804-0}
      \field{series}{{NATO} {ASI} {Series}}
      \field{title}{A {Numerical} {Algorithm} for {Topology} and {Shape} {Optimization}}
      \field{urlday}{10}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{year}{1993}
      \field{urldateera}{ce}
      \field{pages}{239\bibrangedash 248}
      \range{pages}{10}
      \verb{doi}
      \verb 10.1007/978-94-011-1804-0_16
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\7NTK35P5\\Allaire and Francfort - 1993 - A Numerical Algorithm for Topology and Shape Optim.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/978-94-011-1804-0_16
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/978-94-011-1804-0_16
      \endverb
      \keyw{Alternate Direction Method,Convergence History,Design Variable,Optimal Shape Design,Topology Optimization}
    \endentry
    \entry{allaire_topology_1993}{incollection}{}
      \name{author}{2}{}{%
        {{hash=01ec1538b00db5bf5f81d6d2221f5693}{%
           family={Allaire},
           familyi={A\bibinitperiod},
           given={G.},
           giveni={G\bibinitperiod}}}%
        {{hash=6becdcfd3af58342603c891e21ae8f27}{%
           family={Kohn},
           familyi={K\bibinitperiod},
           given={R.\bibnamedelimi V.},
           giveni={R\bibinitperiod\bibinitdelim V\bibinitperiod}}}%
      }
      \name{editor}{2}{}{%
        {{hash=98d3b25fbc7c0c4f72bc274f68c9a705}{%
           family={Bendsøe},
           familyi={B\bibinitperiod},
           given={Martin\bibnamedelima Philip},
           giveni={M\bibinitperiod\bibinitdelim P\bibinitperiod}}}%
        {{hash=ab521e277a18c537b5c248e3f17df8dc}{%
           family={Soares},
           familyi={S\bibinitperiod},
           given={Carlos\bibnamedelimb A.\bibnamedelimi Mota},
           giveni={C\bibinitperiod\bibinitdelim A\bibinitperiod\bibinitdelim M\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \list{location}{1}{%
        {Dordrecht}%
      }
      \list{publisher}{1}{%
        {Springer Netherlands}%
      }
      \strng{namehash}{0caab3f40694d1d7e878823468172073}
      \strng{fullhash}{0caab3f40694d1d7e878823468172073}
      \strng{bibnamehash}{0caab3f40694d1d7e878823468172073}
      \strng{authorbibnamehash}{0caab3f40694d1d7e878823468172073}
      \strng{authornamehash}{0caab3f40694d1d7e878823468172073}
      \strng{authorfullhash}{0caab3f40694d1d7e878823468172073}
      \strng{editorbibnamehash}{fe8c93327cd494fe2b95b40cbf253c42}
      \strng{editornamehash}{fe8c93327cd494fe2b95b40cbf253c42}
      \strng{editorfullhash}{fe8c93327cd494fe2b95b40cbf253c42}
      \field{sortinit}{3}
      \field{sortinithash}{ad6fe7482ffbd7b9f99c9e8b5dccd3d7}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{We study the shape optimization of a two-dimensional elastic body loaded in plane stress. The design criteria are compliance and weight. A relaxed formulation obtained by homogenization is used, whereby perforated composite materials are admitted as structural components. This approach has the advantage of placing no implicit restriction on the topology of the design. We compare our results with those of Bendsoe, Kikuchi, and Suzuki who used an approach similar to ours.}
      \field{booktitle}{Topology {Design} of {Structures}}
      \field{isbn}{978-94-011-1804-0}
      \field{series}{{NATO} {ASI} {Series}}
      \field{title}{Topology {Optimization} and {Optimal} {Shape} {Design} {Using} {Homogenization}}
      \field{urlday}{10}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{year}{1993}
      \field{urldateera}{ce}
      \field{pages}{207\bibrangedash 218}
      \range{pages}{12}
      \verb{doi}
      \verb 10.1007/978-94-011-1804-0_14
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\3ILT4UEK\\Allaire and Kohn - 1993 - Topology Optimization and Optimal Shape Design Usi.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/978-94-011-1804-0_14
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/978-94-011-1804-0_14
      \endverb
      \keyw{Complementary Energy,Conjugate Gradient Method,Optimal Design,Plane Stress,Topology Optimization}
    \endentry
    \entry{rozvany_critical_2009}{article}{}
      \name{author}{1}{}{%
        {{hash=2dd717bb9ecafd6aa2723e522b7aa056}{%
           family={Rozvany},
           familyi={R\bibinitperiod},
           given={G.\bibnamedelimi I.\bibnamedelimi N.},
           giveni={G\bibinitperiod\bibinitdelim I\bibinitperiod\bibinitdelim N\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{2dd717bb9ecafd6aa2723e522b7aa056}
      \strng{fullhash}{2dd717bb9ecafd6aa2723e522b7aa056}
      \strng{bibnamehash}{2dd717bb9ecafd6aa2723e522b7aa056}
      \strng{authorbibnamehash}{2dd717bb9ecafd6aa2723e522b7aa056}
      \strng{authornamehash}{2dd717bb9ecafd6aa2723e522b7aa056}
      \strng{authorfullhash}{2dd717bb9ecafd6aa2723e522b7aa056}
      \field{extraname}{1}
      \field{sortinit}{4}
      \field{sortinithash}{9381316451d1b9788675a07e972a12a7}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{The aim of this article is to evaluate and compare established numerical methods of structural topology optimization that have reached the stage of application in industrial software. It is hoped that our text will spark off a fruitful and constructive debate on this important topic.}
      \field{issn}{1615-147X, 1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{1}
      \field{number}{3}
      \field{title}{A critical review of established methods of structural topology optimization}
      \field{urlday}{10}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{37}
      \field{year}{2009}
      \field{urldateera}{ce}
      \field{pages}{217\bibrangedash 237}
      \range{pages}{21}
      \verb{doi}
      \verb 10.1007/s00158-007-0217-0
      \endverb
      \verb{file}
      \verb Rozvany - 2009 - A critical review of established methods of struct.pdf:D\:\\estragio\\Zotero\\storage\\EUNTMXQ4\\Rozvany - 2009 - A critical review of established methods of struct.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb http://link.springer.com/10.1007/s00158-007-0217-0
      \endverb
      \verb{url}
      \verb http://link.springer.com/10.1007/s00158-007-0217-0
      \endverb
    \endentry
    \entry{petersson_slope_1998}{article}{}
      \name{author}{2}{}{%
        {{hash=6f32b7d50b188dbda2f985ea10292506}{%
           family={Petersson},
           familyi={P\bibinitperiod},
           given={Joakim},
           giveni={J\bibinitperiod}}}%
        {{hash=d76f1c09e8d8d06e1b7c3c254efeae1a}{%
           family={Sigmund},
           familyi={S\bibinitperiod},
           given={Ole},
           giveni={O\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{f7015aab90b430cf3723914a6a85c952}
      \strng{fullhash}{f7015aab90b430cf3723914a6a85c952}
      \strng{bibnamehash}{f7015aab90b430cf3723914a6a85c952}
      \strng{authorbibnamehash}{f7015aab90b430cf3723914a6a85c952}
      \strng{authornamehash}{f7015aab90b430cf3723914a6a85c952}
      \strng{authorfullhash}{f7015aab90b430cf3723914a6a85c952}
      \field{sortinit}{4}
      \field{sortinithash}{9381316451d1b9788675a07e972a12a7}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{The problem of minimum compliance topology optimization of an elastic continuum is considered. A general continuous density–energy relation is assumed, including variable thickness sheet models and artificial power laws. To ensure existence of solutions, the design set is restricted by enforcing pointwise bounds on the density slopes. A finite element discretization procedure is described, and a proof of convergence of finite element solutions to exact solutions is given, as well as numerical examples obtained by a continuation/SLP (sequential linear programming) method. The convergence proof implies that checkerboard patterns and other numerical anomalies will not be present, or at least, that they can be made arbitrarily weak. © 1998 John Wiley \&amp; Sons, Ltd.}
      \field{issn}{1097-0207}
      \field{journaltitle}{International Journal for Numerical Methods in Engineering}
      \field{number}{8}
      \field{title}{Slope constrained topology optimization}
      \field{urlday}{10}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{41}
      \field{year}{1998}
      \field{urldateera}{ce}
      \field{pages}{1417\bibrangedash 1434}
      \range{pages}{18}
      \verb{doi}
      \verb 10.1002/(SICI)1097-0207(19980430)41:8&lt;1417::AID-NME344&gt;3.0.CO;2-N
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\J6QJ9SRJ\\Petersson and Sigmund - 1998 - Slope constrained topology optimization.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://onlinelibrary.wiley.com/doi/abs/10.1002/%28SICI%291097-0207%2819980430%2941%3A8%3C1417%3A%3AAID-NME344%3E3.0.CO%3B2-N
      \endverb
      \verb{url}
      \verb https://onlinelibrary.wiley.com/doi/abs/10.1002/%28SICI%291097-0207%2819980430%2941%3A8%3C1417%3A%3AAID-NME344%3E3.0.CO%3B2-N
      \endverb
      \keyw{finite elements,slope constraints,topology optimization}
    \endentry
    \entry{rojas-labanda_automatic_2015}{article}{}
      \name{author}{2}{}{%
        {{hash=07c39082efb5bffc8f372768778e21cc}{%
           family={Rojas-Labanda},
           familyi={R\bibinithyphendelim L\bibinitperiod},
           given={Susana},
           giveni={S\bibinitperiod}}}%
        {{hash=2ac977bc03dde1f3d4061cda61ab9795}{%
           family={Stolpe},
           familyi={S\bibinitperiod},
           given={Mathias},
           giveni={M\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{9ad9cf6c5fb7d2deb24abe2466f891d7}
      \strng{fullhash}{9ad9cf6c5fb7d2deb24abe2466f891d7}
      \strng{bibnamehash}{9ad9cf6c5fb7d2deb24abe2466f891d7}
      \strng{authorbibnamehash}{9ad9cf6c5fb7d2deb24abe2466f891d7}
      \strng{authornamehash}{9ad9cf6c5fb7d2deb24abe2466f891d7}
      \strng{authorfullhash}{9ad9cf6c5fb7d2deb24abe2466f891d7}
      \field{sortinit}{4}
      \field{sortinithash}{9381316451d1b9788675a07e972a12a7}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Structural topology optimization problems are often modelled using material interpolation schemes to produce almost solid-and-void designs. The problems become non convex due to the use of these techniques. Several articles introduce continuation approaches in the material penalization parameter to reduce the risks of ending in local minima. However, the numerical performance of continuation methods has not been studied in detail. The first purpose of this article is to benchmark existing continuation methods and the classical formulation with fixed penalty parameter in structural topology optimization. This is done using performance profiles on 225 minimum compliance and 150 compliant mechanism design problems. The results show that continuation methods generally find better designs. On the other hand, they typically require a larger number of iterations. In the second part of the article this issue is addressed. We propose an automatic continuation method, where the material penalization parameter is included as a new variable in the problem and a constraint guarantees that the requested penalty is eventually reached. The numerical results suggest that this approach is an appealing alternative to continuation methods. Automatic continuation also generally obtains better designs than the classical formulation using a reduced number of iterations.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{12}
      \field{number}{6}
      \field{title}{Automatic penalty continuation in structural topology optimization}
      \field{urlday}{2}
      \field{urlmonth}{2}
      \field{urlyear}{2022}
      \field{volume}{52}
      \field{year}{2015}
      \field{urldateera}{ce}
      \field{pages}{1205\bibrangedash 1221}
      \range{pages}{17}
      \verb{doi}
      \verb 10.1007/s00158-015-1277-1
      \endverb
      \verb{file}
      \verb Springer Full Text PDF:D\:\\estragio\\Zotero\\storage\\UKFULYCF\\Rojas-Labanda and Stolpe - 2015 - Automatic penalty continuation in structural topol.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/s00158-015-1277-1
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s00158-015-1277-1
      \endverb
    \endentry
    \entry{hozic_new_2021}{article}{}
      \name{author}{4}{}{%
        {{hash=1448acc1a86dde86ec2cc9f3a277b148}{%
           family={Hozić},
           familyi={H\bibinitperiod},
           given={Dženan},
           giveni={D\bibinitperiod}}}%
        {{hash=5121070f4effb78c91f5f70a0261d6a6}{%
           family={Thore},
           familyi={T\bibinitperiod},
           given={Carl-Johan},
           giveni={C\bibinithyphendelim J\bibinitperiod}}}%
        {{hash=5ca4d92332f6837e7ac1363503623bd8}{%
           family={Cameron},
           familyi={C\bibinitperiod},
           given={Christopher},
           giveni={C\bibinitperiod}}}%
        {{hash=6c182b579a3f579ef9451bd8db7ef774}{%
           family={Loukil},
           familyi={L\bibinitperiod},
           given={Mohamed},
           giveni={M\bibinitperiod}}}%
      }
      \strng{namehash}{16d11e5b9a8d6e41f4a714b2505857db}
      \strng{fullhash}{b0274569453389f529499d5c85c1ae13}
      \strng{bibnamehash}{b0274569453389f529499d5c85c1ae13}
      \strng{authorbibnamehash}{b0274569453389f529499d5c85c1ae13}
      \strng{authornamehash}{16d11e5b9a8d6e41f4a714b2505857db}
      \strng{authorfullhash}{b0274569453389f529499d5c85c1ae13}
      \field{sortinit}{4}
      \field{sortinithash}{9381316451d1b9788675a07e972a12a7}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This paper presents a new discrete parametrization method for simultaneous topology and material optimization of composite laminate structures, referred to as Hyperbolic Function Parametrization (HFP). The novelty of HFP is the way the candidate materials are parametrized in the optimization problem. In HFP, a filtering technique based on hyperbolic functions is used, such that only one design variable is used for any given number of material candidates. Compared to state-of-the-art methods such Discrete Material and Topology Optimization (DMTO) and Shape Function with Penalization (SFP), HFP has much fewer optimization variables and constraints but introduces additional non-linearity in the optimization problems. A comparative analysis of HFP, DMTO and SFP are performed based on the problem of maximizing the stiffness of composite plates under a total volume constraint and multiple manufacturing constraints using various loads, boundary conditions and input parameters. The comparison shows that all three methods are highly sensitive to the choice of input parameters for the optimization problem, although the performance of HFP is overall more consistent. HFP method performs similarly to DMTO and SFP in terms of the designs obtained and computational cost. However, HFP obtains similar or better objective function values compared to the DMTO and SFP methods.}
      \field{issn}{0263-8223}
      \field{journaltitle}{Composite Structures}
      \field{month}{11}
      \field{title}{A new method for simultaneous material and topology optimization of composite laminate structures using {Hyperbolic} {Function} {Parametrization}}
      \field{urlday}{9}
      \field{urlmonth}{2}
      \field{urlyear}{2024}
      \field{volume}{276}
      \field{year}{2021}
      \field{urldateera}{ce}
      \field{pages}{114374}
      \range{pages}{1}
      \verb{doi}
      \verb 10.1016/j.compstruct.2021.114374
      \endverb
      \verb{file}
      \verb Full Text:D\:\\estragio\\Zotero\\storage\\QAF7JAW6\\Hozić et al. - 2021 - A new method for simultaneous material and topolog.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://www.sciencedirect.com/science/article/pii/S0263822321008369
      \endverb
      \verb{url}
      \verb https://www.sciencedirect.com/science/article/pii/S0263822321008369
      \endverb
      \keyw{Composite sizing optimization,Hyperbolic function parametrization,Laminated composites,Multi-material optimization,Structural Optimization,Topology Optimization}
    \endentry
    \entry{zhou_progress_2002}{inproceedings}{}
      \name{author}{5}{}{%
        {{hash=2a72f304d2bc33c9c92301f2dc3063b2}{%
           family={Zhou},
           familyi={Z\bibinitperiod},
           given={Ming},
           giveni={M\bibinitperiod}}}%
        {{hash=aa1ba901ff5ae3e0b0ee4831e4955b0b}{%
           family={Fleury},
           familyi={F\bibinitperiod},
           given={Raphael},
           giveni={R\bibinitperiod}}}%
        {{hash=e398c8a2c9ed562033617f29a125dfa3}{%
           family={Shyy},
           familyi={S\bibinitperiod},
           given={Yaw-Kang},
           giveni={Y\bibinithyphendelim K\bibinitperiod}}}%
        {{hash=a6b8c0b3d24b132219bd00c8108dc1ed}{%
           family={Thomas},
           familyi={T\bibinitperiod},
           given={Harold},
           giveni={H\bibinitperiod}}}%
        {{hash=9e84767966eacdc2d8d86ba70ede3a5c}{%
           family={Brennan},
           familyi={B\bibinitperiod},
           given={Jeffrey},
           giveni={J\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \list{location}{1}{%
        {Atlanta, Georgia}%
      }
      \list{publisher}{2}{%
        {American Institute of Aeronautics}%
        {Astronautics}%
      }
      \strng{namehash}{cf8b2059d128511ced2a6a2b2510e595}
      \strng{fullhash}{a4a4af003a4d58638cf319536091f230}
      \strng{bibnamehash}{a4a4af003a4d58638cf319536091f230}
      \strng{authorbibnamehash}{a4a4af003a4d58638cf319536091f230}
      \strng{authornamehash}{cf8b2059d128511ced2a6a2b2510e595}
      \strng{authorfullhash}{a4a4af003a4d58638cf319536091f230}
      \field{sortinit}{4}
      \field{sortinithash}{9381316451d1b9788675a07e972a12a7}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Topology optimization has been shown to be an extremely powerful tool in generating efficient design concepts in the early stage of a design process. Unfortunately, very often designs suggested by topology optimization turn out to be infeasible for certain manufacturing process. At such occasions, it is often very difficult, if not impossible, to transform a design proposal to a manufacturable design. In this paper, design requirements for casting and extrusion production are addressed for topology optimization.}
      \field{booktitle}{9th {AIAA}/{ISSMO} {Symposium} on {Multidisciplinary} {Analysis} and {Optimization}}
      \field{isbn}{978-1-62410-120-5}
      \field{month}{9}
      \field{title}{Progress in {Topology} {Optimization} with {Manufacturing} {Constraints}}
      \field{urlday}{6}
      \field{urlmonth}{5}
      \field{urlyear}{2022}
      \field{year}{2002}
      \field{urldateera}{ce}
      \verb{doi}
      \verb 10.2514/6.2002-5614
      \endverb
    \endentry
    \entry{liu_current_2018}{article}{}
      \name{author}{13}{}{%
        {{hash=6b881d188740fd2dde41d38a7cafb850}{%
           family={Liu},
           familyi={L\bibinitperiod},
           given={Jikai},
           giveni={J\bibinitperiod}}}%
        {{hash=5c35189454736079bb9c690f73aea2c3}{%
           family={Gaynor},
           familyi={G\bibinitperiod},
           given={Andrew\bibnamedelima T.},
           giveni={A\bibinitperiod\bibinitdelim T\bibinitperiod}}}%
        {{hash=a42075c3ada07d21908ad5f41cb1a220}{%
           family={Chen},
           familyi={C\bibinitperiod},
           given={Shikui},
           giveni={S\bibinitperiod}}}%
        {{hash=4de1896cd656cece01578a2f62d7e3fa}{%
           family={Kang},
           familyi={K\bibinitperiod},
           given={Zhan},
           giveni={Z\bibinitperiod}}}%
        {{hash=84c2102ad54186d7477842421e416280}{%
           family={Suresh},
           familyi={S\bibinitperiod},
           given={Krishnan},
           giveni={K\bibinitperiod}}}%
        {{hash=03b8c567ba4b246b18c6e627f8b7ccad}{%
           family={Takezawa},
           familyi={T\bibinitperiod},
           given={Akihiro},
           giveni={A\bibinitperiod}}}%
        {{hash=ad7517ebe80619f75e6261e4aae4f0e1}{%
           family={Li},
           familyi={L\bibinitperiod},
           given={Lei},
           giveni={L\bibinitperiod}}}%
        {{hash=37d1ff1627b2cd19eff36821490c4f06}{%
           family={Kato},
           familyi={K\bibinitperiod},
           given={Junji},
           giveni={J\bibinitperiod}}}%
        {{hash=3d3538d5ede026ea49154e7f4d3487b8}{%
           family={Tang},
           familyi={T\bibinitperiod},
           given={Jinyuan},
           giveni={J\bibinitperiod}}}%
        {{hash=67857bd3a22d47754bccb05202b9067d}{%
           family={Wang},
           familyi={W\bibinitperiod},
           given={Charlie\bibnamedelimb C.\bibnamedelimi L.},
           giveni={C\bibinitperiod\bibinitdelim C\bibinitperiod\bibinitdelim L\bibinitperiod}}}%
        {{hash=b6821df5befbb13e494f84d9b04a49c2}{%
           family={Cheng},
           familyi={C\bibinitperiod},
           given={Lin},
           giveni={L\bibinitperiod}}}%
        {{hash=4663f0b776b2d78c15119ac4c40e3f54}{%
           family={Liang},
           familyi={L\bibinitperiod},
           given={Xuan},
           giveni={X\bibinitperiod}}}%
        {{hash=3593935608ee9a16d2edcba9b6b826d1}{%
           family={To},
           familyi={T\bibinitperiod},
           given={Albert\bibnamedelima C.},
           giveni={A\bibinitperiod\bibinitdelim C\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{04ae6a321f5cda5acababd7288fe873c}
      \strng{fullhash}{7eb544e132ee6e664e14644d7d4aca92}
      \strng{bibnamehash}{7eb544e132ee6e664e14644d7d4aca92}
      \strng{authorbibnamehash}{7eb544e132ee6e664e14644d7d4aca92}
      \strng{authornamehash}{04ae6a321f5cda5acababd7288fe873c}
      \strng{authorfullhash}{7eb544e132ee6e664e14644d7d4aca92}
      \field{extraname}{1}
      \field{sortinit}{4}
      \field{sortinithash}{9381316451d1b9788675a07e972a12a7}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Manufacturing-oriented topology optimization has been extensively studied the past two decades, in particular for the conventional manufacturing methods, for example, machining and injection molding or casting. Both design and manufacturing engineers have benefited from these efforts because of the close-to-optimal and friendly-to-manufacture design solutions. Recently, additive manufacturing (AM) has received significant attention from both academia and industry. AM is characterized by producing geometrically complex components layer-by-layer, and greatly reduces the geometric complexity restrictions imposed on topology optimization by conventional manufacturing. In other words, AM can make near-full use of the freeform structural evolution of topology optimization. Even so, new rules and restrictions emerge due to the diverse and intricate AM processes, which should be carefully addressed when developing the AM-specific topology optimization algorithms. Therefore, the motivation of this perspective paper is to summarize the state-of-art topology optimization methods for a variety of AM topics. At the same time, this paper also expresses the authors’ perspectives on the challenges and opportunities in these topics. The hope is to inspire both researchers and engineers to meet these challenges with innovative solutions.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{6}
      \field{number}{6}
      \field{title}{Current and future trends in topology optimization for additive manufacturing}
      \field{urlday}{9}
      \field{urlmonth}{6}
      \field{urlyear}{2023}
      \field{volume}{57}
      \field{year}{2018}
      \field{urldateera}{ce}
      \field{pages}{2457\bibrangedash 2483}
      \range{pages}{27}
      \verb{doi}
      \verb 10.1007/s00158-018-1994-3
      \endverb
      \verb{file}
      \verb Submitted Version:D\:\\estragio\\Zotero\\storage\\T7NHFIUU\\Liu et al. - 2018 - Current and future trends in topology optimization.pdf:application/pdf
      \endverb
    \endentry
    \entry{aage_giga-voxel_2017}{article}{}
      \name{author}{4}{}{%
        {{hash=fa5a136030c946f96655797e3220c1bb}{%
           family={Aage},
           familyi={A\bibinitperiod},
           given={Niels},
           giveni={N\bibinitperiod}}}%
        {{hash=bde89e664977164160a3e7e4a1a9ad34}{%
           family={Andreassen},
           familyi={A\bibinitperiod},
           given={Erik},
           giveni={E\bibinitperiod}}}%
        {{hash=7eac115f940766787d974635bdfc7da2}{%
           family={Lazarov},
           familyi={L\bibinitperiod},
           given={Boyan\bibnamedelima S.},
           giveni={B\bibinitperiod\bibinitdelim S\bibinitperiod}}}%
        {{hash=d76f1c09e8d8d06e1b7c3c254efeae1a}{%
           family={Sigmund},
           familyi={S\bibinitperiod},
           given={Ole},
           giveni={O\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{f6e3b7eb5f293c4b66695b6c363a0628}
      \strng{fullhash}{9f21daca9a2b8347bfde3442e353ed75}
      \strng{bibnamehash}{9f21daca9a2b8347bfde3442e353ed75}
      \strng{authorbibnamehash}{9f21daca9a2b8347bfde3442e353ed75}
      \strng{authornamehash}{f6e3b7eb5f293c4b66695b6c363a0628}
      \strng{authorfullhash}{9f21daca9a2b8347bfde3442e353ed75}
      \field{sortinit}{4}
      \field{sortinithash}{9381316451d1b9788675a07e972a12a7}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{journaltitle}{Nature}
      \field{month}{10}
      \field{number}{7674}
      \field{title}{Giga-voxel computational morphogenesis for structural design}
      \field{urlday}{14}
      \field{urlmonth}{10}
      \field{urlyear}{2020}
      \field{volume}{550}
      \field{year}{2017}
      \field{urldateera}{ce}
      \field{pages}{84\bibrangedash 86}
      \range{pages}{3}
      \verb{doi}
      \verb 10.1038/nature23911
      \endverb
    \endentry
    \entry{salazar_de_troya_adaptive_2018}{article}{}
      \name{author}{2}{}{%
        {{hash=8a351e4c0c0f916c2d92392a29a3075d}{%
           family={Salazar\bibnamedelimb de\bibnamedelima Troya},
           familyi={S\bibinitperiod\bibinitdelim d\bibinitperiod\bibinitdelim T\bibinitperiod},
           given={Miguel\bibnamedelima A.},
           giveni={M\bibinitperiod\bibinitdelim A\bibinitperiod}}}%
        {{hash=2dc94736fafc9292d9d5fe6bbacf2606}{%
           family={Tortorelli},
           familyi={T\bibinitperiod},
           given={Daniel\bibnamedelima A.},
           giveni={D\bibinitperiod\bibinitdelim A\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{4a72da76f0c01cf909b46fa54a2008e1}
      \strng{fullhash}{4a72da76f0c01cf909b46fa54a2008e1}
      \strng{bibnamehash}{4a72da76f0c01cf909b46fa54a2008e1}
      \strng{authorbibnamehash}{4a72da76f0c01cf909b46fa54a2008e1}
      \strng{authornamehash}{4a72da76f0c01cf909b46fa54a2008e1}
      \strng{authorfullhash}{4a72da76f0c01cf909b46fa54a2008e1}
      \field{sortinit}{4}
      \field{sortinithash}{9381316451d1b9788675a07e972a12a7}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{We present a topology structural optimization framework with adaptive mesh refinement and stress-constraints. Finite element approximation and geometry representation benefit from such refinement by enabling more accurate stress field predictions and greater resolution of the optimal structural boundaries. We combine a volume fraction filter to impose a minimum design feature size, the RAMP penalization to generate “black-and-white designs” and a RAMP-like stress definition to resolve the “stress singularity problem.” Regions with stress concentrations dominate the optimized design. As such, rigorous simulations are required to accurately approximate the stress field. To achieve this goal, we invoke a threshold operation and mesh refinement during the optimization. We do so in an optimal fashion, by applying adaptive mesh refinement techniques that use error indicators to refine and coarsen the mesh as needed. In this way, we obtain more accurate simulations and greater resolution of the design domain. We present results in two dimensions to demonstrate the efficiency of our method.}
      \field{issn}{1615-147X, 1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{12}
      \field{number}{6}
      \field{title}{Adaptive mesh refinement in stress-constrained topology optimization}
      \field{urlday}{27}
      \field{urlmonth}{6}
      \field{urlyear}{2022}
      \field{volume}{58}
      \field{year}{2018}
      \field{urldateera}{ce}
      \field{pages}{2369\bibrangedash 2386}
      \range{pages}{18}
      \verb{doi}
      \verb 10.1007/s00158-018-2084-2
      \endverb
    \endentry
    \entry{zhang_adaptive_2020}{article}{}
      \name{author}{3}{}{%
        {{hash=c890707eba6aca3d6c5625dcf97b7a71}{%
           family={Zhang},
           familyi={Z\bibinitperiod},
           given={Shanglong},
           giveni={S\bibinitperiod}}}%
        {{hash=f09ef59ab53dfd087886eb88932e0bef}{%
           family={Gain},
           familyi={G\bibinitperiod},
           given={Arun\bibnamedelima L.},
           giveni={A\bibinitperiod\bibinitdelim L\bibinitperiod}}}%
        {{hash=1707fd6c8a20694afeda449ef30c7b5f}{%
           family={Norato},
           familyi={N\bibinitperiod},
           given={Julián\bibnamedelima A.},
           giveni={J\bibinitperiod\bibinitdelim A\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{04504519648214e6599895d54d0513c4}
      \strng{fullhash}{04504519648214e6599895d54d0513c4}
      \strng{bibnamehash}{04504519648214e6599895d54d0513c4}
      \strng{authorbibnamehash}{04504519648214e6599895d54d0513c4}
      \strng{authornamehash}{04504519648214e6599895d54d0513c4}
      \strng{authorfullhash}{04504519648214e6599895d54d0513c4}
      \field{sortinit}{4}
      \field{sortinithash}{9381316451d1b9788675a07e972a12a7}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This work introduces an Adaptive Mesh Refinement (AMR) strategy for the topology optimization of structures made of discrete geometric components using the geometry projection method. Practical structures made of geometric shapes such as bars and plates typically exhibit low volume fractions with respect to the volume of the design region they occupy. To maintain an accurate analysis and to ensure well-defined sensitivities in the geometry projection, it is required that the element size is smaller than the smallest dimension of each component. For low-volume-fraction structures, this leads to finite element meshes with very large numbers of elements. To improve the efficiency of the analysis and optimization, we propose a strategy to adaptively refine the mesh and reduce the number of elements by having a finer mesh on the geometric components, and a coarser mesh away from them. The refinement indicator stems very naturally from the geometry projection and is thus straightforward to implement. We demonstrate the effectiveness of the proposed AMR method by performing topology optimization for the design of minimum-compliance and stress-constrained structures made of bars and plates.}
      \field{issn}{0045-7825}
      \field{journaltitle}{Computer Methods in Applied Mechanics and Engineering}
      \field{month}{6}
      \field{title}{Adaptive mesh refinement for topology optimization with discrete geometric components}
      \field{urlday}{11}
      \field{urlmonth}{4}
      \field{urlyear}{2023}
      \field{volume}{364}
      \field{year}{2020}
      \field{urldateera}{ce}
      \field{pages}{112930}
      \range{pages}{1}
      \verb{doi}
      \verb 10.1016/j.cma.2020.112930
      \endverb
      \verb{file}
      \verb ScienceDirect Full Text PDF:D\:\\estragio\\Zotero\\storage\\BUQXUEQ7\\Zhang et al. - 2020 - Adaptive mesh refinement for topology optimization.pdf:application/pdf
      \endverb
      \keyw{Adaptive mesh refinement,Geometry projection,Topology optimization}
    \endentry
    \entry{sigmund_non-optimality_2016}{article}{}
      \name{author}{3}{}{%
        {{hash=d76f1c09e8d8d06e1b7c3c254efeae1a}{%
           family={Sigmund},
           familyi={S\bibinitperiod},
           given={Ole},
           giveni={O\bibinitperiod}}}%
        {{hash=fa5a136030c946f96655797e3220c1bb}{%
           family={Aage},
           familyi={A\bibinitperiod},
           given={Niels},
           giveni={N\bibinitperiod}}}%
        {{hash=bde89e664977164160a3e7e4a1a9ad34}{%
           family={Andreassen},
           familyi={A\bibinitperiod},
           given={Erik},
           giveni={E\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{d9640e2615b8860628d64015691fc806}
      \strng{fullhash}{d9640e2615b8860628d64015691fc806}
      \strng{bibnamehash}{d9640e2615b8860628d64015691fc806}
      \strng{authorbibnamehash}{d9640e2615b8860628d64015691fc806}
      \strng{authornamehash}{d9640e2615b8860628d64015691fc806}
      \strng{authorfullhash}{d9640e2615b8860628d64015691fc806}
      \field{sortinit}{4}
      \field{sortinithash}{9381316451d1b9788675a07e972a12a7}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{8}
      \field{number}{2}
      \field{title}{On the (non-)optimality of {Michell} structures}
      \field{urlday}{16}
      \field{urlmonth}{6}
      \field{urlyear}{2021}
      \field{volume}{54}
      \field{year}{2016}
      \field{urldateera}{ce}
      \field{pages}{361\bibrangedash 373}
      \range{pages}{13}
      \verb{doi}
      \verb 10.1007/s00158-016-1420-7
      \endverb
    \endentry
    \entry{wein_review_2020}{article}{}
      \name{author}{3}{}{%
        {{hash=8202ffde7576eec540ef243a97355362}{%
           family={Wein},
           familyi={W\bibinitperiod},
           given={Fabian},
           giveni={F\bibinitperiod}}}%
        {{hash=e51e01a7e0ade448f2459963aeb252b1}{%
           family={Dunning},
           familyi={D\bibinitperiod},
           given={Peter\bibnamedelima D.},
           giveni={P\bibinitperiod\bibinitdelim D\bibinitperiod}}}%
        {{hash=1707fd6c8a20694afeda449ef30c7b5f}{%
           family={Norato},
           familyi={N\bibinitperiod},
           given={Julián\bibnamedelima A.},
           giveni={J\bibinitperiod\bibinitdelim A\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{b3c1a6ede5804480161f5efa71f0921a}
      \strng{fullhash}{b3c1a6ede5804480161f5efa71f0921a}
      \strng{bibnamehash}{b3c1a6ede5804480161f5efa71f0921a}
      \strng{authorbibnamehash}{b3c1a6ede5804480161f5efa71f0921a}
      \strng{authornamehash}{b3c1a6ede5804480161f5efa71f0921a}
      \strng{authorfullhash}{b3c1a6ede5804480161f5efa71f0921a}
      \field{sortinit}{4}
      \field{sortinithash}{9381316451d1b9788675a07e972a12a7}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{In this review we identify a new category of methods for implementing and solving structural optimization problems that has emerged over the last 20 years, which we propose to call feature-mapping methods. The two defining aspects of these methods are that the design is parameterized by a high-level geometric description and that features are mapped onto a non-body-fitted mesh for analysis. One motivation for using these methods is to gain better control over the geometry to, for example, facilitate imposing direct constraints on geometric features, while avoiding issues with re-meshing. The review starts by providing some key definitions and then examines the ingredients that these methods use to map geometric features onto a fixed mesh. One of these ingredients corresponds to the mechanism for mapping the geometry of a single feature onto a fixed analysis grid, from which an ersatz material or an immersed-boundary approach is used for the analysis. For the former case, which we refer to as the pseudo-density approach, a test problem is formulated to investigate aspects of the material interpolation, boundary smoothing, and numerical integration. We also review other ingredients of feature-mapping techniques, including approaches for combining features (which are required to perform topology optimization) and methods for imposing a minimum separation distance among features. A literature review of feature-mapping methods is provided for shape optimization, combined feature/free-form optimization, and topology optimization. Finally, we discuss potential future research directions for feature-mapping methods.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{10}
      \field{number}{4}
      \field{title}{A review on feature-mapping methods for structural optimization}
      \field{urlday}{30}
      \field{urlmonth}{5}
      \field{urlyear}{2023}
      \field{volume}{62}
      \field{year}{2020}
      \field{urldateera}{ce}
      \field{pages}{1597\bibrangedash 1638}
      \range{pages}{42}
      \verb{doi}
      \verb 10.1007/s00158-020-02649-6
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\4BKZVZ2Z\\Wein et al. - 2020 - A review on feature-mapping methods for structural.pdf:application/pdf
      \endverb
      \keyw{Feature-mapping,Fixed-grid,High-level design,Structural optimization}
    \endentry
    \entry{guo_doing_2014}{article}{}
      \name{author}{3}{}{%
        {{hash=991f97b5b245ece2a1c7daba022fff1c}{%
           family={Guo},
           familyi={G\bibinitperiod},
           given={Xu},
           giveni={X\bibinitperiod}}}%
        {{hash=787d2f5c7c2d13159e310e5f1f9097d7}{%
           family={Zhang},
           familyi={Z\bibinitperiod},
           given={Weisheng},
           giveni={W\bibinitperiod}}}%
        {{hash=35e299dd461d3bae8ad33bc0a63d8897}{%
           family={Zhong},
           familyi={Z\bibinitperiod},
           given={Wenliang},
           giveni={W\bibinitperiod}}}%
      }
      \strng{namehash}{2603e4af72c8a4074f01154d5c284bac}
      \strng{fullhash}{2603e4af72c8a4074f01154d5c284bac}
      \strng{bibnamehash}{2603e4af72c8a4074f01154d5c284bac}
      \strng{authorbibnamehash}{2603e4af72c8a4074f01154d5c284bac}
      \strng{authornamehash}{2603e4af72c8a4074f01154d5c284bac}
      \strng{authorfullhash}{2603e4af72c8a4074f01154d5c284bac}
      \field{sortinit}{4}
      \field{sortinithash}{9381316451d1b9788675a07e972a12a7}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{issn}{0021-8936}
      \field{journaltitle}{Journal of Applied Mechanics}
      \field{month}{5}
      \field{number}{8}
      \field{title}{Doing {Topology} {Optimization} {Explicitly} and {Geometrically}—{A} {New} {Moving} {Morphable} {Components} {Based} {Framework}}
      \field{urlday}{26}
      \field{urlmonth}{9}
      \field{urlyear}{2021}
      \field{volume}{81}
      \field{year}{2014}
      \field{urldateera}{ce}
      \verb{doi}
      \verb 10.1115/1.4027609
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\IMBT3WAH\\Guo et al. - 2014 - Doing Topology Optimization Explicitly and Geometr.pdf:application/pdf
      \endverb
    \endentry
    \entry{zhang_new_2017}{article}{}
      \name{author}{5}{}{%
        {{hash=787d2f5c7c2d13159e310e5f1f9097d7}{%
           family={Zhang},
           familyi={Z\bibinitperiod},
           given={Weisheng},
           giveni={W\bibinitperiod}}}%
        {{hash=ecfd1d34e9c9c1aec231ae3da61ff906}{%
           family={Li},
           familyi={L\bibinitperiod},
           given={Dong},
           giveni={D\bibinitperiod}}}%
        {{hash=baa10f0a98053417c882dde2ca5129b8}{%
           family={Yuan},
           familyi={Y\bibinitperiod},
           given={Jie},
           giveni={J\bibinitperiod}}}%
        {{hash=1a83f6247e11c8dec8e0143dc90631c8}{%
           family={Song},
           familyi={S\bibinitperiod},
           given={Junfu},
           giveni={J\bibinitperiod}}}%
        {{hash=991f97b5b245ece2a1c7daba022fff1c}{%
           family={Guo},
           familyi={G\bibinitperiod},
           given={Xu},
           giveni={X\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{5af40787aa47b1747130f4d8fd862ba6}
      \strng{fullhash}{d85004df08790691f603a1050aba746d}
      \strng{bibnamehash}{d85004df08790691f603a1050aba746d}
      \strng{authorbibnamehash}{d85004df08790691f603a1050aba746d}
      \strng{authornamehash}{5af40787aa47b1747130f4d8fd862ba6}
      \strng{authorfullhash}{d85004df08790691f603a1050aba746d}
      \field{extraname}{1}
      \field{sortinit}{4}
      \field{sortinithash}{9381316451d1b9788675a07e972a12a7}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{In the present paper, a new method for solving three-dimensional topology optimization problem is proposed. This method is constructed under the so-called moving morphable components based solution framework. The novel aspect of the proposed method is that a set of structural components is introduced to describe the topology of a three-dimensional structure and the optimal structural topology is found by optimizing the layout of the components explicitly. The standard finite element method with ersatz material is adopted for structural response analysis and the shape sensitivity analysis only need to be carried out along the structural boundary. Compared to the existing methods, the description of structural topology is totally independent of the finite element/finite difference resolution in the proposed solution framework and therefore the number of design variables can be reduced substantially. Some widely investigated benchmark examples, in the three-dimensional topology optimization designs, are presented to demonstrate the effectiveness of the proposed approach.}
      \field{issn}{1432-0924}
      \field{journaltitle}{Computational Mechanics}
      \field{month}{4}
      \field{number}{4}
      \field{title}{A new three-dimensional topology optimization method based on moving morphable components ({MMCs})}
      \field{urlday}{11}
      \field{urlmonth}{4}
      \field{urlyear}{2023}
      \field{volume}{59}
      \field{year}{2017}
      \field{urldateera}{ce}
      \field{pages}{647\bibrangedash 665}
      \range{pages}{19}
      \verb{doi}
      \verb 10.1007/s00466-016-1365-0
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\A6DFZE6H\\Zhang et al. - 2017 - A new three-dimensional topology optimization meth.pdf:application/pdf
      \endverb
      \keyw{Moving morphable components method,Shape sensitivity analysis,Three-dimensional problem,Topology optimization}
    \endentry
    \entry{norato_geometry_2015}{article}{}
      \name{author}{3}{}{%
        {{hash=534892dec126d7b0663a8afe62854310}{%
           family={Norato},
           familyi={N\bibinitperiod},
           given={J.\bibnamedelimi A.},
           giveni={J\bibinitperiod\bibinitdelim A\bibinitperiod}}}%
        {{hash=ee8f1ca2bd9ed2e7779e47f9918de209}{%
           family={Bell},
           familyi={B\bibinitperiod},
           given={B.\bibnamedelimi K.},
           giveni={B\bibinitperiod\bibinitdelim K\bibinitperiod}}}%
        {{hash=4caf98a4b6b232023a7a520e17f32e2b}{%
           family={Tortorelli},
           familyi={T\bibinitperiod},
           given={D.\bibnamedelimi A.},
           giveni={D\bibinitperiod\bibinitdelim A\bibinitperiod}}}%
      }
      \strng{namehash}{be6533ad7c5d8a568fe08db6c6c1b70a}
      \strng{fullhash}{be6533ad7c5d8a568fe08db6c6c1b70a}
      \strng{bibnamehash}{be6533ad7c5d8a568fe08db6c6c1b70a}
      \strng{authorbibnamehash}{be6533ad7c5d8a568fe08db6c6c1b70a}
      \strng{authornamehash}{be6533ad7c5d8a568fe08db6c6c1b70a}
      \strng{authorfullhash}{be6533ad7c5d8a568fe08db6c6c1b70a}
      \field{sortinit}{4}
      \field{sortinithash}{9381316451d1b9788675a07e972a12a7}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This article describes a method for the continuum-based topology optimization of structures made of discrete elements. In particular, we examine the optimization of linearly elastic planar structures made of bars of fixed width and semicircular ends. The design space for the optimization consists of the endpoint locations of the bar's medial axes and their out-of-plane thicknesses. To circumvent re-meshing upon design changes, we project the design onto a fixed analysis grid using a differentiable geometry projection that results in a density field indicating the fraction of solid material anywhere in the design space, as in density-based topology optimization methods. The out-of-plane thickness is penalized so that the optimizer is capable of removing bars during the optimization. The differentiability of the projection allows for the computation via the chain rule of design sensitivities of responses of interest, and therefore it allows for the use of robust and efficient gradient-based optimization methods. Notably, this approach makes it easier to fabricate optimal designs by using off-the-shelf stock material. Furthermore, the method considers the case where bars overlap at their joints (i.e. their thicknesses are added at the joint) and when they do not. Finally, our proposed method naturally accommodates the imposition of several fixed length scales. We demonstrate the proposed approach on classical problems of compliance-based topology optimization and identify its benefits as well as research directions to be addressed in the future.}
      \field{issn}{0374-2830}
      \field{journaltitle}{Computer Methods in Applied Mechanics and Engineering}
      \field{month}{8}
      \field{title}{A geometry projection method for continuum-based topology optimization with discrete elements}
      \field{urlday}{26}
      \field{urlmonth}{9}
      \field{urlyear}{2021}
      \field{volume}{293}
      \field{year}{2015}
      \field{urldateera}{ce}
      \field{pages}{306\bibrangedash 327}
      \range{pages}{22}
      \verb{doi}
      \verb 10.1016/j.cma.2015.05.005
      \endverb
      \keyw{Topology optimization,Geometry projection,Manufacturability,Multiscale topology optimization}
    \endentry
    \entry{zhang_geometry_2016}{article}{}
      \name{author}{4}{}{%
        {{hash=c890707eba6aca3d6c5625dcf97b7a71}{%
           family={Zhang},
           familyi={Z\bibinitperiod},
           given={Shanglong},
           giveni={S\bibinitperiod}}}%
        {{hash=1707fd6c8a20694afeda449ef30c7b5f}{%
           family={Norato},
           familyi={N\bibinitperiod},
           given={Julián\bibnamedelima A.},
           giveni={J\bibinitperiod\bibinitdelim A\bibinitperiod}}}%
        {{hash=f09ef59ab53dfd087886eb88932e0bef}{%
           family={Gain},
           familyi={G\bibinitperiod},
           given={Arun\bibnamedelima L.},
           giveni={A\bibinitperiod\bibinitdelim L\bibinitperiod}}}%
        {{hash=3dec456e6ddc0283b692522125bc645e}{%
           family={Lyu},
           familyi={L\bibinitperiod},
           given={Naesung},
           giveni={N\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{57cc589a7c101142881b6dfb18d1a48c}
      \strng{fullhash}{3df4d926d3176235278c6af8661b79fe}
      \strng{bibnamehash}{3df4d926d3176235278c6af8661b79fe}
      \strng{authorbibnamehash}{3df4d926d3176235278c6af8661b79fe}
      \strng{authornamehash}{57cc589a7c101142881b6dfb18d1a48c}
      \strng{authorfullhash}{3df4d926d3176235278c6af8661b79fe}
      \field{extraname}{2}
      \field{sortinit}{4}
      \field{sortinithash}{9381316451d1b9788675a07e972a12a7}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{We introduce a topology optimization method for the stiffness-based design of structures made of plates. Our method renders topologies made distinctly of plates, thereby producing designs that better conform to manufacturing processes tailored to plate structures, such as those that employ stock plates that are cut and joined by various means. To force the structural members to be plates, we employ the geometry projection method to project an analytical description of a set of fixed-thickness plates onto a continuous density field defined over a 3-dimensional, uniform finite element grid for analysis. A size variable is assigned to each plate and penalized so that the optimizer can entirely remove a plate from the design. The proposed method accommodates the case where the plates in the topology are rectangular and solid, and the case where the boundaries of the plates can change and holes can be introduced. The latter case is attained by composition with a free density field. We present examples that demonstrate the effectiveness of our method and discuss future work.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{11}
      \field{number}{5}
      \field{title}{A geometry projection method for the topology optimization of plate structures}
      \field{urlday}{11}
      \field{urlmonth}{4}
      \field{urlyear}{2023}
      \field{volume}{54}
      \field{year}{2016}
      \field{urldateera}{ce}
      \field{pages}{1173\bibrangedash 1190}
      \range{pages}{18}
      \verb{doi}
      \verb 10.1007/s00158-016-1466-6
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\ULXDGZ6W\\Zhang et al. - 2016 - A geometry projection method for the topology opti.pdf:application/pdf
      \endverb
      \keyw{Design for manufacturing,Geometry projection,Plate structures,Topology optimization}
    \endentry
    \entry{coniglio_generalized_2020}{article}{}
      \name{author}{4}{}{%
        {{hash=b075ef4af0301f1a29954bda2e5593a3}{%
           family={Coniglio},
           familyi={C\bibinitperiod},
           given={Simone},
           giveni={S\bibinitperiod}}}%
        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
        {{hash=6644efcab5ec64500fab130cc2c03cd3}{%
           family={Gogu},
           familyi={G\bibinitperiod},
           given={Christian},
           giveni={C\bibinitperiod}}}%
        {{hash=567fded967b2cf76d13efcb2513820a4}{%
           family={Amargier},
           familyi={A\bibinitperiod},
           given={Rémi},
           giveni={R\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{2d7c6898d5ee167ef60da47176eb5e91}
      \strng{fullhash}{fd96b779a6b7d1aae2b4145ba6318a43}
      \strng{bibnamehash}{fd96b779a6b7d1aae2b4145ba6318a43}
      \strng{authorbibnamehash}{fd96b779a6b7d1aae2b4145ba6318a43}
      \strng{authornamehash}{2d7c6898d5ee167ef60da47176eb5e91}
      \strng{authorfullhash}{fd96b779a6b7d1aae2b4145ba6318a43}
      \field{sortinit}{4}
      \field{sortinithash}{9381316451d1b9788675a07e972a12a7}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{shorttitle}
      \field{issn}{1134-3060, 1886-1784}
      \field{journaltitle}{Archives of Computational Methods in Engineering}
      \field{month}{11}
      \field{number}{5}
      \field{shorttitle}{Generalized {Geometry} {Projection}}
      \field{title}{Generalized {Geometry} {Projection}: {A} {Unified} {Approach} for {Geometric} {Feature} {Based} {Topology} {Optimization}}
      \field{urlday}{11}
      \field{urlmonth}{4}
      \field{urlyear}{2023}
      \field{volume}{27}
      \field{year}{2020}
      \field{urldateera}{ce}
      \field{pages}{1573\bibrangedash 1610}
      \range{pages}{38}
      \verb{doi}
      \verb 10.1007/s11831-019-09362-8
      \endverb
      \verb{file}
      \verb Coniglio et al. - 2020 - Generalized Geometry Projection A Unified Approac.pdf:D\:\\estragio\\Zotero\\storage\\PZTD74AT\\Coniglio et al. - 2020 - Generalized Geometry Projection A Unified Approac.pdf:application/pdf
      \endverb
    \endentry
    \entry{kazemi_multi-material_2020}{article}{}
      \name{author}{3}{}{%
        {{hash=7f82a11141a3f8f3c95ba79d47a604df}{%
           family={Kazemi},
           familyi={K\bibinitperiod},
           given={Hesaneh},
           giveni={H\bibinitperiod}}}%
        {{hash=710da74e86502b67cc936f6bac84e46e}{%
           family={Vaziri},
           familyi={V\bibinitperiod},
           given={Ashkan},
           giveni={A\bibinitperiod}}}%
        {{hash=1707fd6c8a20694afeda449ef30c7b5f}{%
           family={Norato},
           familyi={N\bibinitperiod},
           given={Julián\bibnamedelima A.},
           giveni={J\bibinitperiod\bibinitdelim A\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{8480e585be302bfc0f12a11de8368871}
      \strng{fullhash}{8480e585be302bfc0f12a11de8368871}
      \strng{bibnamehash}{8480e585be302bfc0f12a11de8368871}
      \strng{authorbibnamehash}{8480e585be302bfc0f12a11de8368871}
      \strng{authornamehash}{8480e585be302bfc0f12a11de8368871}
      \strng{authorfullhash}{8480e585be302bfc0f12a11de8368871}
      \field{sortinit}{5}
      \field{sortinithash}{20e9b4b0b173788c5dace24730f47d8c}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This work presents a computational method for the design of architected truss lattice materials where each strut can be made of one of a set of available materials. We design the lattices to extremize effective properties. As customary in topology optimization, we design a periodic unit cell of the lattice and obtain the effective properties via numerical homogenization. Each bar is represented as a cylindrical offset surface of a medial axis parameterized by the positions of the endpoints of the medial axis. These parameters are smoothly mapped onto a continuous density field for the primal and sensitivity analysis via the geometry projection method. A size variable per material is ascribed to each bar and penalized as in density-based topology optimization to facilitate the entire removal of bars from the design. During the optimization, we allow bars to be made of a mixture of the available materials. However, to ensure each bar is either exclusively made of one material or removed altogether from the optimal design, we impose optimization constraints that ensure each size variable is 0 or 1, and that at most one material size variable is 1. The proposed material interpolation scheme readily accommodates any number of materials. To obtain lattices with desired material symmetries, we design only a reference region of the unit cell and reflect its geometry projection with respect to the appropriate planes of symmetry. Also, to ensure bars remain whole upon reflection inside the unit cell or with respect to the periodic boundaries, we impose a no-cut constraint on the bars. We demonstrate the efficacy of our method via numerical examples of bulk and shear moduli maximization and Poisson’s ratio minimization for two- and three-material lattices with cubic symmetry.}
      \field{issn}{0045-7825}
      \field{journaltitle}{Computer Methods in Applied Mechanics and Engineering}
      \field{month}{5}
      \field{title}{Multi-material topology optimization of lattice structures using geometry projection}
      \field{urlday}{13}
      \field{urlmonth}{10}
      \field{urlyear}{2020}
      \field{volume}{363}
      \field{year}{2020}
      \field{urldateera}{ce}
      \field{pages}{112895}
      \range{pages}{1}
      \verb{doi}
      \verb 10.1016/j.cma.2020.112895
      \endverb
      \verb{file}
      \verb ScienceDirect Full Text PDF:D\:\\estragio\\Zotero\\storage\\6BCIRJE4\\Kazemi et al. - 2020 - Multi-material topology optimization of lattice st.pdf:application/pdf
      \endverb
      \keyw{Topology optimization,Lattice structures,Multi-material}
    \endentry
    \entry{cheng_relaxed_1997}{article}{}
      \name{author}{2}{}{%
        {{hash=d9b6d97e0b44221d37f9418e38f9d876}{%
           family={Cheng},
           familyi={C\bibinitperiod},
           given={G.\bibnamedelimi D.},
           giveni={G\bibinitperiod\bibinitdelim D\bibinitperiod}}}%
        {{hash=d1cf3b5875e193af09fb48f09d5f8c55}{%
           family={Guo},
           familyi={G\bibinitperiod},
           given={X.},
           giveni={X\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{3686ca50d81342dcd2f88f73b5dbfff8}
      \strng{fullhash}{3686ca50d81342dcd2f88f73b5dbfff8}
      \strng{bibnamehash}{3686ca50d81342dcd2f88f73b5dbfff8}
      \strng{authorbibnamehash}{3686ca50d81342dcd2f88f73b5dbfff8}
      \strng{authornamehash}{3686ca50d81342dcd2f88f73b5dbfff8}
      \strng{authorfullhash}{3686ca50d81342dcd2f88f73b5dbfff8}
      \field{sortinit}{5}
      \field{sortinithash}{20e9b4b0b173788c5dace24730f47d8c}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This paper presents a so-called $\varepsilon$-relaxed approach for structural topology optimization problems of discrete structures. The distinctive feature of this new approach is that unlike the typical treatment of topology optimization problems based on the ground structure approach, we eliminate the singular optima from the problem formulation and thus unify the sizing and topology optimization within the same framework. As a result, numerical methods developed for sizing optimization problems can be applied directly to the solution of topology optimization problems without any further treatment. The application of the proposed approach and its effectiveness are illustrated with several numerical examples.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural optimization}
      \field{month}{6}
      \field{number}{4}
      \field{title}{$\varepsilon$-relaxed approach in structural topology optimization}
      \field{urlday}{28}
      \field{urlmonth}{2}
      \field{urlyear}{2023}
      \field{volume}{13}
      \field{year}{1997}
      \field{urldateera}{ce}
      \field{pages}{258\bibrangedash 266}
      \range{pages}{9}
      \verb{doi}
      \verb 10.1007/BF01197454
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\DLL8FCBH\\Cheng and Guo - 1997 - e-relaxed approach in structural topology optimiza.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/BF01197454
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/BF01197454
      \endverb
      \keyw{Civil Engineer,Topology Optimization,Distinctive Feature,Ground Structure,Problem Formulation}
    \endentry
    \entry{rozvany_design-dependent_2001}{article}{}
      \name{author}{1}{}{%
        {{hash=2dd717bb9ecafd6aa2723e522b7aa056}{%
           family={Rozvany},
           familyi={R\bibinitperiod},
           given={G.I.N.},
           giveni={G\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{2dd717bb9ecafd6aa2723e522b7aa056}
      \strng{fullhash}{2dd717bb9ecafd6aa2723e522b7aa056}
      \strng{bibnamehash}{2dd717bb9ecafd6aa2723e522b7aa056}
      \strng{authorbibnamehash}{2dd717bb9ecafd6aa2723e522b7aa056}
      \strng{authornamehash}{2dd717bb9ecafd6aa2723e522b7aa056}
      \strng{authorfullhash}{2dd717bb9ecafd6aa2723e522b7aa056}
      \field{extraname}{2}
      \field{sortinit}{5}
      \field{sortinithash}{20e9b4b0b173788c5dace24730f47d8c}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{A historical perspective of design-dependent constraints and singular topologies is presented and their theoretical background as well as fundamental features discussed, together with methods for treating computational difficulties. This note contains some rather surprising new facts about singular topologies and it is hoped that it will provide both a comprehensive review and additional insights.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{4}
      \field{number}{2}
      \field{title}{On design-dependent constraints and singular topologies}
      \field{urlday}{7}
      \field{urlmonth}{4}
      \field{urlyear}{2021}
      \field{volume}{21}
      \field{year}{2001}
      \field{urldateera}{ce}
      \field{pages}{164\bibrangedash 172}
      \range{pages}{9}
      \verb{doi}
      \verb 10.1007/s001580050181
      \endverb
    \endentry
    \entry{gao_topology_2015}{article}{}
      \name{author}{2}{}{%
        {{hash=67e6bf1dac33f72e25c55728171ad957}{%
           family={Gao},
           familyi={G\bibinitperiod},
           given={Xingjun},
           giveni={X\bibinitperiod}}}%
        {{hash=e2f96a4ea2aa5cccd5b3976bbe203345}{%
           family={Ma},
           familyi={M\bibinitperiod},
           given={Haitao},
           giveni={H\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{f9420a019eafaf72f288b09d346d3254}
      \strng{fullhash}{f9420a019eafaf72f288b09d346d3254}
      \strng{bibnamehash}{f9420a019eafaf72f288b09d346d3254}
      \strng{authorbibnamehash}{f9420a019eafaf72f288b09d346d3254}
      \strng{authornamehash}{f9420a019eafaf72f288b09d346d3254}
      \strng{authorfullhash}{f9420a019eafaf72f288b09d346d3254}
      \field{sortinit}{5}
      \field{sortinithash}{20e9b4b0b173788c5dace24730f47d8c}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This paper presents a study on topology optimization of continuum structures under buckling constraints. New algorithms are developed for minimization of structural compliance considering constraints on volume and buckling load factors. The SIMP (Solid Isotropic Material with Penalization) material model is employed and nodal relative densities are used as topology design variables. A new approach based on the eigenvalue shift and pseudo mode identiﬁcation is proposed for eliminating the effect of pseudo buckling modes. Two-phase optimization algorithms are also proposed for achieving better optimized designs. Numerical examples are presented to illustrate the effectiveness of the new methods.}
      \field{issn}{00457949}
      \field{journaltitle}{Computers \&amp; Structures}
      \field{month}{9}
      \field{title}{Topology optimization of continuum structures under buckling constraints}
      \field{urlday}{28}
      \field{urlmonth}{2}
      \field{urlyear}{2023}
      \field{volume}{157}
      \field{year}{2015}
      \field{urldateera}{ce}
      \field{pages}{142\bibrangedash 152}
      \range{pages}{11}
      \verb{doi}
      \verb 10.1016/j.compstruc.2015.05.020
      \endverb
      \verb{file}
      \verb Gao and Ma - 2015 - Topology optimization of continuum structures unde.pdf:D\:\\estragio\\Zotero\\storage\\ZGUAG4BH\\Gao and Ma - 2015 - Topology optimization of continuum structures unde.pdf:application/pdf
      \endverb
    \endentry
    \entry{he_python_2019}{article}{}
      \name{author}{3}{}{%
        {{hash=b5cf365122e2b66e22018811665e9437}{%
           family={He},
           familyi={H\bibinitperiod},
           given={Linwei},
           giveni={L\bibinitperiod}}}%
        {{hash=c187b1075ee4dfc79e5c9154527f9040}{%
           family={Gilbert},
           familyi={G\bibinitperiod},
           given={Matthew},
           giveni={M\bibinitperiod}}}%
        {{hash=f28364b04fc73aeaa763895071b0b476}{%
           family={Song},
           familyi={S\bibinitperiod},
           given={Xingyi},
           giveni={X\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{261c151f79c5dbe520fd2c0607589c0c}
      \strng{fullhash}{261c151f79c5dbe520fd2c0607589c0c}
      \strng{bibnamehash}{261c151f79c5dbe520fd2c0607589c0c}
      \strng{authorbibnamehash}{261c151f79c5dbe520fd2c0607589c0c}
      \strng{authornamehash}{261c151f79c5dbe520fd2c0607589c0c}
      \strng{authorfullhash}{261c151f79c5dbe520fd2c0607589c0c}
      \field{sortinit}{5}
      \field{sortinithash}{20e9b4b0b173788c5dace24730f47d8c}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{8}
      \field{number}{2}
      \field{title}{A {Python} script for adaptive layout optimization of trusses}
      \field{urlday}{15}
      \field{urlmonth}{12}
      \field{urlyear}{2020}
      \field{volume}{60}
      \field{year}{2019}
      \field{urldateera}{ce}
      \field{pages}{835\bibrangedash 847}
      \range{pages}{13}
      \verb{doi}
      \verb 10.1007/s00158-019-02226-6
      \endverb
    \endentry
    \entry{kirsch_optimal_1989}{article}{}
      \name{author}{1}{}{%
        {{hash=effe3f1738f379672a1034006b971c63}{%
           family={Kirsch},
           familyi={K\bibinitperiod},
           given={Uri},
           giveni={U\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{effe3f1738f379672a1034006b971c63}
      \strng{fullhash}{effe3f1738f379672a1034006b971c63}
      \strng{bibnamehash}{effe3f1738f379672a1034006b971c63}
      \strng{authorbibnamehash}{effe3f1738f379672a1034006b971c63}
      \strng{authornamehash}{effe3f1738f379672a1034006b971c63}
      \strng{authorfullhash}{effe3f1738f379672a1034006b971c63}
      \field{extraname}{1}
      \field{sortinit}{5}
      \field{sortinithash}{20e9b4b0b173788c5dace24730f47d8c}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{The topology of truss structures is optimized by assuming zero lower bounds on cross-sections. It is shown that the optimal topology might correspond to a singular solution even for simple structures. Assuming the force method analysis formulation, the problem can be stated in a linear programming (LP) form under certain assumptions. It is then possible to derive analytically some conditions related to optimal topologies. In addition, the difficulty of singular optimal solutions is eliminated. The effect of compatibility conditions on optimal topologies is studied. It is shown that for particular geometries or loading conditions, where some element forces change from tension to compression or vice versa, the optimal topology might represent an unstable structure. Analytical conditions are derived to obtain geometries of multiple optimal topologies. Part of the latter solutions usually represent statically determinate structures. It is shown that a transition in the set of active constraints at the optimum occurs at these particular geometries. The phenomena presented in this study might lead to a better understanding of some properties associated with optimum structural topologies, and to improved design procedures.}
      \field{issn}{0045-7825}
      \field{journaltitle}{Computer Methods in Applied Mechanics and Engineering}
      \field{month}{1}
      \field{number}{1}
      \field{title}{Optimal topologies of truss structures}
      \field{urlday}{21}
      \field{urlmonth}{3}
      \field{urlyear}{2021}
      \field{volume}{72}
      \field{year}{1989}
      \field{urldateera}{ce}
      \field{pages}{15\bibrangedash 28}
      \range{pages}{14}
      \verb{doi}
      \verb 10.1016/0045-7825(89)90119-9
      \endverb
      \verb{file}
      \verb ScienceDirect Full Text PDF:D\:\\estragio\\Zotero\\storage\\ECRUX6ET\\Kirsch - 1989 - Optimal topologies of truss structures.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://www.sciencedirect.com/science/article/pii/0045782589901199
      \endverb
      \verb{url}
      \verb https://www.sciencedirect.com/science/article/pii/0045782589901199
      \endverb
    \endentry
    \entry{rozvany_layout_1995}{article}{}
      \name{author}{3}{}{%
        {{hash=2dd717bb9ecafd6aa2723e522b7aa056}{%
           family={Rozvany},
           familyi={R\bibinitperiod},
           given={G.\bibnamedelimi I.\bibnamedelimi N.},
           giveni={G\bibinitperiod\bibinitdelim I\bibinitperiod\bibinitdelim N\bibinitperiod}}}%
        {{hash=193e92bb57a8aeb7a8a809f2e4f7221f}{%
           family={Bends{ø}e},
           familyi={B\bibinitperiod},
           given={M.\bibnamedelimi P.},
           giveni={M\bibinitperiod\bibinitdelim P\bibinitperiod}}}%
        {{hash=5a9612ff262f953a44ab4d8f06da5d1e}{%
           family={Kirsch},
           familyi={K\bibinitperiod},
           given={U.},
           giveni={U\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{254007297bad5fae7e717cce259e5aa5}
      \strng{fullhash}{254007297bad5fae7e717cce259e5aa5}
      \strng{bibnamehash}{254007297bad5fae7e717cce259e5aa5}
      \strng{authorbibnamehash}{254007297bad5fae7e717cce259e5aa5}
      \strng{authornamehash}{254007297bad5fae7e717cce259e5aa5}
      \strng{authorfullhash}{254007297bad5fae7e717cce259e5aa5}
      \field{sortinit}{5}
      \field{sortinithash}{20e9b4b0b173788c5dace24730f47d8c}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Layout or topology optimization deals with the selection of the best configuration for structural systems and constitutes one of the newest and most rapidly expanding fields of structural design, although some of its basic concepts were established almost a century ago. While mathematically and computationally perhaps the most challenging, it is also economically the most rewarding design task. This review article is based on a unified formulation and covers in detail both exact, analytical methods and approximate, discretized methods of layout optimization. Although discretized solutions are unavoidable for most practical, real-world problems, only explicit analytical solutions provide (i) a reliable means for checking the validity and convergence of numerical methods and (ii) a basis for assessing the relative economy of other designs. Moreover, some of the most efficient new numerical methods of layout optimization are iterative versions of analytical methods. Particularly promising are recent extensions of the exact layout theory to multiload, multipurpose elastic systems.}
      \field{issn}{0003-6900, 2379-0407}
      \field{journaltitle}{Applied Mechanics Reviews}
      \field{month}{2}
      \field{number}{2}
      \field{title}{Layout {Optimization} of {Structures}}
      \field{urlday}{30}
      \field{urlmonth}{3}
      \field{urlyear}{2021}
      \field{volume}{48}
      \field{year}{1995}
      \field{urldateera}{ce}
      \field{pages}{41\bibrangedash 119}
      \range{pages}{79}
      \verb{doi}
      \verb 10.1115/1.3005097
      \endverb
    \endentry
    \entry{kirsch_optimal_1980}{article}{}
      \name{author}{1}{}{%
        {{hash=effe3f1738f379672a1034006b971c63}{%
           family={Kirsch},
           familyi={K\bibinitperiod},
           given={Uri},
           giveni={U\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{effe3f1738f379672a1034006b971c63}
      \strng{fullhash}{effe3f1738f379672a1034006b971c63}
      \strng{bibnamehash}{effe3f1738f379672a1034006b971c63}
      \strng{authorbibnamehash}{effe3f1738f379672a1034006b971c63}
      \strng{authornamehash}{effe3f1738f379672a1034006b971c63}
      \strng{authorfullhash}{effe3f1738f379672a1034006b971c63}
      \field{extraname}{2}
      \field{sortinit}{5}
      \field{sortinithash}{20e9b4b0b173788c5dace24730f47d8c}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Optimal design of elastic trusses is formulated as an approximate linear programming problem. Using the force method of analysis, the redundant forces are expressed in linearized terms of the design variables. The solution of the resulting linear programming problem can be viewed as an exact optimum for a truss with different displacements corresponding to the unknown redundants. The latter displacements, computed directly from the linear programming solution, indicate the degree of not satisfying the compatibility conditions. This information can be used to introduce imaginary displacements in subsequent iteration cycles. An iterative procedure of solution is proposed in which both the design and the imaginary displacements are modified until the compatible optimal solution is reached. Each iteration cycle requires the solution of a linear programming problem. The proposed procedure provides more flexibility in the solution process than the usual algorithms based on a sequence of linear programs and may improve the convergence. Numerical examples illustrate the application of this procedure in optimal design of simple trusses.}
      \field{issn}{0045-7949}
      \field{journaltitle}{Computers \&amp; Structures}
      \field{month}{7}
      \field{number}{1}
      \field{title}{Optimal design of trusses by approximate compatibility}
      \field{urlday}{22}
      \field{urlmonth}{10}
      \field{urlyear}{2021}
      \field{volume}{12}
      \field{year}{1980}
      \field{urldateera}{ce}
      \field{pages}{93\bibrangedash 98}
      \range{pages}{6}
      \verb{doi}
      \verb 10.1016/0045-7949(80)90097-8
      \endverb
      \verb{file}
      \verb ScienceDirect Full Text PDF:D\:\\estragio\\Zotero\\storage\\GKBN3PGB\\Kirsch - 1980 - Optimal design of trusses by approximate compatibi.pdf:application/pdf
      \endverb
    \endentry
    \entry{cheng_aspects_1995}{article}{}
      \name{author}{1}{}{%
        {{hash=112f6df29c44bf60dd57629dca6325c7}{%
           family={Cheng},
           familyi={C\bibinitperiod},
           given={G.},
           giveni={G\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{112f6df29c44bf60dd57629dca6325c7}
      \strng{fullhash}{112f6df29c44bf60dd57629dca6325c7}
      \strng{bibnamehash}{112f6df29c44bf60dd57629dca6325c7}
      \strng{authorbibnamehash}{112f6df29c44bf60dd57629dca6325c7}
      \strng{authornamehash}{112f6df29c44bf60dd57629dca6325c7}
      \strng{authorfullhash}{112f6df29c44bf60dd57629dca6325c7}
      \field{sortinit}{5}
      \field{sortinithash}{20e9b4b0b173788c5dace24730f47d8c}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{issn}{0934-4373, 1615-1488}
      \field{journaltitle}{Structural Optimization}
      \field{month}{12}
      \field{number}{3-4}
      \field{title}{Some aspects of truss topology optimization}
      \field{urlday}{22}
      \field{urlmonth}{2}
      \field{urlyear}{2022}
      \field{volume}{10}
      \field{year}{1995}
      \field{urldateera}{ce}
      \field{pages}{173\bibrangedash 179}
      \range{pages}{7}
      \verb{doi}
      \verb 10.1007/BF01742589
      \endverb
    \endentry
    \entry{achtziger_local_1999}{article}{}
      \name{author}{1}{}{%
        {{hash=453fe478aaef8cda186519d42b21f6c3}{%
           family={Achtziger},
           familyi={A\bibinitperiod},
           given={W.},
           giveni={W\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{453fe478aaef8cda186519d42b21f6c3}
      \strng{fullhash}{453fe478aaef8cda186519d42b21f6c3}
      \strng{bibnamehash}{453fe478aaef8cda186519d42b21f6c3}
      \strng{authorbibnamehash}{453fe478aaef8cda186519d42b21f6c3}
      \strng{authornamehash}{453fe478aaef8cda186519d42b21f6c3}
      \strng{authorfullhash}{453fe478aaef8cda186519d42b21f6c3}
      \field{extraname}{1}
      \field{sortinit}{5}
      \field{sortinithash}{20e9b4b0b173788c5dace24730f47d8c}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{shorttitle}
      \field{issn}{0934-4373, 1615-1488}
      \field{journaltitle}{Structural Optimization}
      \field{month}{12}
      \field{number}{4}
      \field{shorttitle}{Local stability of trusses in the context of topology optimization {Part} {I}}
      \field{title}{Local stability of trusses in the context of topology optimization {Part} {I}: {Exact} modelling}
      \field{urlday}{14}
      \field{urlmonth}{10}
      \field{urlyear}{2021}
      \field{volume}{17}
      \field{year}{1999}
      \field{urldateera}{ce}
      \field{pages}{235\bibrangedash 246}
      \range{pages}{12}
      \verb{doi}
      \verb 10.1007/BF01206999
      \endverb
    \endentry
    \entry{maxwell_ireciprocal_1870}{article}{}
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        {{hash=d35afaae60ddd0f2a8d5a9fa24f26c50}{%
           family={Maxwell},
           familyi={M\bibinitperiod},
           given={J.\bibnamedelimi Clerk},
           giveni={J\bibinitperiod\bibinitdelim C\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{d35afaae60ddd0f2a8d5a9fa24f26c50}
      \strng{fullhash}{d35afaae60ddd0f2a8d5a9fa24f26c50}
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      \strng{authorfullhash}{d35afaae60ddd0f2a8d5a9fa24f26c50}
      \field{sortinit}{5}
      \field{sortinithash}{20e9b4b0b173788c5dace24730f47d8c}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{issn}{2053-5945, 0080-4568}
      \field{journaltitle}{Earth and Environmental Science Transactions of The Royal Society of Edinburgh}
      \field{number}{1}
      \field{title}{I.—{On} {Reciprocal} {Figures}, {Frames}, and {Diagrams} of {Forces}}
      \field{urlday}{2}
      \field{urlmonth}{9}
      \field{urlyear}{2021}
      \field{volume}{26}
      \field{year}{1870}
      \field{urldateera}{ce}
      \field{pages}{1\bibrangedash 40}
      \range{pages}{40}
      \verb{doi}
      \verb 10.1017/S0080456800026351
      \endverb
      \verb{urlraw}
      \verb https://www.cambridge.org/core/journals/earth-and-environmental-science-transactions-of-royal-society-of-edinburgh/article/ion-reciprocal-figures-frames-and-diagrams-of-forces/C0E7FD99D84DCE62BE39737575E6C347
      \endverb
      \verb{url}
      \verb https://www.cambridge.org/core/journals/earth-and-environmental-science-transactions-of-royal-society-of-edinburgh/article/ion-reciprocal-figures-frames-and-diagrams-of-forces/C0E7FD99D84DCE62BE39737575E6C347
      \endverb
    \endentry
    \entry{michell_limits_1904}{article}{}
      \name{author}{1}{}{%
        {{hash=e4a2620c42989a0b49132225b112c80f}{%
           family={Michell},
           familyi={M\bibinitperiod},
           given={A.\bibnamedelimi G.\bibnamedelimi M.},
           giveni={A\bibinitperiod\bibinitdelim G\bibinitperiod\bibinitdelim M\bibinitperiod}}}%
      }
      \strng{namehash}{e4a2620c42989a0b49132225b112c80f}
      \strng{fullhash}{e4a2620c42989a0b49132225b112c80f}
      \strng{bibnamehash}{e4a2620c42989a0b49132225b112c80f}
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      \strng{authornamehash}{e4a2620c42989a0b49132225b112c80f}
      \strng{authorfullhash}{e4a2620c42989a0b49132225b112c80f}
      \field{sortinit}{5}
      \field{sortinithash}{20e9b4b0b173788c5dace24730f47d8c}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{issn}{1941-5982}
      \field{journaltitle}{The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science}
      \field{month}{11}
      \field{number}{47}
      \field{title}{The limits of economy of material in frame-structures}
      \field{urlday}{14}
      \field{urlmonth}{1}
      \field{urlyear}{2021}
      \field{volume}{8}
      \field{year}{1904}
      \field{urldateera}{ce}
      \field{pages}{589\bibrangedash 597}
      \range{pages}{9}
      \verb{doi}
      \verb 10.1080/14786440409463229
      \endverb
      \verb{file}
      \verb Submitted Version:D\:\\estragio\\Zotero\\storage\\85BGL7CV\\M.C.E - 1904 - LVIII. The limits of economy of material in frame-.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1080/14786440409463229
      \endverb
      \verb{url}
      \verb https://doi.org/10.1080/14786440409463229
      \endverb
    \endentry
    \entry{gilbert_layout_2003}{article}{}
      \name{author}{2}{}{%
        {{hash=c187b1075ee4dfc79e5c9154527f9040}{%
           family={Gilbert},
           familyi={G\bibinitperiod},
           given={Matthew},
           giveni={M\bibinitperiod}}}%
        {{hash=b36ef59d73d5b8a68c1b2dec068985de}{%
           family={Tyas},
           familyi={T\bibinitperiod},
           given={Andrew},
           giveni={A\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{c442cfa8092c128645fd5a3cd09325ed}
      \strng{fullhash}{c442cfa8092c128645fd5a3cd09325ed}
      \strng{bibnamehash}{c442cfa8092c128645fd5a3cd09325ed}
      \strng{authorbibnamehash}{c442cfa8092c128645fd5a3cd09325ed}
      \strng{authornamehash}{c442cfa8092c128645fd5a3cd09325ed}
      \strng{authorfullhash}{c442cfa8092c128645fd5a3cd09325ed}
      \field{sortinit}{5}
      \field{sortinithash}{20e9b4b0b173788c5dace24730f47d8c}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{journaltitle}{Engineering Computations}
      \field{month}{12}
      \field{number}{8}
      \field{title}{Layout optimization of large‐scale pin‐jointed frames}
      \field{urlday}{9}
      \field{urlmonth}{12}
      \field{urlyear}{2020}
      \field{volume}{20}
      \field{year}{2003}
      \field{urldateera}{ce}
      \field{pages}{1044\bibrangedash 1064}
      \range{pages}{21}
      \verb{doi}
      \verb 10.1108/02644400310503017
      \endverb
    \endentry
    \entry{pedersen_optimal_1973}{article}{}
      \name{author}{1}{}{%
        {{hash=4e4b2e4c84bf20045bcf9599673e53c6}{%
           family={Pedersen},
           familyi={P\bibinitperiod},
           given={Pauli},
           giveni={P\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {EN}%
      }
      \strng{namehash}{4e4b2e4c84bf20045bcf9599673e53c6}
      \strng{fullhash}{4e4b2e4c84bf20045bcf9599673e53c6}
      \strng{bibnamehash}{4e4b2e4c84bf20045bcf9599673e53c6}
      \strng{authorbibnamehash}{4e4b2e4c84bf20045bcf9599673e53c6}
      \strng{authornamehash}{4e4b2e4c84bf20045bcf9599673e53c6}
      \strng{authorfullhash}{4e4b2e4c84bf20045bcf9599673e53c6}
      \field{sortinit}{6}
      \field{sortinithash}{b33bc299efb3c36abec520a4c896a66d}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{An iterative procedure for determining the joint positions corresponding to a minimum mass space truss is presented. Displacement constraints and nonconstant stress constraints (stability) are taken into account. The truss is presumed to carry consecutively a large number of different systems of forces. The iteration includes a sequence of linear programming problems (SLP, with move-limits), and for each of these problems only the nearby constraints are considered. Analytical expressions are given for the gradients describing the linear problems. A dome is optimized using different constraints.}
      \field{journaltitle}{Journal of the Structural Division}
      \field{month}{12}
      \field{number}{12}
      \field{title}{Optimal {Joint} {Positions} for {Space} {Trusses}}
      \field{urlday}{28}
      \field{urlmonth}{2}
      \field{urlyear}{2023}
      \field{volume}{99}
      \field{year}{1973}
      \field{urldateera}{ce}
      \field{pages}{2459\bibrangedash 2476}
      \range{pages}{18}
      \verb{doi}
      \verb 10.1061/JSDEAG.0003669
      \endverb
      \verb{urlraw}
      \verb https://ascelibrary.org/doi/10.1061/JSDEAG.0003669
      \endverb
      \verb{url}
      \verb https://ascelibrary.org/doi/10.1061/JSDEAG.0003669
      \endverb
    \endentry
    \entry{achtziger_simultaneous_2007}{article}{}
      \name{author}{1}{}{%
        {{hash=be14cd2ace252d6ec45e16ea92c74e0f}{%
           family={Achtziger},
           familyi={A\bibinitperiod},
           given={Wolfgang},
           giveni={W\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{be14cd2ace252d6ec45e16ea92c74e0f}
      \strng{fullhash}{be14cd2ace252d6ec45e16ea92c74e0f}
      \strng{bibnamehash}{be14cd2ace252d6ec45e16ea92c74e0f}
      \strng{authorbibnamehash}{be14cd2ace252d6ec45e16ea92c74e0f}
      \strng{authornamehash}{be14cd2ace252d6ec45e16ea92c74e0f}
      \strng{authorfullhash}{be14cd2ace252d6ec45e16ea92c74e0f}
      \field{extraname}{2}
      \field{sortinit}{6}
      \field{sortinithash}{b33bc299efb3c36abec520a4c896a66d}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{The paper addresses the classical problem of optimal truss design where cross-sectional areas and the positions of joints are simultaneously optimized. Se-veral approaches are discussed from a general point of view. In particular, we focus on the difference between simultaneous and alternating optimization of geometry and topology. We recall a rigorously mathematical approach based on the implicit programming technique which considers the classical single load minimum compliance problem subject to a volume constraint. This approach is refined leading to three new problem formulations which can be treated by methods of Mathematical Programming. In particular, these formulations cover the effect of melting end nodes, i.e., vanishing potential bars due to changes in the geometry. In one of these new problem formulations, the objective function is a polynomial of degree three and the constraints are bilinear or just sign constraints. Because heuristics is avoided, certain optimality properties can be proven for resulting structures. The paper closes with two numerical test examples.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{4}
      \field{number}{4}
      \field{title}{On simultaneous optimization of truss geometry and topology}
      \field{urlday}{29}
      \field{urlmonth}{10}
      \field{urlyear}{2021}
      \field{volume}{33}
      \field{year}{2007}
      \field{urldateera}{ce}
      \field{pages}{285\bibrangedash 304}
      \range{pages}{20}
      \verb{doi}
      \verb 10.1007/s00158-006-0092-0
      \endverb
      \verb{file}
      \verb Springer Full Text PDF:D\:\\estragio\\Zotero\\storage\\EWLSUFX6\\Achtziger - 2007 - On simultaneous optimization of truss geometry and.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/s00158-006-0092-0
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s00158-006-0092-0
      \endverb
    \endentry
    \entry{descamps_lower-bound_2013}{article}{}
      \name{author}{2}{}{%
        {{hash=a867726c6de8cbbc5b38459f1179c726}{%
           family={Descamps},
           familyi={D\bibinitperiod},
           given={Benoît},
           giveni={B\bibinitperiod}}}%
        {{hash=1462acafce6f777c7120022f3f81fcff}{%
           family={Filomeno\bibnamedelima Coelho},
           familyi={F\bibinitperiod\bibinitdelim C\bibinitperiod},
           given={Rajan},
           giveni={R\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{b9c8eaf45dc9f4fd7d05c4f4af3eeb22}
      \strng{fullhash}{b9c8eaf45dc9f4fd7d05c4f4af3eeb22}
      \strng{bibnamehash}{b9c8eaf45dc9f4fd7d05c4f4af3eeb22}
      \strng{authorbibnamehash}{b9c8eaf45dc9f4fd7d05c4f4af3eeb22}
      \strng{authornamehash}{b9c8eaf45dc9f4fd7d05c4f4af3eeb22}
      \strng{authorfullhash}{b9c8eaf45dc9f4fd7d05c4f4af3eeb22}
      \field{extraname}{1}
      \field{sortinit}{6}
      \field{sortinithash}{b33bc299efb3c36abec520a4c896a66d}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{In this contribution, we propose an effective formulation to address the stress-based minimum volume problem of truss structures. Starting from the lower-bound formulation in topology optimization, the problem is further expanded to geometry optimization and multiple loading scenarios, and systematically reformulated to alleviate numerical difficulties related to the melting node effect and stress singularities. The subsequent simultaneous analysis and design (SAND) formulation is well suited for a direct treatment by introducing a barrier function. Using exact second derivatives, this difficult class of problem is solved by sequential quadratic programming with trust regions. These building blocks result into an integrated design process. Two examples–including a large-scale application–illustrate the robustness of the proposed formulation.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{7}
      \field{number}{1}
      \field{title}{A lower-bound formulation for the geometry and topology optimization of truss structures under multiple loading}
      \field{urlday}{29}
      \field{urlmonth}{10}
      \field{urlyear}{2021}
      \field{volume}{48}
      \field{year}{2013}
      \field{urldateera}{ce}
      \field{pages}{49\bibrangedash 58}
      \range{pages}{10}
      \verb{doi}
      \verb 10.1007/s00158-012-0876-3
      \endverb
      \verb{file}
      \verb Springer Full Text PDF:D\:\\estragio\\Zotero\\storage\\9QV3L4QL\\Descamps and Filomeno Coelho - 2013 - A lower-bound formulation for the geometry and top.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/s00158-012-0876-3
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s00158-012-0876-3
      \endverb
    \endentry
    \entry{he_rationalization_2015}{article}{}
      \name{author}{2}{}{%
        {{hash=972234bc6cedbf8c53e9cdde1d02f16a}{%
           family={He},
           familyi={H\bibinitperiod},
           given={L.},
           giveni={L\bibinitperiod}}}%
        {{hash=9d7322a84f0f9b0b90e0e094b8c4ccdd}{%
           family={Gilbert},
           familyi={G\bibinitperiod},
           given={M.},
           giveni={M\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{279017e85b0d418bd9ca1bcf3c49aabb}
      \strng{fullhash}{279017e85b0d418bd9ca1bcf3c49aabb}
      \strng{bibnamehash}{279017e85b0d418bd9ca1bcf3c49aabb}
      \strng{authorbibnamehash}{279017e85b0d418bd9ca1bcf3c49aabb}
      \strng{authornamehash}{279017e85b0d418bd9ca1bcf3c49aabb}
      \strng{authorfullhash}{279017e85b0d418bd9ca1bcf3c49aabb}
      \field{sortinit}{6}
      \field{sortinithash}{b33bc299efb3c36abec520a4c896a66d}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Numerical layout optimization provides a computationally efﬁcient and generally applicable means of identifying the optimal arrangement of bars in a truss. When the plastic layout optimization formulation is used, a wide variety of problem types can be solved using linear programming. However, the solutions obtained are frequently quite complex, particularly when ﬁne numerical discretizations are employed. To address this, the efﬁcacy of two rationalization techniques are explored in this paper: (i) introduction of ‘joint lengths’, and (ii) application of geometry optimization. In the former case this involves the use of a modiﬁed layout optimization formulation, which remains linear, whilst in the latter case a non-linear optimization post-processing step, involving adjusting the locations of nodes in the layout optimized solution, is undertaken. The two rationalization techniques are applied to example problems involving both point and distributed loads, self-weight and multiple load cases. It is demonstrated that the introduction of joint lengths reduces structural complexity at negligible computational cost, though generally leads to increased volumes. Conversely, the use of geometry optimization carries a computational cost but is effective in reducing both structural complexity and the computed volume.}
      \field{issn}{1615-147X, 1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{10}
      \field{number}{4}
      \field{title}{Rationalization of trusses generated via layout optimization}
      \field{urlday}{11}
      \field{urlmonth}{1}
      \field{urlyear}{2021}
      \field{volume}{52}
      \field{year}{2015}
      \field{urldateera}{ce}
      \field{pages}{677\bibrangedash 694}
      \range{pages}{18}
      \verb{doi}
      \verb 10.1007/s00158-015-1260-x
      \endverb
      \verb{file}
      \verb SMOGeometryOptimization_Part2.pdf:D\:\\estragio\\Zotero\\storage\\Q2MPHQNA\\SMOGeometryOptimization_Part2.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb http://link.springer.com/10.1007/s00158-015-1260-x
      \endverb
      \verb{url}
      \verb http://link.springer.com/10.1007/s00158-015-1260-x
      \endverb
    \endentry
    \entry{lu_reducing_2023}{article}{}
      \name{author}{2}{}{%
        {{hash=ff82f455a06b3c34786ab4e11bbec2c2}{%
           family={Lu},
           familyi={L\bibinitperiod},
           given={Hongjia},
           giveni={H\bibinitperiod}}}%
        {{hash=8378d5b4061a021880b29f2f73452923}{%
           family={Xie},
           familyi={X\bibinitperiod},
           given={Yi\bibnamedelima Min},
           giveni={Y\bibinitperiod\bibinitdelim M\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{76db2936ab6f08f910b0d77b73c9d804}
      \strng{fullhash}{76db2936ab6f08f910b0d77b73c9d804}
      \strng{bibnamehash}{76db2936ab6f08f910b0d77b73c9d804}
      \strng{authorbibnamehash}{76db2936ab6f08f910b0d77b73c9d804}
      \strng{authornamehash}{76db2936ab6f08f910b0d77b73c9d804}
      \strng{authorfullhash}{76db2936ab6f08f910b0d77b73c9d804}
      \field{sortinit}{6}
      \field{sortinithash}{b33bc299efb3c36abec520a4c896a66d}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Despite the long history of the truss layout optimization approach, its practical applications have been limited, partly due to high manufacturing costs associated with complex optimized structures consisting of members with different cross-sectional areas and member lengths. To address this issue, this study considers optimizing truss structures comprising limited types of members. On this topic, two distinct problems are considered, wherein the first problem, members of the same type share the same cross-sectional area (i.e., section-type problem); and in the second problem, members of the same type share the same cross-sectional area and length (i.e., member-type problem). A novel post-processing approach is proposed to tackle the target problems. In this approach, the optimized structures from the traditional layout and geometry optimization approaches are used as the starting points, members of which are then separated into groups by the k-means clustering approach. Subsequently, the clustered structures are geometrically optimized to reduce the area and length deviations (i.e., the differences between member area/length values and the corresponding cluster means). Several 2D and 3D examples are presented to demonstrate the capability of the proposed approaches. For the section-type problem, the area deviations can be reduced to near 0 for any given cluster number. The member-type problem is relatively more complex, but by providing more clusters, the maximum length deviation can be reduced below the target thresholds. Through the proposed clustering approach, the number of different members in the optimized trusses can be substantially decreased, thereby significantly reducing manufacturing costs.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{2}
      \field{number}{3}
      \field{title}{Reducing the number of different members in truss layout optimization}
      \field{urlday}{24}
      \field{urlmonth}{2}
      \field{urlyear}{2023}
      \field{volume}{66}
      \field{year}{2023}
      \field{urldateera}{ce}
      \field{pages}{52}
      \range{pages}{1}
      \verb{doi}
      \verb 10.1007/s00158-023-03514-y
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\QAEPP9DL\\Lu and Xie - 2023 - Reducing the number of different members in truss .pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/s00158-023-03514-y
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s00158-023-03514-y
      \endverb
      \keyw{Truss structure,Layout optimization,K-means clustering,Member-type constraints}
    \endentry
    \entry{savine_component-based_2021}{article}{}
      \name{author}{5}{}{%
        {{hash=acd3e18b1b704325a033b8c9d2d967fc}{%
           family={Savine},
           familyi={S\bibinitperiod},
           given={Florent},
           giveni={F\bibinitperiod}}}%
        {{hash=6ffe413a21f4954b0aac85ca037c7876}{%
           family={Irisarri},
           familyi={I\bibinitperiod},
           given={François-Xavier},
           giveni={F\bibinithyphendelim X\bibinitperiod}}}%
        {{hash=d9c42bf5ce7591763a45d8334a00d4e1}{%
           family={Julien},
           familyi={J\bibinitperiod},
           given={Cédric},
           giveni={C\bibinitperiod}}}%
        {{hash=9e83c441d66327b5e71de3056be5e4bc}{%
           family={Vincenti},
           familyi={V\bibinitperiod},
           given={Angela},
           giveni={A\bibinitperiod}}}%
        {{hash=bc49b61075552b2f8a00880a34655178}{%
           family={Guerin},
           familyi={G\bibinitperiod},
           given={Yannick},
           giveni={Y\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{d8cf2add4b58a01a55c4bb2c869de57e}
      \strng{fullhash}{5b3c973b894a7201de3b95d8fb56a7f3}
      \strng{bibnamehash}{5b3c973b894a7201de3b95d8fb56a7f3}
      \strng{authorbibnamehash}{5b3c973b894a7201de3b95d8fb56a7f3}
      \strng{authornamehash}{d8cf2add4b58a01a55c4bb2c869de57e}
      \strng{authorfullhash}{5b3c973b894a7201de3b95d8fb56a7f3}
      \field{sortinit}{6}
      \field{sortinithash}{b33bc299efb3c36abec520a4c896a66d}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{In the present work, an optimization method is proposed in order to produce innovative stiffening layouts for large stiffened cylindrical shell structures, as they appear in the aerospace industry. A component-based logic is applied on a ground mesh of structural elements (shells and beams), which was inspired by techniques of explicit topology optimization on solid elements (plane or tridimensional massive models). Geometric components, representing the layout of the stiffeners (i.e. location, shape and size), are projected onto the ground mesh, resulting in controlled sets of active beam elements. These sets constitute the structural representation of the stiffeners’ layout in the optimization model, which is then used to evaluate the objective and constraint functions of the optimization problem as well as their semi-analytical sensitivities. By applying the optimization method to compliance minimization problems, we show the efficiency and accuracy of the proposed method and its capability to handle a typical aerospace structure, such as a space-launcher part: a stiffened cylindrical shell in presence of an access hatch.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{10}
      \field{number}{4}
      \field{title}{A component-based method for the optimization of stiffener layout on large cylindrical rib-stiffened shell structures}
      \field{urlday}{8}
      \field{urlmonth}{6}
      \field{urlyear}{2023}
      \field{volume}{64}
      \field{year}{2021}
      \field{urldateera}{ce}
      \field{pages}{1843\bibrangedash 1861}
      \range{pages}{19}
      \verb{doi}
      \verb 10.1007/s00158-021-02945-9
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\RII6JRR9\\Savine et al. - 2021 - A component-based method for the optimization of s.pdf:application/pdf
      \endverb
      \keyw{Component-based method,Explicit topology optimization,Ground structure,Stiffened shell structure,Stiffener layout optimization}
    \endentry
    \entry{parkes_joints_1975}{article}{}
      \name{author}{1}{}{%
        {{hash=ae75b1273e2b72d1d88ba56eea634690}{%
           family={Parkes},
           familyi={P\bibinitperiod},
           given={E.W.},
           giveni={E\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{ae75b1273e2b72d1d88ba56eea634690}
      \strng{fullhash}{ae75b1273e2b72d1d88ba56eea634690}
      \strng{bibnamehash}{ae75b1273e2b72d1d88ba56eea634690}
      \strng{authorbibnamehash}{ae75b1273e2b72d1d88ba56eea634690}
      \strng{authornamehash}{ae75b1273e2b72d1d88ba56eea634690}
      \strng{authorfullhash}{ae75b1273e2b72d1d88ba56eea634690}
      \field{sortinit}{6}
      \field{sortinithash}{b33bc299efb3c36abec520a4c896a66d}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{journaltitle}{International Journal of Solids and Structures}
      \field{month}{9}
      \field{number}{9}
      \field{title}{Joints in optimum frameworks}
      \field{urlday}{24}
      \field{urlmonth}{6}
      \field{urlyear}{2021}
      \field{volume}{11}
      \field{year}{1975}
      \field{urldateera}{ce}
      \field{pages}{1017\bibrangedash 1022}
      \range{pages}{6}
      \verb{doi}
      \verb 10.1016/0020-7683(75)90044-X
      \endverb
    \endentry
    \entry{schaedler_architected_2016}{article}{}
      \name{author}{2}{}{%
        {{hash=58ab4e11da4cf01e6471a077750e5d14}{%
           family={Schaedler},
           familyi={S\bibinitperiod},
           given={Tobias\bibnamedelima A.},
           giveni={T\bibinitperiod\bibinitdelim A\bibinitperiod}}}%
        {{hash=219e594ea052ca6cc78c4fa86ef26855}{%
           family={Carter},
           familyi={C\bibinitperiod},
           given={William\bibnamedelima B.},
           giveni={W\bibinitperiod\bibinitdelim B\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{1820eb608b0ea0707960c2e71164f069}
      \strng{fullhash}{1820eb608b0ea0707960c2e71164f069}
      \strng{bibnamehash}{1820eb608b0ea0707960c2e71164f069}
      \strng{authorbibnamehash}{1820eb608b0ea0707960c2e71164f069}
      \strng{authornamehash}{1820eb608b0ea0707960c2e71164f069}
      \strng{authorfullhash}{1820eb608b0ea0707960c2e71164f069}
      \field{sortinit}{6}
      \field{sortinithash}{b33bc299efb3c36abec520a4c896a66d}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Additive manufacturing enables fabrication of materials with intricate cellular architecture, whereby progress in 3D printing techniques is increasing the possible conﬁgurations of voids and solids ad inﬁnitum. Examples are microlattices with graded porosity and truss structures optimized for speciﬁc loading conditions. The cellular architecture determines the mechanical properties and density of these materials and can inﬂuence a wide range of other properties, e.g., acoustic, thermal, and biological properties. By combining optimized cellular architectures with high-performance metals and ceramics, several lightweight materials that exhibit strength and stiffness previously unachievable at low densities were recently demonstrated. This review introduces the ﬁeld of architected materials; summarizes the most common fabrication methods, with an emphasis on additive manufacturing; and discusses recent progress in the development of architected materials. The review also discusses important applications, including lightweight structures, energy absorption, metamaterials, thermal management, and bioscaffolds.}
      \field{issn}{1531-7331, 1545-4118}
      \field{journaltitle}{Annual Review of Materials Research}
      \field{month}{7}
      \field{number}{1}
      \field{title}{Architected {Cellular} {Materials}}
      \field{urlday}{2}
      \field{urlmonth}{10}
      \field{urlyear}{2020}
      \field{volume}{46}
      \field{year}{2016}
      \field{urldateera}{ce}
      \field{pages}{187\bibrangedash 210}
      \range{pages}{24}
      \verb{doi}
      \verb 10.1146/annurev-matsci-070115-031624
      \endverb
      \verb{file}
      \verb Schaedler et Carter - 2016 - Architected Cellular Materials.pdf:D\:\\estragio\\Zotero\\storage\\KCZ86Z5A\\Schaedler et Carter - 2016 - Architected Cellular Materials.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb http://www.annualreviews.org/doi/10.1146/annurev-matsci-070115-031624
      \endverb
      \verb{url}
      \verb http://www.annualreviews.org/doi/10.1146/annurev-matsci-070115-031624
      \endverb
    \endentry
    \entry{kohn_optimal_1986}{article}{}
      \name{author}{2}{}{%
        {{hash=efed0d9f0d90b38fea25e014b8a1740b}{%
           family={Kohn},
           familyi={K\bibinitperiod},
           given={Robert\bibnamedelima V.},
           giveni={R\bibinitperiod\bibinitdelim V\bibinitperiod}}}%
        {{hash=93733dfde0c47db226efad798ab3b662}{%
           family={Strang},
           familyi={S\bibinitperiod},
           given={Gilbert},
           giveni={G\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{3e120e21c3727cd5a44aa58a32779ab2}
      \strng{fullhash}{3e120e21c3727cd5a44aa58a32779ab2}
      \strng{bibnamehash}{3e120e21c3727cd5a44aa58a32779ab2}
      \strng{authorbibnamehash}{3e120e21c3727cd5a44aa58a32779ab2}
      \strng{authornamehash}{3e120e21c3727cd5a44aa58a32779ab2}
      \strng{authorfullhash}{3e120e21c3727cd5a44aa58a32779ab2}
      \field{sortinit}{6}
      \field{sortinithash}{b33bc299efb3c36abec520a4c896a66d}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{issn}{1097-0312}
      \field{journaltitle}{Communications on Pure and Applied Mathematics}
      \field{number}{1}
      \field{title}{Optimal design and relaxation of variational problems}
      \field{urlday}{14}
      \field{urlmonth}{9}
      \field{urlyear}{2021}
      \field{volume}{39}
      \field{year}{1986}
      \field{urldateera}{ce}
      \field{pages}{113\bibrangedash 137}
      \range{pages}{25}
      \verb{doi}
      \verb 10.1002/cpa.3160390107
      \endverb
    \endentry
    \entry{allaire_optimal_1999}{article}{}
      \name{author}{2}{}{%
        {{hash=01ec1538b00db5bf5f81d6d2221f5693}{%
           family={Allaire},
           familyi={A\bibinitperiod},
           given={G.},
           giveni={G\bibinitperiod}}}%
        {{hash=90c35e87a61102299d149d1587272017}{%
           family={Aubry},
           familyi={A\bibinitperiod},
           given={S.},
           giveni={S\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{f91c3d47d6616007ec45d79dd4606b4a}
      \strng{fullhash}{f91c3d47d6616007ec45d79dd4606b4a}
      \strng{bibnamehash}{f91c3d47d6616007ec45d79dd4606b4a}
      \strng{authorbibnamehash}{f91c3d47d6616007ec45d79dd4606b4a}
      \strng{authornamehash}{f91c3d47d6616007ec45d79dd4606b4a}
      \strng{authorfullhash}{f91c3d47d6616007ec45d79dd4606b4a}
      \field{sortinit}{6}
      \field{sortinithash}{b33bc299efb3c36abec520a4c896a66d}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural optimization}
      \field{month}{4}
      \field{number}{2}
      \field{title}{On optimal microstructures for a plane shape optimization problem}
      \field{urlday}{14}
      \field{urlmonth}{9}
      \field{urlyear}{2021}
      \field{volume}{17}
      \field{year}{1999}
      \field{urldateera}{ce}
      \field{pages}{86\bibrangedash 94}
      \range{pages}{9}
      \verb{doi}
      \verb 10.1007/BF01195933
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/BF01195933
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/BF01195933
      \endverb
    \endentry
    \entry{fleck_micro-architectured_2010}{article}{}
      \name{author}{3}{}{%
        {{hash=e2b30fe12c7d9bde635a5c2346741c56}{%
           family={Fleck},
           familyi={F\bibinitperiod},
           given={N.\bibnamedelimi A.},
           giveni={N\bibinitperiod\bibinitdelim A\bibinitperiod}}}%
        {{hash=5233a32272aa7ffdd5842786a86d44a7}{%
           family={Deshpande},
           familyi={D\bibinitperiod},
           given={V.\bibnamedelimi S.},
           giveni={V\bibinitperiod\bibinitdelim S\bibinitperiod}}}%
        {{hash=4efbe37e741cfa6637ad06d22dcb5217}{%
           family={Ashby},
           familyi={A\bibinitperiod},
           given={M.\bibnamedelimi F.},
           giveni={M\bibinitperiod\bibinitdelim F\bibinitperiod}}}%
      }
      \strng{namehash}{b47cc7c4ab4698e0ecb086516c2b3b9f}
      \strng{fullhash}{b47cc7c4ab4698e0ecb086516c2b3b9f}
      \strng{bibnamehash}{b47cc7c4ab4698e0ecb086516c2b3b9f}
      \strng{authorbibnamehash}{b47cc7c4ab4698e0ecb086516c2b3b9f}
      \strng{authornamehash}{b47cc7c4ab4698e0ecb086516c2b3b9f}
      \strng{authorfullhash}{b47cc7c4ab4698e0ecb086516c2b3b9f}
      \field{sortinit}{6}
      \field{sortinithash}{b33bc299efb3c36abec520a4c896a66d}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{shorttitle}
      \field{abstract}{Micro-architectured materials offer the opportunity of obtaining unique combinations of material properties. First, a historical perspective is given to the expansion of material property space by the introduction of new alloys and new microstructures. Principles of design of micro-architecture are then given and the role of nodal connectivity is emphasized for monoscale and multi-scale microstructures. The stiffness, strength and damage tolerance of lattice materials are reviewed and compared with those of fully dense solids. It is demonstrated that micro-architectured materials are able to occupy regions of material property space (such as high stiffness, strength and fracture toughness at low density) that were hitherto empty. Some challenges for the development of future materials are highlighted.}
      \field{journaltitle}{Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences}
      \field{month}{9}
      \field{number}{2121}
      \field{shorttitle}{Micro-architectured materials}
      \field{title}{Micro-architectured materials: past, present and future}
      \field{urlday}{2}
      \field{urlmonth}{10}
      \field{urlyear}{2020}
      \field{volume}{466}
      \field{year}{2010}
      \field{urldateera}{ce}
      \field{pages}{2495\bibrangedash 2516}
      \range{pages}{22}
      \verb{doi}
      \verb 10.1098/rspa.2010.0215
      \endverb
      \verb{file}
      \verb Fleck et al. - 2010 - Micro-architectured materials past, present and f.pdf:D\:\\estragio\\Zotero\\storage\\UENPTKIB\\Fleck et al. - 2010 - Micro-architectured materials past, present and f.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://royalsocietypublishing.org/doi/full/10.1098/rspa.2010.0215
      \endverb
      \verb{url}
      \verb https://royalsocietypublishing.org/doi/full/10.1098/rspa.2010.0215
      \endverb
    \endentry
    \entry{nz_hypholoma_2023}{misc}{}
      \name{author}{1}{}{%
        {{hash=4ae1f6897f320210050cd219b56eb724}{%
           family={NZ},
           familyi={N\bibinitperiod},
           given={Bernard\bibnamedelima Spragg},
           giveni={B\bibinitperiod\bibinitdelim S\bibinitperiod}}}%
      }
      \strng{namehash}{4ae1f6897f320210050cd219b56eb724}
      \strng{fullhash}{4ae1f6897f320210050cd219b56eb724}
      \strng{bibnamehash}{4ae1f6897f320210050cd219b56eb724}
      \strng{authorbibnamehash}{4ae1f6897f320210050cd219b56eb724}
      \strng{authornamehash}{4ae1f6897f320210050cd219b56eb724}
      \strng{authorfullhash}{4ae1f6897f320210050cd219b56eb724}
      \field{sortinit}{6}
      \field{sortinithash}{b33bc299efb3c36abec520a4c896a66d}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Hypholoma fasciculare, commonly known as the sulphur tuft or clustered woodlover, is a common woodland mushroom, often in evidence when hardly any other mushrooms are to be found. This saprotrophic small gill fungus grows prolifically in large clumps on stumps, dead roots or rotting trunks of broadleaved trees.}
      \field{month}{4}
      \field{title}{Hypholoma fasciculare,}
      \field{urlday}{10}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{year}{2023}
      \field{urldateera}{ce}
      \verb{file}
      \verb Hypholoma fasciculare,:D\:\\estragio\\Zotero\\storage\\4WVJVVJ4\\NZ - 2023 - Hypholoma fasciculare,.jpg:image/jpg
      \endverb
      \verb{urlraw}
      \verb https://www.flickr.com/photos/volvob12b/52833345708/
      \endverb
      \verb{url}
      \verb https://www.flickr.com/photos/volvob12b/52833345708/
      \endverb
      \keyw{forestfloor,funghi,fungi,fungus,hypholomafasciculare,lumixfz10002,macro,mushrooms,nature,sulphurtuft,wetknee}
    \endentry
    \entry{library_leaf_nodate}{misc}{}
      \name{author}{1}{}{%
        {{hash=2611011cfe42ecc659ccf50f25aeb5d2}{%
           family={LIBRARY},
           familyi={L\bibinitperiod},
           given={STEVE\bibnamedelimb GSCHMEISSNER/SCIENCE\bibnamedelima PHOTO},
           giveni={S\bibinitperiod\bibinitdelim G\bibinitperiod\bibinitdelim P\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{2611011cfe42ecc659ccf50f25aeb5d2}
      \strng{fullhash}{2611011cfe42ecc659ccf50f25aeb5d2}
      \strng{bibnamehash}{2611011cfe42ecc659ccf50f25aeb5d2}
      \strng{authorbibnamehash}{2611011cfe42ecc659ccf50f25aeb5d2}
      \strng{authornamehash}{2611011cfe42ecc659ccf50f25aeb5d2}
      \strng{authorfullhash}{2611011cfe42ecc659ccf50f25aeb5d2}
      \field{sortinit}{6}
      \field{sortinithash}{b33bc299efb3c36abec520a4c896a66d}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Leaf structure. Coloured scanning electron micrograph (SEM) of a freeze-fracture through a seedling leaf. STEVE GSCHMEISSNER/SCIENCE PHOTO LIBRARY}
      \field{journaltitle}{Science Photo Library}
      \field{title}{Leaf structure, {SEM}}
      \field{urlday}{10}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{urldateera}{ce}
      \verb{urlraw}
      \verb https://www.sciencephoto.com/media/30288/view/leaf-structure-sem
      \endverb
      \verb{url}
      \verb https://www.sciencephoto.com/media/30288/view/leaf-structure-sem
      \endverb
    \endentry
    \entry{gripspix_mostly_off_health_issues_wing_2007}{misc}{}
      \name{author}{1}{}{%
        {{hash=5298076ed48a5272442529cc6befeeb1}{%
           family={{gripspix (mostly off, health issues)}},
           familyi={g\bibinitperiod}}}%
      }
      \strng{namehash}{5298076ed48a5272442529cc6befeeb1}
      \strng{fullhash}{5298076ed48a5272442529cc6befeeb1}
      \strng{bibnamehash}{5298076ed48a5272442529cc6befeeb1}
      \strng{authorbibnamehash}{5298076ed48a5272442529cc6befeeb1}
      \strng{authornamehash}{5298076ed48a5272442529cc6befeeb1}
      \strng{authorfullhash}{5298076ed48a5272442529cc6befeeb1}
      \field{sortinit}{6}
      \field{sortinithash}{b33bc299efb3c36abec520a4c896a66d}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{The wing shows a interesting structure: there are cells with a certain angle (120° and 90°). The structure is the same you can see, when you put foam between two glass plates. (Lit.: Hildebrandt, S: Mathematics and optimal form; Deutsche Ausgabe S. 5)}
      \field{month}{8}
      \field{title}{Wing of a dragonfly, detail}
      \field{urlday}{10}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{year}{2007}
      \field{urldateera}{ce}
      \verb{file}
      \verb Wing of a dragonfly, detail:D\:\\estragio\\Zotero\\storage\\LPWVGJQ6\\gripspix (mostly off, health issues) - 2007 - Wing of a dragonfly, detail.jpg:image/jpg
      \endverb
      \verb{urlraw}
      \verb https://www.flickr.com/photos/gripspix/1233292309/
      \endverb
      \verb{url}
      \verb https://www.flickr.com/photos/gripspix/1233292309/
      \endverb
      \keyw{abigfave,detail,dragonfly,insect,macro,mathematics,minas,nature,naturesfinest,optimalform,structure,wing}
    \endentry
    \entry{noauthor_bone_03_nodate}{misc}{}
      \name{author}{1}{}{%
        {{hash=fa3793c7acf07085357dadf011ab0109}{%
           family={Archimorph},
           familyi={A\bibinitperiod}}}%
      }
      \strng{namehash}{fa3793c7acf07085357dadf011ab0109}
      \strng{fullhash}{fa3793c7acf07085357dadf011ab0109}
      \strng{bibnamehash}{fa3793c7acf07085357dadf011ab0109}
      \strng{authorbibnamehash}{fa3793c7acf07085357dadf011ab0109}
      \strng{authornamehash}{fa3793c7acf07085357dadf011ab0109}
      \strng{authorfullhash}{fa3793c7acf07085357dadf011ab0109}
      \field{sortinit}{6}
      \field{sortinithash}{b33bc299efb3c36abec520a4c896a66d}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{title}{bone\_03}
      \field{urlday}{10}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{urldateera}{ce}
      \verb{urlraw}
      \verb https://archimorph.files.wordpress.com/2010/01/bone_03.jpg
      \endverb
      \verb{url}
      \verb https://archimorph.files.wordpress.com/2010/01/bone_03.jpg
      \endverb
    \endentry
    \entry{dai_size_2008}{article}{}
      \name{author}{2}{}{%
        {{hash=c6f774aa0fb59a4a7bf81710ffd309f9}{%
           family={Dai},
           familyi={D\bibinitperiod},
           given={G.\bibnamedelimi M.},
           giveni={G\bibinitperiod\bibinitdelim M\bibinitperiod}}}%
        {{hash=6fc666191c90a7606809ec95541edc80}{%
           family={Zhang},
           familyi={Z\bibinitperiod},
           given={W.\bibnamedelimi H.},
           giveni={W\bibinitperiod\bibinitdelim H\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{8aeea3200c4ce830bfeb29df32ea66ce}
      \strng{fullhash}{8aeea3200c4ce830bfeb29df32ea66ce}
      \strng{bibnamehash}{8aeea3200c4ce830bfeb29df32ea66ce}
      \strng{authorbibnamehash}{8aeea3200c4ce830bfeb29df32ea66ce}
      \strng{authornamehash}{8aeea3200c4ce830bfeb29df32ea66ce}
      \strng{authorfullhash}{8aeea3200c4ce830bfeb29df32ea66ce}
      \field{sortinit}{6}
      \field{sortinithash}{b33bc299efb3c36abec520a4c896a66d}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{In this paper, multilayered sandwich beam structures are considered. Within the scope of static analyses and stiffness design of such type of lightweight and functional structures, size effects of the basic cell are studied both theoretically and numerically in a systematic way for the first time. The direct FE discretization method, the homogenization method and the classical beam theory are examined systematically to reveal, on one hand, the existence of the size effect, and on the other hand, the ability of each method in capturing the size effect upon the static stress distribution and structural deflection. Particularly, limitations of the homogenization method are clarified although the latter is widely applied today in the equivalent modeling and topology design of cellular materials of sandwich structures. By means of the above methods, bending problems of multilayered beams and cellular core sandwiches are solved to illustrate variations of the deflection, stress as well as the computing accuracies in terms of the size of the basic cell. It is shown that the size effect is important when the basic cell has a considerable dimension relative to the structural size and that this effect decreases rapidly with the size reduction of the basic cell. Theoretically, the homogenized result corresponds to the limit solution when the size of the basic cell tends to be infinitely small.}
      \field{issn}{0020-7683}
      \field{journaltitle}{International Journal of Solids and Structures}
      \field{month}{5}
      \field{number}{9}
      \field{title}{Size effects of basic cell in static analysis of sandwich beams}
      \field{urlday}{19}
      \field{urlmonth}{1}
      \field{urlyear}{2021}
      \field{volume}{45}
      \field{year}{2008}
      \field{urldateera}{ce}
      \field{pages}{2512\bibrangedash 2533}
      \range{pages}{22}
      \verb{doi}
      \verb 10.1016/j.ijsolstr.2007.12.007
      \endverb
      \verb{file}
      \verb ScienceDirect Full Text PDF:D\:\\estragio\\Zotero\\storage\\WM9WY5WH\\Dai and Zhang - 2008 - Size effects of basic cell in static analysis of s.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb http://www.sciencedirect.com/science/article/pii/S0020768307005094
      \endverb
      \verb{url}
      \verb http://www.sciencedirect.com/science/article/pii/S0020768307005094
      \endverb
      \keyw{Topology optimization,Basic cell,Homogenization method,Multilayered structure,Sandwich beam,Size effect}
    \endentry
    \entry{kalamkarov_asymptotic_2009}{article}{}
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        {{hash=0f4a30439cc4e75b3ea11370be79dc72}{%
           family={Kalamkarov},
           familyi={K\bibinitperiod},
           given={Alexander\bibnamedelima L.},
           giveni={A\bibinitperiod\bibinitdelim L\bibinitperiod}}}%
        {{hash=48c8dfc63672fdbe0e36a33b376c4088}{%
           family={Andrianov},
           familyi={A\bibinitperiod},
           given={Igor\bibnamedelima V.},
           giveni={I\bibinitperiod\bibinitdelim V\bibinitperiod}}}%
        {{hash=b8f68c60e75c7f00ed792b1f052f40f1}{%
           family={Danishevs’kyy},
           familyi={D\bibinitperiod},
           given={Vladyslav\bibnamedelima V.},
           giveni={V\bibinitperiod\bibinitdelim V\bibinitperiod}}}%
      }
      \strng{namehash}{315bbee390a83f7fcd549f17ab0ec6a2}
      \strng{fullhash}{315bbee390a83f7fcd549f17ab0ec6a2}
      \strng{bibnamehash}{315bbee390a83f7fcd549f17ab0ec6a2}
      \strng{authorbibnamehash}{315bbee390a83f7fcd549f17ab0ec6a2}
      \strng{authornamehash}{315bbee390a83f7fcd549f17ab0ec6a2}
      \strng{authorfullhash}{315bbee390a83f7fcd549f17ab0ec6a2}
      \field{sortinit}{6}
      \field{sortinithash}{b33bc299efb3c36abec520a4c896a66d}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{issn}{0003-6900}
      \field{journaltitle}{Applied Mechanics Reviews}
      \field{month}{3}
      \field{number}{3}
      \field{title}{Asymptotic {Homogenization} of {Composite} {Materials} and {Structures}}
      \field{urlday}{15}
      \field{urlmonth}{9}
      \field{urlyear}{2021}
      \field{volume}{62}
      \field{year}{2009}
      \field{urldateera}{ce}
      \verb{doi}
      \verb 10.1115/1.3090830
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1115/1.3090830
      \endverb
      \verb{url}
      \verb https://doi.org/10.1115/1.3090830
      \endverb
    \endentry
    \entry{coelho_scale-size_2016}{article}{}
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        {{hash=3bb86ec92af6ef7f79f4683c254c7c07}{%
           family={Coelho},
           familyi={C\bibinitperiod},
           given={P.\bibnamedelimi G.},
           giveni={P\bibinitperiod\bibinitdelim G\bibinitperiod}}}%
        {{hash=a0e3a5e24b2e15f6b4edea5d273046dd}{%
           family={Amiano},
           familyi={A\bibinitperiod},
           given={L.\bibnamedelimi D.},
           giveni={L\bibinitperiod\bibinitdelim D\bibinitperiod}}}%
        {{hash=a46b64f3808c21131762bc2d0b5ba331}{%
           family={Guedes},
           familyi={G\bibinitperiod},
           given={J.\bibnamedelimi M.},
           giveni={J\bibinitperiod\bibinitdelim M\bibinitperiod}}}%
        {{hash=4896101cf215b6e277e82303df407498}{%
           family={Rodrigues},
           familyi={R\bibinitperiod},
           given={H.\bibnamedelimi C.},
           giveni={H\bibinitperiod\bibinitdelim C\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{9b747f03fb8b57cbe9810c9d27227a0b}
      \strng{fullhash}{bd2232277b207095530aa1bc2dddb487}
      \strng{bibnamehash}{bd2232277b207095530aa1bc2dddb487}
      \strng{authorbibnamehash}{bd2232277b207095530aa1bc2dddb487}
      \strng{authornamehash}{9b747f03fb8b57cbe9810c9d27227a0b}
      \strng{authorfullhash}{bd2232277b207095530aa1bc2dddb487}
      \field{sortinit}{6}
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      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Periodic homogenization models are often used to compute the elastic properties of periodic composite materials based on the shape/periodicity of a given material unit-cell. Conversely, in material design, the unit-cell is not known a priori, and the goal is to design it to attain specific properties values – inverse homogenization problem. This problem is often solved by formulating it as an optimization problem. In this approach, the unit-cell is assumed infinitely small and with periodic boundary conditions. However, in practice, the composite material comprises a finite number of measurable unit-cells and the stress/strain fields are not periodic near the structure boundary. It is thus critical to investigate whether the obtained topologies are affected when applied in the context of real composites. This is done here by scaling the unit-cell an increasing number of times and accessing the apparent properties of the resulting composite by means of standard numerical experiments.}
      \field{issn}{0045-7949}
      \field{journaltitle}{Computers \&amp; Structures}
      \field{month}{10}
      \field{series}{{CIVIL}-{COMP}}
      \field{title}{Scale-size effects analysis of optimal periodic material microstructures designed by the inverse homogenization method}
      \field{urlday}{19}
      \field{urlmonth}{1}
      \field{urlyear}{2021}
      \field{volume}{174}
      \field{year}{2016}
      \field{urldateera}{ce}
      \field{pages}{21\bibrangedash 32}
      \range{pages}{12}
      \verb{doi}
      \verb 10.1016/j.compstruc.2015.10.001
      \endverb
      \verb{file}
      \verb ScienceDirect Full Text PDF:D\:\\estragio\\Zotero\\storage\\I5YFRE4M\\Coelho et al. - 2016 - Scale-size effects analysis of optimal periodic ma.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb http://www.sciencedirect.com/science/article/pii/S0045794915002746
      \endverb
      \verb{url}
      \verb http://www.sciencedirect.com/science/article/pii/S0045794915002746
      \endverb
      \keyw{Optimization,Homogenization,Topology,Microstructures,Cellular,Scale}
    \endentry
    \entry{zhang_multiscale_2018}{article}{}
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        {{hash=28f91f3a4b62ce57b7a533e742e8aae1}{%
           family={Zhang},
           familyi={Z\bibinitperiod},
           given={Yan},
           giveni={Y\bibinitperiod}}}%
        {{hash=d2290dd0ed5b43d5f15a81522cdab00f}{%
           family={Xiao},
           familyi={X\bibinitperiod},
           given={Mi},
           giveni={M\bibinitperiod}}}%
        {{hash=2620b9afd37cca5b9b7354f67c036d4d}{%
           family={Li},
           familyi={L\bibinitperiod},
           given={Hao},
           giveni={H\bibinitperiod}}}%
        {{hash=a8eab9075a7e8567d259e822a8ff36e6}{%
           family={Gao},
           familyi={G\bibinitperiod},
           given={Liang},
           giveni={L\bibinitperiod}}}%
        {{hash=3180625e42c349e7a66e5e0119946f63}{%
           family={Chu},
           familyi={C\bibinitperiod},
           given={Sheng},
           giveni={S\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{37b129e5ba18129997157b8fc224c8d9}
      \strng{fullhash}{a9e8a0b080d9cbbde61e46c13552be00}
      \strng{bibnamehash}{a9e8a0b080d9cbbde61e46c13552be00}
      \strng{authorbibnamehash}{a9e8a0b080d9cbbde61e46c13552be00}
      \strng{authornamehash}{37b129e5ba18129997157b8fc224c8d9}
      \strng{authorfullhash}{a9e8a0b080d9cbbde61e46c13552be00}
      \field{extraname}{3}
      \field{sortinit}{6}
      \field{sortinithash}{b33bc299efb3c36abec520a4c896a66d}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{issn}{0927-0256}
      \field{journaltitle}{Computational Materials Science}
      \field{month}{12}
      \field{title}{Multiscale concurrent topology optimization for cellular structures with multiple microstructures based on ordered {SIMP} interpolation}
      \field{urlday}{16}
      \field{urlmonth}{10}
      \field{urlyear}{2020}
      \field{volume}{155}
      \field{year}{2018}
      \field{urldateera}{ce}
      \field{pages}{74\bibrangedash 91}
      \range{pages}{18}
      \verb{doi}
      \verb 10.1016/j.commatsci.2018.08.030
      \endverb
      \verb{urlraw}
      \verb http://www.sciencedirect.com/science/article/pii/S0927025618305524
      \endverb
      \verb{url}
      \verb http://www.sciencedirect.com/science/article/pii/S0927025618305524
      \endverb
      \keyw{Topology optimization,Cellular structures,Multiscale concurrent design,Ordered SIMP interpolation,Parametric level set method}
    \endentry
    \entry{deshpande_foam_2001}{article}{}
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        {{hash=4efbe37e741cfa6637ad06d22dcb5217}{%
           family={Ashby},
           familyi={A\bibinitperiod},
           given={M.\bibnamedelimi F.},
           giveni={M\bibinitperiod\bibinitdelim F\bibinitperiod}}}%
        {{hash=e2b30fe12c7d9bde635a5c2346741c56}{%
           family={Fleck},
           familyi={F\bibinitperiod},
           given={N.\bibnamedelimi A.},
           giveni={N\bibinitperiod\bibinitdelim A\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{447245b73881f285da84992d5f7c9412}
      \strng{fullhash}{447245b73881f285da84992d5f7c9412}
      \strng{bibnamehash}{447245b73881f285da84992d5f7c9412}
      \strng{authorbibnamehash}{447245b73881f285da84992d5f7c9412}
      \strng{authornamehash}{447245b73881f285da84992d5f7c9412}
      \strng{authorfullhash}{447245b73881f285da84992d5f7c9412}
      \field{sortinit}{7}
      \field{sortinithash}{108d0be1b1bee9773a1173443802c0a3}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{shorttitle}
      \field{journaltitle}{Acta Materialia}
      \field{month}{4}
      \field{number}{6}
      \field{shorttitle}{Foam topology}
      \field{title}{Foam topology: bending versus stretching dominated architectures}
      \field{urlday}{2}
      \field{urlmonth}{10}
      \field{urlyear}{2020}
      \field{volume}{49}
      \field{year}{2001}
      \field{urldateera}{ce}
      \field{pages}{1035\bibrangedash 1040}
      \range{pages}{6}
      \verb{doi}
      \verb 10.1016/S1359-6454(00)00379-7
      \endverb
      \keyw{Foams,Mechanical properties,Structure}
    \endentry
    \entry{ashby_properties_2006}{article}{}
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      \field{sortinithash}{108d0be1b1bee9773a1173443802c0a3}
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      \field{labeltitlesource}{title}
      \field{journaltitle}{Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences}
      \field{month}{1}
      \field{number}{1838}
      \field{title}{The properties of foams and lattices}
      \field{urlday}{7}
      \field{urlmonth}{10}
      \field{urlyear}{2020}
      \field{volume}{364}
      \field{year}{2006}
      \field{urldateera}{ce}
      \field{pages}{15\bibrangedash 30}
      \range{pages}{16}
      \verb{doi}
      \verb 10.1098/rsta.2005.1678
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      \verb{urlraw}
      \verb https://royalsocietypublishing.org/doi/10.1098/rsta.2005.1678
      \endverb
      \verb{url}
      \verb https://royalsocietypublishing.org/doi/10.1098/rsta.2005.1678
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    \entry{evans_concepts_2010}{article}{}
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           family={He},
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        {{hash=5233a32272aa7ffdd5842786a86d44a7}{%
           family={Deshpande},
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        {{hash=7f10bc8978e05ed377464951f9d14434}{%
           family={Hutchinson},
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        {{hash=4d6cc47806f6184b2ae38b72570e65a3}{%
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        {{hash=bb3cd9dac41a0f99c8419f1075574520}{%
           family={Barvosa-Carter},
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           given={W.},
           giveni={W\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{608c0d974341e5b9c7d2d4181e343390}
      \strng{fullhash}{016aa6eea91908d4665e34d48588a5e9}
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      \field{labeltitlesource}{title}
      \field{issn}{0734-743X}
      \field{journaltitle}{International Journal of Impact Engineering}
      \field{title}{Concepts for {Enhanced} {Energy} {Absorption} {Using} {Hollow} {Micro}-{Lattices}}
      \field{urlday}{17}
      \field{urlmonth}{9}
      \field{urlyear}{2021}
      \field{year}{2010}
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           family={Ro},
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           given={Christopher\bibnamedelima J.},
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        {{hash=c3e56001cffb34f61fa9c87daa99a1ed}{%
           family={Sorensen},
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           given={Adam\bibnamedelima E.},
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        {{hash=c7c88662d620a87f528119fce4ef1363}{%
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        {{hash=ab567f08fbc2a093aab286a744de9acc}{%
           family={Yang},
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        {{hash=219e594ea052ca6cc78c4fa86ef26855}{%
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           given={Alan\bibnamedelima J.},
           giveni={A\bibinitperiod\bibinitdelim J\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{792a04833581c0d0837f5b6e76880033}
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      \field{issn}{1527-2648}
      \field{journaltitle}{Advanced Engineering Materials}
      \field{number}{3}
      \field{title}{Designing {Metallic} {Microlattices} for {Energy} {Absorber} {Applications}}
      \field{urlday}{17}
      \field{urlmonth}{9}
      \field{urlyear}{2021}
      \field{volume}{16}
      \field{year}{2014}
      \field{urldateera}{ce}
      \field{pages}{276\bibrangedash 283}
      \range{pages}{8}
      \verb{doi}
      \verb 10.1002/adem.201300206
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           family={Warren},
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           family={Goodall},
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           given={Russell},
           giveni={R\bibinitperiod}}}%
        {{hash=84217d1bfa45838363cbb4afb1a7d4b5}{%
           family={Todd},
           familyi={T\bibinitperiod},
           given={Iain},
           giveni={I\bibinitperiod}}}%
        {{hash=dbcf7815fcbf7444d675e40a04806b65}{%
           family={Askes},
           familyi={A\bibinitperiod},
           given={Harm},
           giveni={H\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{6757bd676149b13cd40fc65bff692da4}
      \strng{fullhash}{286725745d16b19cccc3eddeb1f03e9f}
      \strng{bibnamehash}{286725745d16b19cccc3eddeb1f03e9f}
      \strng{authorbibnamehash}{286725745d16b19cccc3eddeb1f03e9f}
      \strng{authornamehash}{6757bd676149b13cd40fc65bff692da4}
      \strng{authorfullhash}{286725745d16b19cccc3eddeb1f03e9f}
      \field{sortinit}{7}
      \field{sortinithash}{108d0be1b1bee9773a1173443802c0a3}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{shorttitle}
      \field{issn}{0734-743X}
      \field{journaltitle}{International Journal of Impact Engineering}
      \field{month}{3}
      \field{shorttitle}{Energy absorption in lattice structures in dynamics}
      \field{title}{Energy absorption in lattice structures in dynamics: {Experiments}}
      \field{urlday}{17}
      \field{urlmonth}{9}
      \field{urlyear}{2021}
      \field{volume}{89}
      \field{year}{2016}
      \field{urldateera}{ce}
      \field{pages}{49\bibrangedash 61}
      \range{pages}{13}
      \verb{doi}
      \verb 10.1016/j.ijimpeng.2015.10.007
      \endverb
      \verb{urlraw}
      \verb https://www.sciencedirect.com/science/article/pii/S0734743X15002134
      \endverb
      \verb{url}
      \verb https://www.sciencedirect.com/science/article/pii/S0734743X15002134
      \endverb
      \keyw{Advance manufacturing,Hopkinson pressure bar (HPB),Impact and blast protection,Lattice structures}
    \endentry
    \entry{opgenoord_aeroelastic_2018}{inproceedings}{}
      \name{author}{2}{}{%
        {{hash=9a4676ce16d52df1aa7892cc01fef54d}{%
           family={Opgenoord},
           familyi={O\bibinitperiod},
           given={Max\bibnamedelima M.},
           giveni={M\bibinitperiod\bibinitdelim M\bibinitperiod}}}%
        {{hash=a51c06eb9ede4de9ef30715d223beb5c}{%
           family={Willcox},
           familyi={W\bibinitperiod},
           given={Karen\bibnamedelima E.},
           giveni={K\bibinitperiod\bibinitdelim E\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \list{location}{1}{%
        {Atlanta, Georgia}%
      }
      \list{publisher}{2}{%
        {American Institute of Aeronautics}%
        {Astronautics}%
      }
      \strng{namehash}{1b1275f889d783d30eee944937823236}
      \strng{fullhash}{1b1275f889d783d30eee944937823236}
      \strng{bibnamehash}{1b1275f889d783d30eee944937823236}
      \strng{authorbibnamehash}{1b1275f889d783d30eee944937823236}
      \strng{authornamehash}{1b1275f889d783d30eee944937823236}
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      \field{sortinithash}{108d0be1b1bee9773a1173443802c0a3}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{booktitle}{2018 {Multidisciplinary} {Analysis} and {Optimization} {Conference}}
      \field{month}{6}
      \field{title}{Aeroelastic {Tailoring} using {Additively} {Manufactured} {Lattice} {Structures}}
      \field{urlday}{5}
      \field{urlmonth}{10}
      \field{urlyear}{2020}
      \field{year}{2018}
      \field{urldateera}{ce}
      \verb{doi}
      \verb 10.2514/6.2018-4055
      \endverb
      \verb{urlraw}
      \verb https://arc.aiaa.org/doi/10.2514/6.2018-4055
      \endverb
      \verb{url}
      \verb https://arc.aiaa.org/doi/10.2514/6.2018-4055
      \endverb
    \endentry
    \entry{cramer_elastic_2019}{article}{}
      \name{author}{11}{}{%
        {{hash=c4b92a262209610f7ca22dca389539e1}{%
           family={Cramer},
           familyi={C\bibinitperiod},
           given={Nicholas\bibnamedelima B.},
           giveni={N\bibinitperiod\bibinitdelim B\bibinitperiod}}}%
        {{hash=313412b7b87239ec487a05e4bc1ebaa2}{%
           family={Cellucci},
           familyi={C\bibinitperiod},
           given={Daniel\bibnamedelima W.},
           giveni={D\bibinitperiod\bibinitdelim W\bibinitperiod}}}%
        {{hash=de9d0dc74d4ec7c33f828b81e9dfbdbe}{%
           family={Formoso},
           familyi={F\bibinitperiod},
           given={Olivia\bibnamedelima B.},
           giveni={O\bibinitperiod\bibinitdelim B\bibinitperiod}}}%
        {{hash=fb844abc5ed12a860277b3320573596f}{%
           family={Gregg},
           familyi={G\bibinitperiod},
           given={Christine\bibnamedelima E.},
           giveni={C\bibinitperiod\bibinitdelim E\bibinitperiod}}}%
        {{hash=5230f55680a41212167d3ed2eab519f8}{%
           family={Jenett},
           familyi={J\bibinitperiod},
           given={Benjamin\bibnamedelima E.},
           giveni={B\bibinitperiod\bibinitdelim E\bibinitperiod}}}%
        {{hash=28f4204999fd9d16ed6ccade9a80f85a}{%
           family={Kim},
           familyi={K\bibinitperiod},
           given={Joseph\bibnamedelima H.},
           giveni={J\bibinitperiod\bibinitdelim H\bibinitperiod}}}%
        {{hash=f01185d29620d0c738eb31cb2026e99d}{%
           family={Lendraitis},
           familyi={L\bibinitperiod},
           given={Martynas},
           giveni={M\bibinitperiod}}}%
        {{hash=571cdbadfb89884af86de092b2141659}{%
           family={Swei},
           familyi={S\bibinitperiod},
           given={Sean\bibnamedelima S.},
           giveni={S\bibinitperiod\bibinitdelim S\bibinitperiod}}}%
        {{hash=146a00e4727657311cad76f4624f3335}{%
           family={Trinh},
           familyi={T\bibinitperiod},
           given={Greenfield\bibnamedelima T.},
           giveni={G\bibinitperiod\bibinitdelim T\bibinitperiod}}}%
        {{hash=46ad41b28a154ee54cae4788895b8137}{%
           family={Trinh},
           familyi={T\bibinitperiod},
           given={Khanh\bibnamedelima V.},
           giveni={K\bibinitperiod\bibinitdelim V\bibinitperiod}}}%
        {{hash=167d96b89d4ec4a25094057c319979eb}{%
           family={Cheung},
           familyi={C\bibinitperiod},
           given={Kenneth\bibnamedelima C.},
           giveni={K\bibinitperiod\bibinitdelim C\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{39bde62302bf3125a9aa2c761f488538}
      \strng{fullhash}{66617fcfa0ce163c8f219ede752f7b5e}
      \strng{bibnamehash}{66617fcfa0ce163c8f219ede752f7b5e}
      \strng{authorbibnamehash}{66617fcfa0ce163c8f219ede752f7b5e}
      \strng{authornamehash}{39bde62302bf3125a9aa2c761f488538}
      \strng{authorfullhash}{66617fcfa0ce163c8f219ede752f7b5e}
      \field{sortinit}{7}
      \field{sortinithash}{108d0be1b1bee9773a1173443802c0a3}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Ultralight materials present an opportunity to dramatically increase the efficiency of load-bearing aerostructures. To date, however, these ultralight materials have generally been confined to the laboratory bench-top, due to dimensional constraints of the manufacturing processes. We show a programmable material system applied as a large-scale, ultralight, and conformable aeroelastic structure. The use of a modular, lattice-based, ultralight material results in stiffness typical of an elastomer (2.6 MPa) at a mass density typical of an aerogel . This, combined with a building block based manufacturing and configuration strategy, enables the rapid realization of new adaptive structures and mechanisms. The heterogeneous design with programmable anisotropy allows for enhanced elastic and global shape deformation in response to external loading, making it useful for tuned fluid-structure interaction. We demonstrate an example application experiment using two building block types for the primary structure of a 4.27 m wingspan aircraft, where we spatially program elastic shape morphing to increase aerodynamic efficiency and improve roll control authority, demonstrated with full-scale wind tunnel testing.}
      \field{issn}{0964-1726}
      \field{journaltitle}{Smart Materials and Structures}
      \field{month}{4}
      \field{number}{5}
      \field{title}{Elastic shape morphing of ultralight structures by programmable assembly}
      \field{urlday}{2}
      \field{urlmonth}{10}
      \field{urlyear}{2020}
      \field{volume}{28}
      \field{year}{2019}
      \field{urldateera}{ce}
      \field{pages}{055006}
      \range{pages}{1}
      \verb{doi}
      \verb 10.1088/1361-665X/ab0ea2
      \endverb
    \endentry
    \entry{hutmacher_scaffolds_2000}{article}{}
      \name{author}{1}{}{%
        {{hash=85d1ec12bddc8ecdf9c68742780b6cda}{%
           family={Hutmacher},
           familyi={H\bibinitperiod},
           given={Dietmar\bibnamedelima W.},
           giveni={D\bibinitperiod\bibinitdelim W\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{85d1ec12bddc8ecdf9c68742780b6cda}
      \strng{fullhash}{85d1ec12bddc8ecdf9c68742780b6cda}
      \strng{bibnamehash}{85d1ec12bddc8ecdf9c68742780b6cda}
      \strng{authorbibnamehash}{85d1ec12bddc8ecdf9c68742780b6cda}
      \strng{authornamehash}{85d1ec12bddc8ecdf9c68742780b6cda}
      \strng{authorfullhash}{85d1ec12bddc8ecdf9c68742780b6cda}
      \field{sortinit}{7}
      \field{sortinithash}{108d0be1b1bee9773a1173443802c0a3}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{issn}{0142-9612}
      \field{journaltitle}{Biomaterials}
      \field{month}{12}
      \field{number}{24}
      \field{series}{Orthopaedic {Polymeric} {Biomaterials}: {Applications} of {Biodegradables}}
      \field{title}{Scaffolds in tissue engineering bone and cartilage}
      \field{urlday}{17}
      \field{urlmonth}{9}
      \field{urlyear}{2021}
      \field{volume}{21}
      \field{year}{2000}
      \field{urldateera}{ce}
      \field{pages}{2529\bibrangedash 2543}
      \range{pages}{15}
      \verb{doi}
      \verb 10.1016/S0142-9612(00)00121-6
      \endverb
      \verb{urlraw}
      \verb https://www.sciencedirect.com/science/article/pii/S0142961200001216
      \endverb
      \verb{url}
      \verb https://www.sciencedirect.com/science/article/pii/S0142961200001216
      \endverb
      \keyw{Biodegradable and bioresorbable polymers,Design and fabrication of 3-D scaffold,Tissue engineering of bone and cartilage}
    \endentry
    \entry{mota_additive_2015}{article}{}
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        {{hash=e48dc079b2009e213d4c387bc72f688e}{%
           family={Mota},
           familyi={M\bibinitperiod},
           given={Carlos},
           giveni={C\bibinitperiod}}}%
        {{hash=beac3caffc2e8440f50688542c283d1b}{%
           family={Puppi},
           familyi={P\bibinitperiod},
           given={Dario},
           giveni={D\bibinitperiod}}}%
        {{hash=441db9ef2d56a2560fc017c02dce8287}{%
           family={Chiellini},
           familyi={C\bibinitperiod},
           given={Federica},
           giveni={F\bibinitperiod}}}%
        {{hash=a179c633417596b0f19b1a16f6d8582e}{%
           family={Chiellini},
           familyi={C\bibinitperiod},
           given={Emo},
           giveni={E\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {eng}%
      }
      \strng{namehash}{7a153e557f3589a2b0decec33951b647}
      \strng{fullhash}{28f1ba54fb3cb7edc7638643324dc555}
      \strng{bibnamehash}{28f1ba54fb3cb7edc7638643324dc555}
      \strng{authorbibnamehash}{28f1ba54fb3cb7edc7638643324dc555}
      \strng{authornamehash}{7a153e557f3589a2b0decec33951b647}
      \strng{authorfullhash}{28f1ba54fb3cb7edc7638643324dc555}
      \field{sortinit}{7}
      \field{sortinithash}{108d0be1b1bee9773a1173443802c0a3}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{issn}{1932-7005}
      \field{journaltitle}{Journal of Tissue Engineering and Regenerative Medicine}
      \field{month}{3}
      \field{number}{3}
      \field{title}{Additive manufacturing techniques for the production of tissue engineering constructs}
      \field{volume}{9}
      \field{year}{2015}
      \field{pages}{174\bibrangedash 190}
      \range{pages}{17}
      \verb{doi}
      \verb 10.1002/term.1635
      \endverb
      \keyw{additive manufacturing,Animals,Humans,Printing,Three-Dimensional,regenerative medicine,scaffold,solid freeform fabrication,tissue and organ printing,tissue engineering,Tissue Engineering,Tissue Scaffolds}
    \endentry
    \entry{nikolova_recent_2019}{article}{}
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        {{hash=2c9c408abb96ff394cd0c6bfad2108a0}{%
           family={Nikolova},
           familyi={N\bibinitperiod},
           given={Maria\bibnamedelima P.},
           giveni={M\bibinitperiod\bibinitdelim P\bibinitperiod}}}%
        {{hash=b0b7bb24a706fa5b68cf461582749a33}{%
           family={Chavali},
           familyi={C\bibinitperiod},
           given={Murthy\bibnamedelima S.},
           giveni={M\bibinitperiod\bibinitdelim S\bibinitperiod}}}%
      }
      \strng{namehash}{ee79554df05b98dd4b688609d2aca404}
      \strng{fullhash}{ee79554df05b98dd4b688609d2aca404}
      \strng{bibnamehash}{ee79554df05b98dd4b688609d2aca404}
      \strng{authorbibnamehash}{ee79554df05b98dd4b688609d2aca404}
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      \strng{authorfullhash}{ee79554df05b98dd4b688609d2aca404}
      \field{sortinit}{7}
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      \field{labelnamesource}{author}
      \field{labeltitlesource}{shorttitle}
      \field{issn}{2452-199X}
      \field{journaltitle}{Bioactive Materials}
      \field{month}{10}
      \field{shorttitle}{Recent advances in biomaterials for {3D} scaffolds}
      \field{title}{Recent advances in biomaterials for {3D} scaffolds: {A} review}
      \field{urlday}{17}
      \field{urlmonth}{9}
      \field{urlyear}{2021}
      \field{volume}{4}
      \field{year}{2019}
      \field{urldateera}{ce}
      \field{pages}{271\bibrangedash 292}
      \range{pages}{22}
      \verb{doi}
      \verb 10.1016/j.bioactmat.2019.10.005
      \endverb
      \verb{urlraw}
      \verb https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6829098/
      \endverb
      \verb{url}
      \verb https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6829098/
      \endverb
    \endentry
    \entry{lu_heat_1998}{article}{}
      \name{author}{3}{}{%
        {{hash=c81a3c63564789385533024ebe90717d}{%
           family={Lu},
           familyi={L\bibinitperiod},
           given={T.\bibnamedelimi J.},
           giveni={T\bibinitperiod\bibinitdelim J\bibinitperiod}}}%
        {{hash=469a69d32da1e1074a20d383ba613ed9}{%
           family={Stone},
           familyi={S\bibinitperiod},
           given={Howard\bibnamedelima A.},
           giveni={H\bibinitperiod\bibinitdelim A\bibinitperiod}}}%
        {{hash=4efbe37e741cfa6637ad06d22dcb5217}{%
           family={Ashby},
           familyi={A\bibinitperiod},
           given={M.\bibnamedelimi F.},
           giveni={M\bibinitperiod\bibinitdelim F\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {English (US)}%
      }
      \strng{namehash}{b88809f69e059e2ea057dc52bc0efa24}
      \strng{fullhash}{b88809f69e059e2ea057dc52bc0efa24}
      \strng{bibnamehash}{b88809f69e059e2ea057dc52bc0efa24}
      \strng{authorbibnamehash}{b88809f69e059e2ea057dc52bc0efa24}
      \strng{authornamehash}{b88809f69e059e2ea057dc52bc0efa24}
      \strng{authorfullhash}{b88809f69e059e2ea057dc52bc0efa24}
      \field{sortinit}{7}
      \field{sortinithash}{108d0be1b1bee9773a1173443802c0a3}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{issn}{1359-6454}
      \field{journaltitle}{Acta Materialia}
      \field{month}{6}
      \field{number}{10}
      \field{title}{Heat transfer in open-cell metal foams}
      \field{urlday}{17}
      \field{urlmonth}{9}
      \field{urlyear}{2021}
      \field{volume}{46}
      \field{year}{1998}
      \field{urldateera}{ce}
      \field{pages}{3619\bibrangedash 3635}
      \range{pages}{17}
      \verb{doi}
      \verb 10.1016/S1359-6454(98)00031-7
      \endverb
      \verb{urlraw}
      \verb https://collaborate.princeton.edu/en/publications/heat-transfer-in-open-cell-metal-foams
      \endverb
      \verb{url}
      \verb https://collaborate.princeton.edu/en/publications/heat-transfer-in-open-cell-metal-foams
      \endverb
    \endentry
    \entry{wadley_thermal_2007}{article}{}
      \name{author}{2}{}{%
        {{hash=d753ac7e38db8387afd604be0a65e7a4}{%
           family={Wadley},
           familyi={W\bibinitperiod},
           given={Haydn\bibnamedelimb N.\bibnamedelimi G.},
           giveni={H\bibinitperiod\bibinitdelim N\bibinitperiod\bibinitdelim G\bibinitperiod}}}%
        {{hash=fdbd7ae1ec0f20885835bf02ae5a9575}{%
           family={Queheillalt},
           familyi={Q\bibinitperiod},
           given={Douglas\bibnamedelima T.},
           giveni={D\bibinitperiod\bibinitdelim T\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{f2d2ba80f013eab8adbe76dfb4add8c3}
      \strng{fullhash}{f2d2ba80f013eab8adbe76dfb4add8c3}
      \strng{bibnamehash}{f2d2ba80f013eab8adbe76dfb4add8c3}
      \strng{authorbibnamehash}{f2d2ba80f013eab8adbe76dfb4add8c3}
      \strng{authornamehash}{f2d2ba80f013eab8adbe76dfb4add8c3}
      \strng{authorfullhash}{f2d2ba80f013eab8adbe76dfb4add8c3}
      \field{sortinit}{7}
      \field{sortinithash}{108d0be1b1bee9773a1173443802c0a3}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Numerous methods have recently emerged for fabricating cellular lattice structures with unit cells that can be repeated to create 3D space filling systems with very high interconnected pore fractions. These lattice structures possess exceptional mechanical strength resulting in highly efficient load supporting systems when configured as the cores of sandwich panels. These same structures also provide interesting possibilities for cross flow heat exchange. In this scenario, heat is transported from a locally heated facesheet through the lattice structure by conduction and is dissipated by a cross flow that propagates through the low flow resistant pore passages. The combination of efficient thermal conduction along the lattice trusses and low flow resistance through the pore channels results in highly efficient cross flow heat exchange. Recent research is investigating the use of hollow truss structures that enable their simultaneous use as heat pipes which significantly increases the efficiency of heat transport through the lattice and their mechanical strength. The relationships between heat transfer, frictional flow losses and topology of the lattice structure are discussed and opportunities for future developments identified.}
      \field{issn}{1662-9752}
      \field{journaltitle}{Materials Science Forum}
      \field{title}{Thermal {Applications} of {Cellular} {Lattice} {Structures}}
      \field{urlday}{17}
      \field{urlmonth}{9}
      \field{urlyear}{2021}
      \field{volume}{539-543}
      \field{year}{2007}
      \field{urldateera}{ce}
      \field{pages}{242\bibrangedash 247}
      \range{pages}{6}
      \verb{doi}
      \verb 10.4028/www.scientific.net/MSF.539-543.242
      \endverb
      \verb{urlraw}
      \verb https://www.scientific.net/MSF.539-543.242
      \endverb
      \verb{url}
      \verb https://www.scientific.net/MSF.539-543.242
      \endverb
    \endentry
    \entry{airshowconsultants_real_2013}{misc}{}
      \name{author}{1}{}{%
        {{hash=6e45e0d99e749c73357229ab653074b5}{%
           family={AirShowConsultants},
           familyi={A\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{6e45e0d99e749c73357229ab653074b5}
      \strng{fullhash}{6e45e0d99e749c73357229ab653074b5}
      \strng{bibnamehash}{6e45e0d99e749c73357229ab653074b5}
      \strng{authorbibnamehash}{6e45e0d99e749c73357229ab653074b5}
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      \strng{authorfullhash}{6e45e0d99e749c73357229ab653074b5}
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      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{The Vickers Wellington was a giant. Alright, it only had two engines and an 80 foot wingspan, but its deeds were the stuff of legend, and without this aircraft there would be no 1,000 bomber raids …}
      \field{journaltitle}{Shortfinals - aviation and more!}
      \field{month}{6}
      \field{title}{The {REAL} monster from {Loch} {Ness} – {Vickers} {Wellington}}
      \field{urlday}{11}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{year}{2013}
      \field{urldateera}{ce}
      \verb{urlraw}
      \verb https://shortfinals.org/2013/06/15/the-real-monster-from-loch-ness-vickers-wellington-r-for-robert/
      \endverb
      \verb{url}
      \verb https://shortfinals.org/2013/06/15/the-real-monster-from-loch-ness-vickers-wellington-r-for-robert/
      \endverb
    \endentry
    \entry{bensoussan_asymptotic_1978}{book}{}
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        {{hash=4a36e88b37487daae13c8e601165eace}{%
           family={Bensoussan},
           familyi={B\bibinitperiod},
           given={Alain},
           giveni={A\bibinitperiod}}}%
        {{hash=8acdd9c6b23c3b223619c0caa46a68c8}{%
           family={Lions},
           familyi={L\bibinitperiod},
           given={J.-L.},
           giveni={J\bibinithyphendelim L\bibinitperiod}}}%
        {{hash=5ffc027847e6bd6c9ba16811bd9e6930}{%
           family={Papanicolaou},
           familyi={P\bibinitperiod},
           given={George},
           giveni={G\bibinitperiod}}}%
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      \list{location}{1}{%
        {Amsterdam ; New York : New York}%
      }
      \list{publisher}{2}{%
        {North-Holland Pub. Co. ; sole distributors for the U.S.A.}%
        {Canada, Elsevier North-Holland}%
      }
      \strng{namehash}{a378eddb621f087aaeebb7a1956e990a}
      \strng{fullhash}{a378eddb621f087aaeebb7a1956e990a}
      \strng{bibnamehash}{a378eddb621f087aaeebb7a1956e990a}
      \strng{authorbibnamehash}{a378eddb621f087aaeebb7a1956e990a}
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      \field{isbn}{978-0-444-85172-7}
      \field{number}{v. 5}
      \field{series}{Studies in mathematics and its applications}
      \field{title}{Asymptotic analysis for periodic structures}
      \field{year}{1978}
      \keyw{Asymptotic theory,Boundary value problems,Differential equations,Partial,Numerical solutions,Probabilities}
    \endentry
    \entry{jenett_digital_2017}{article}{}
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        {{hash=adf0762ed660a193284dd64970657a51}{%
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           familyi={J\bibinitperiod},
           given={Benjamin},
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        {{hash=97d82c7b7ea13010f9886cd3d0b6af1a}{%
           family={Calisch},
           familyi={C\bibinitperiod},
           given={Sam},
           giveni={S\bibinitperiod}}}%
        {{hash=57e958e8d8c65542ed2f77e51b4ae912}{%
           family={Cellucci},
           familyi={C\bibinitperiod},
           given={Daniel},
           giveni={D\bibinitperiod}}}%
        {{hash=3a2810eae1b0cde1e8e9ec1566bdc7f5}{%
           family={Cramer},
           familyi={C\bibinitperiod},
           given={Nick},
           giveni={N\bibinitperiod}}}%
        {{hash=113a59d98dd032dc5604a9b82a5700b9}{%
           family={Gershenfeld},
           familyi={G\bibinitperiod},
           given={Neil},
           giveni={N\bibinitperiod}}}%
        {{hash=fdfd203ad8e9caf3ee6d4caf4a5e2faa}{%
           family={Swei},
           familyi={S\bibinitperiod},
           given={Sean},
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        {{hash=167d96b89d4ec4a25094057c319979eb}{%
           family={Cheung},
           familyi={C\bibinitperiod},
           given={Kenneth\bibnamedelima C.},
           giveni={K\bibinitperiod\bibinitdelim C\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{a40f2ef59f5e8041746be52219788385}
      \strng{fullhash}{9fb8be9243290c4add836d6612e61c1b}
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      \field{labeltitlesource}{title}
      \field{journaltitle}{Soft Robotics}
      \field{month}{3}
      \field{number}{1}
      \field{title}{Digital {Morphing} {Wing}: {Active} {Wing} {Shaping} {Concept} {Using} {Composite} {Lattice}-{Based} {Cellular} {Structures}}
      \field{urlday}{12}
      \field{urlmonth}{10}
      \field{urlyear}{2020}
      \field{volume}{4}
      \field{year}{2017}
      \field{urldateera}{ce}
      \field{pages}{33\bibrangedash 48}
      \range{pages}{16}
      \verb{doi}
      \verb 10.1089/soro.2016.0032
      \endverb
    \endentry
    \entry{dong_mechanical_2015}{article}{}
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        {{hash=57fe2b17ec18a2c399fdffb2146a1404}{%
           family={Dong},
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           given={Liang},
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        {{hash=97d4f3c392a867802c761e4b314041ff}{%
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           given={Vikram},
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        {{hash=304c1473fd00d9cfb5e98e85b139f3ff}{%
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           given={Haydn},
           giveni={H\bibinitperiod}}}%
      }
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        {en}%
      }
      \strng{namehash}{e56a2b981c7aa8663c6022ec0af2b25a}
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      \strng{bibnamehash}{e56a2b981c7aa8663c6022ec0af2b25a}
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      \field{abstract}{A simple snap-fit and vacuum brazing method has been developed to fabricate three dimensional space filling octet-truss lattice structures from Ti–6Al–4V alloy sheets. Using strut lengths of 7–25mm resulted in a relative density of the lattices ranging from 2\% to 16\%. The lattice elastic stiffness constants and strengths have been characterized under through-thickness compression and in-plane shear as a function of their relative density, and are shown to be well predicted by previously proposed micromechanical models adapted to account for the increased nodal mass and strut separations of the snap-fit lattice design. The Ti–6Al–4V octet-truss lattices exhibit excellent mechanical properties compared to other cellular material – cell topology combinations, and appear to be promising candidates for high temperature applications where a robust mechanical performance is required.}
      \field{issn}{0020-7683}
      \field{journaltitle}{International Journal of Solids and Structures}
      \field{month}{5}
      \field{title}{Mechanical response of {Ti}–{6Al}–{4V} octet-truss lattice structures}
      \field{urlday}{14}
      \field{urlmonth}{10}
      \field{urlyear}{2020}
      \field{volume}{60-61}
      \field{year}{2015}
      \field{urldateera}{ce}
      \field{pages}{107\bibrangedash 124}
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      \endverb
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      \verb{url}
      \verb http://www.sciencedirect.com/science/article/pii/S0020768315000669
      \endverb
      \keyw{Strength,Elastic stiffness,Octet-truss lattice,Titanium alloys}
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      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{10}
      \field{number}{4}
      \field{title}{Fail-safe truss topology optimization}
      \field{urlday}{30}
      \field{urlmonth}{3}
      \field{urlyear}{2021}
      \field{volume}{60}
      \field{year}{2019}
      \field{urldateera}{ce}
      \field{pages}{1605\bibrangedash 1618}
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      \verb{url}
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      \field{shorttitle}{Topology optimization of multi-scale structures}
      \field{title}{Topology optimization of multi-scale structures: a review}
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      \field{urlyear}{2021}
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    \entry{hunt_wraptor_2019}{article}{}
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        {en}%
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      \field{issn}{0263-8223}
      \field{journaltitle}{Composite Structures}
      \field{month}{12}
      \field{shorttitle}{{WrapToR} composite truss structures}
      \field{title}{{WrapToR} composite truss structures: {Improved} process and structural efficiency}
      \field{urlday}{4}
      \field{urlmonth}{7}
      \field{urlyear}{2021}
      \field{volume}{230}
      \field{year}{2019}
      \field{urldateera}{ce}
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      \verb 10.1016/j.compstruct.2019.111467
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      \verb{url}
      \verb https://www.sciencedirect.com/science/article/pii/S0263822319305835
      \endverb
      \keyw{Mechanical testing,Buckling,Composite truss structure,Filament winding}
    \endentry
    \entry{gershenfeld_macrofabrication_2015}{article}{}
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           family={Calisch},
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      \strng{namehash}{d51fbacd396183c6d2adb5f273e9391a}
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      \field{issn}{1554-2769}
      \field{journaltitle}{Architectural Design}
      \field{number}{5}
      \field{shorttitle}{Macrofabrication with {Digital} {Materials}}
      \field{title}{Macrofabrication with {Digital} {Materials}: {Robotic} {Assembly}}
      \field{urlday}{10}
      \field{urlmonth}{9}
      \field{urlyear}{2021}
      \field{volume}{85}
      \field{year}{2015}
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      \keyw{‘Geoprinting’,carbon-fibre loops,cuboct digital composite structure,digital composites project,finite element analysis (FEA),ganged resin transfer moulding (GRTM),Hurricane Katrina,James Clerk Maxwell,MIT's Center for Bits and Atoms,superstorm Sandy}
    \endentry
    \entry{jenett_bill-e_2017}{inproceedings}{}
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           given={Kenneth},
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      }
      \list{language}{1}{%
        {en}%
      }
      \list{location}{1}{%
        {Grapevine, Texas}%
      }
      \list{publisher}{2}{%
        {American Institute of Aeronautics}%
        {Astronautics}%
      }
      \strng{namehash}{ca5fab633fea255bf5fbf65375b75d56}
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      \field{booktitle}{25th {AIAA}/{AHS} {Adaptive} {Structures} {Conference}}
      \field{month}{1}
      \field{title}{{BILL}-{E}: {Robotic} {Platform} for {Locomotion} and {Manipulation} of {Lightweight} {Space} {Structures}}
      \field{urlday}{10}
      \field{urlmonth}{9}
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      \field{year}{2017}
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    \entry{niehs_recognition_2020}{inproceedings}{}
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        {{hash=c4104f2faa9df10356c59f9633cfe68d}{%
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        {{hash=6ac044c7f6e5da950b96068c256b09e5}{%
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        {{hash=adf0762ed660a193284dd64970657a51}{%
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      \field{booktitle}{2020 {IEEE} {International} {Conference} on {Robotics} and {Automation} ({ICRA})}
      \field{month}{5}
      \field{title}{Recognition and {Reconfiguration} of {Lattice}-{Based} {Cellular} {Structures} by {Simple} {Robots}}
      \field{year}{2020}
      \field{pages}{8252\bibrangedash 8259}
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      \verb{doi}
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      \keyw{Robot sensing systems,Autonomous robots,Lattices,Shape,Tiles}
    \endentry
    \entry{opgenoord_transonic_2018}{thesis}{}
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      \strng{bibnamehash}{1e532a214ee6299c5dc8de6edb5def5d}
      \strng{authorbibnamehash}{1e532a214ee6299c5dc8de6edb5def5d}
      \strng{authornamehash}{1e532a214ee6299c5dc8de6edb5def5d}
      \strng{authorfullhash}{1e532a214ee6299c5dc8de6edb5def5d}
      \field{sortinit}{8}
      \field{sortinithash}{a231b008ebf0ecbe0b4d96dcc159445f}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{month}{8}
      \field{title}{Transonic {Flutter} {Prediction} and {Aeroelastic} {Tailoring} for {Next}-{Generation} {Transport} {Aircraft}}
      \field{type}{phdthesis}
      \field{year}{2018}
    \endentry
    \entry{park_design_2022}{article}{}
      \name{author}{3}{}{%
        {{hash=3eaac82373f7b0dc528b6353c7422121}{%
           family={Park},
           familyi={P\bibinitperiod},
           given={Kwang-Min},
           giveni={K\bibinithyphendelim M\bibinitperiod}}}%
        {{hash=709966ecf28518816ced82c9e3829735}{%
           family={Min},
           familyi={M\bibinitperiod},
           given={Kyung-Sung},
           giveni={K\bibinithyphendelim S\bibinitperiod}}}%
        {{hash=7f2de28faedbba0f6ccbc0ace1096800}{%
           family={Roh},
           familyi={R\bibinitperiod},
           given={Young-Sook},
           giveni={Y\bibinithyphendelim S\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{7b14d9d928d7495c30fea9656d14a2ee}
      \strng{fullhash}{7b14d9d928d7495c30fea9656d14a2ee}
      \strng{bibnamehash}{7b14d9d928d7495c30fea9656d14a2ee}
      \strng{authorbibnamehash}{7b14d9d928d7495c30fea9656d14a2ee}
      \strng{authornamehash}{7b14d9d928d7495c30fea9656d14a2ee}
      \strng{authorfullhash}{7b14d9d928d7495c30fea9656d14a2ee}
      \field{sortinit}{8}
      \field{sortinithash}{a231b008ebf0ecbe0b4d96dcc159445f}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{shorttitle}
      \field{abstract}{Additive manufacturing enables innovative structural design for industrial applications, which allows the fabrication of lattice structures with enhanced mechanical properties, including a high strength-to-relative-density ratio. However, to commercialize lattice structures, it is necessary to define the designability of lattice geometries and characterize the associated mechanical responses, including the compressive strength. The objective of this study was to provide an optimized design process for lattice structures and develop a lattice structure characterization database that can be used to differentiate unit cell topologies and guide the unit cell selection for compression-dominated structures. Linear static finite element analysis (FEA), nonlinear FEA, and experimental tests were performed on 11 types of unit cell-based lattice structures with dimensions of 20 mm × 20 mm × 20 mm. Consequently, under the same relative density conditions, simple cubic, octahedron, truncated cube, and truncated octahedron-based lattice structures with a 3 × 3 × 3 array pattern showed the best axial compressive strength properties. Correlations among the unit cell types, lattice structure topologies, relative densities, unit cell array patterns, and mechanical properties were identified, indicating their influence in describing and predicting the behaviors of lattice structures.}
      \field{issn}{1996-1944}
      \field{journaltitle}{Materials}
      \field{month}{1}
      \field{note}{Number: 1 Publisher: Multidisciplinary Digital Publishing Institute}
      \field{number}{1}
      \field{shorttitle}{Design {Optimization} of {Lattice} {Structures} under {Compression}}
      \field{title}{Design {Optimization} of {Lattice} {Structures} under {Compression}: {Study} of {Unit} {Cell} {Types} and {Cell} {Arrangements}}
      \field{urlday}{5}
      \field{urlmonth}{2}
      \field{urlyear}{2024}
      \field{volume}{15}
      \field{year}{2022}
      \field{urldateera}{ce}
      \field{pages}{97}
      \range{pages}{1}
      \verb{doi}
      \verb 10.3390/ma15010097
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\RKCIJLVS\\Park et al. - 2022 - Design Optimization of Lattice Structures under Co.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://www.mdpi.com/1996-1944/15/1/97
      \endverb
      \verb{url}
      \verb https://www.mdpi.com/1996-1944/15/1/97
      \endverb
      \keyw{3D printing,additive manufacturing,design optimization,mechanical properties,selective laser melting,unit cell,variable-density lattice structures}
    \endentry
    \entry{xu_design_2016}{article}{}
      \name{author}{5}{}{%
        {{hash=af062549b51f2c8147108b40bcda17fc}{%
           family={Xu},
           familyi={X\bibinitperiod},
           given={Shanqing},
           giveni={S\bibinitperiod}}}%
        {{hash=3fa98a4fcbafa9bbbc6a93f2c1819af4}{%
           family={Shen},
           familyi={S\bibinitperiod},
           given={Jianhu},
           giveni={J\bibinitperiod}}}%
        {{hash=ccb8cae1fb9a304a529e14b66f624e7d}{%
           family={Zhou},
           familyi={Z\bibinitperiod},
           given={Shiwei},
           giveni={S\bibinitperiod}}}%
        {{hash=3b955d07585b092f29d14ccc08478da7}{%
           family={Huang},
           familyi={H\bibinitperiod},
           given={Xiaodong},
           giveni={X\bibinitperiod}}}%
        {{hash=8378d5b4061a021880b29f2f73452923}{%
           family={Xie},
           familyi={X\bibinitperiod},
           given={Yi\bibnamedelima Min},
           giveni={Y\bibinitperiod\bibinitdelim M\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{b385709a31c4ac3b39c99c61d60324ed}
      \strng{fullhash}{b45b7807bffe0bcb924e9f7b35c92030}
      \strng{bibnamehash}{b45b7807bffe0bcb924e9f7b35c92030}
      \strng{authorbibnamehash}{b45b7807bffe0bcb924e9f7b35c92030}
      \strng{authornamehash}{b385709a31c4ac3b39c99c61d60324ed}
      \strng{authorfullhash}{b45b7807bffe0bcb924e9f7b35c92030}
      \field{sortinit}{8}
      \field{sortinithash}{a231b008ebf0ecbe0b4d96dcc159445f}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Recent advances in additive manufacturing make it possible to fabricate periodic lattice structures with complex configurations. However, a proper design strategy to achieve lattice structures with controlled anisotropy is still unavailable. There is an urgent need to fill this knowledge gap in order to develop mechanical metamaterials with prescribed properties. Here we propose two different methodologies to design lattice structures with controlled anisotropy. As examples, we created two new families of lattice structures with isotropic elasticity and cubic symmetric geometry. The findings of this work provide simple and effective strategies for exploring lightweight metamaterials with desired mechanical properties.}
      \field{issn}{0264-1275}
      \field{journaltitle}{Materials \&amp; Design}
      \field{month}{3}
      \field{title}{Design of lattice structures with controlled anisotropy}
      \field{urlday}{20}
      \field{urlmonth}{10}
      \field{urlyear}{2020}
      \field{volume}{93}
      \field{year}{2016}
      \field{urldateera}{ce}
      \field{pages}{443\bibrangedash 447}
      \range{pages}{5}
      \verb{doi}
      \verb 10.1016/j.matdes.2016.01.007
      \endverb
      \verb{file}
      \verb ScienceDirect Full Text PDF:D\:\\estragio\\Zotero\\storage\\PMMTEW6R\\Xu et al. - 2016 - Design of lattice structures with controlled aniso.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb http://www.sciencedirect.com/science/article/pii/S0264127516300120
      \endverb
      \verb{url}
      \verb http://www.sciencedirect.com/science/article/pii/S0264127516300120
      \endverb
      \keyw{Homogenization,Lattice structures,Anisotropy,Metamaterials}
    \endentry
    \entry{song_investigation_2021}{article}{}
      \name{author}{6}{}{%
        {{hash=e9a8af0fc472b905fa95817f04a6e52e}{%
           family={Song},
           familyi={S\bibinitperiod},
           given={Jun},
           giveni={J\bibinitperiod}}}%
        {{hash=e1a7508e7506b61d8f3cf1921b7a64a5}{%
           family={Tang},
           familyi={T\bibinitperiod},
           given={Qian},
           giveni={Q\bibinitperiod}}}%
        {{hash=ef2eacb83e3cab09e32701198aa3ea23}{%
           family={Feng},
           familyi={F\bibinitperiod},
           given={Qixiang},
           giveni={Q\bibinitperiod}}}%
        {{hash=9b20ab98b4b424a2e7b866fc97d9259d}{%
           family={Ma},
           familyi={M\bibinitperiod},
           given={Shuai},
           giveni={S\bibinitperiod}}}%
        {{hash=b8e34fd9701f0d40628937ad47c27465}{%
           family={Guo},
           familyi={G\bibinitperiod},
           given={Fuyu},
           giveni={F\bibinitperiod}}}%
        {{hash=6813fb4b0e009cb44b90f75fa60c4f85}{%
           family={Han},
           familyi={H\bibinitperiod},
           given={Quanquan},
           giveni={Q\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{1cce1dbff0d2ffe3ad766b478f0f9907}
      \strng{fullhash}{8d24321105b3d82713dad1062d971461}
      \strng{bibnamehash}{8d24321105b3d82713dad1062d971461}
      \strng{authorbibnamehash}{8d24321105b3d82713dad1062d971461}
      \strng{authornamehash}{1cce1dbff0d2ffe3ad766b478f0f9907}
      \strng{authorfullhash}{8d24321105b3d82713dad1062d971461}
      \field{sortinit}{8}
      \field{sortinithash}{a231b008ebf0ecbe0b4d96dcc159445f}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Selective laser melting (SLM)-produced variable-density (VD) lattice structures are deemed a promising solution to lightweight design. However, due to the large number of cells in the structures, designing VD structures is still time-consuming and exhibits poor adaptability to external load. Therefore, in order to decrease the number of design variables in VD design, this paper proposed a modelling approach for VD lattice structures manufactured using SLM. The stress values provided by ﬁnite element analysis (FEA) were grouped according to k-means clustering, where the sizes of lattice cells in the same group remain identical. Then the relative densities of cells’ in all groups are obtained and the VD model is generated. By taking the design of a VD lattice beam as an example, the feasibility of the proposed method was veriﬁed by conducting FEA and three-point bending tests on SLM-produced Ti6Al4V samples, as well as using morphological observation measures. The results show that the number of design variables for reconstructing the beam was decreased from 125 to 8, and the VD samples reached the designed carrying capacity and also presented superior lightweight performance compared with their isovolumetric homogenous counterparts.}
      \field{issn}{02641275}
      \field{journaltitle}{Materials \&amp; Design}
      \field{month}{12}
      \field{title}{Investigation on the modelling approach for variable-density lattice structures fabricated using selective laser melting}
      \field{urlday}{18}
      \field{urlmonth}{2}
      \field{urlyear}{2022}
      \field{volume}{212}
      \field{year}{2021}
      \field{urldateera}{ce}
      \field{pages}{110236}
      \range{pages}{1}
      \verb{doi}
      \verb 10.1016/j.matdes.2021.110236
      \endverb
      \verb{file}
      \verb Song et al. - 2021 - Investigation on the modelling approach for variab.pdf:D\:\\estragio\\Zotero\\storage\\IM7GCE8P\\Song et al. - 2021 - Investigation on the modelling approach for variab.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://linkinghub.elsevier.com/retrieve/pii/S0264127521007917
      \endverb
      \verb{url}
      \verb https://linkinghub.elsevier.com/retrieve/pii/S0264127521007917
      \endverb
    \endentry
    \entry{zhou_coc_1991}{article}{}
      \name{author}{2}{}{%
        {{hash=3edb51e096c6e1b022984c9159c4df2d}{%
           family={Zhou},
           familyi={Z\bibinitperiod},
           given={M.},
           giveni={M\bibinitperiod}}}%
        {{hash=2dd717bb9ecafd6aa2723e522b7aa056}{%
           family={Rozvany},
           familyi={R\bibinitperiod},
           given={G.\bibnamedelimi I.\bibnamedelimi N.},
           giveni={G\bibinitperiod\bibinitdelim I\bibinitperiod\bibinitdelim N\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{3722e7f924b6b5d5b00a74ea085c5bf9}
      \strng{fullhash}{3722e7f924b6b5d5b00a74ea085c5bf9}
      \strng{bibnamehash}{3722e7f924b6b5d5b00a74ea085c5bf9}
      \strng{authorbibnamehash}{3722e7f924b6b5d5b00a74ea085c5bf9}
      \strng{authornamehash}{3722e7f924b6b5d5b00a74ea085c5bf9}
      \strng{authorfullhash}{3722e7f924b6b5d5b00a74ea085c5bf9}
      \field{sortinit}{8}
      \field{sortinithash}{a231b008ebf0ecbe0b4d96dcc159445f}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{shorttitle}
      \field{abstract}{After outlining analytical methods for layout optimization and illustrating them with examples, the COC algorithm is applied to the simultaneous optimization of the topology and geometry of trusses with many thousand potential members. The numerical results obtained are shown to be in close agreement (up to twelve significant digits) with analytical results. Finally, the problem of generalized shape optimization (finding the best boundary topology and shape) is discussed.}
      \field{issn}{0045-7825}
      \field{journaltitle}{Computer Methods in Applied Mechanics and Engineering}
      \field{month}{8}
      \field{number}{1}
      \field{series}{Second {World} {Congress} on {Computational} {Mechanics}}
      \field{shorttitle}{The {COC} algorithm, {Part} {II}}
      \field{title}{The {COC} algorithm, {Part} {II}: {Topological}, geometrical and generalized shape optimization}
      \field{urlday}{14}
      \field{urlmonth}{9}
      \field{urlyear}{2021}
      \field{volume}{89}
      \field{year}{1991}
      \field{urldateera}{ce}
      \field{pages}{309\bibrangedash 336}
      \range{pages}{28}
      \verb{doi}
      \verb 10.1016/0045-7825(91)90046-9
      \endverb
      \verb{file}
      \verb ScienceDirect Full Text PDF:D\:\\estragio\\Zotero\\storage\\4VK2TZP2\\Zhou and Rozvany - 1991 - The COC algorithm, Part II Topological, geometric.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://www.sciencedirect.com/science/article/pii/0045782591900469
      \endverb
      \verb{url}
      \verb https://www.sciencedirect.com/science/article/pii/0045782591900469
      \endverb
    \endentry
    \entry{wang_concurrent_2020}{article}{}
      \name{author}{6}{}{%
        {{hash=5f314f633295db632e90990a3f8297a1}{%
           family={Wang},
           familyi={W\bibinitperiod},
           given={Chuang},
           giveni={C\bibinitperiod}}}%
        {{hash=3096b3ab155327f6bd7040fd0525c85b}{%
           family={Gu},
           familyi={G\bibinitperiod},
           given={Xiaojun},
           giveni={X\bibinitperiod}}}%
        {{hash=c828950c799bfbcdc00af051cb188668}{%
           family={Zhu},
           familyi={Z\bibinitperiod},
           given={Jihong},
           giveni={J\bibinitperiod}}}%
        {{hash=bf1ff213b7aecc840a52e2eecdc6d183}{%
           family={Zhou},
           familyi={Z\bibinitperiod},
           given={Han},
           giveni={H\bibinitperiod}}}%
        {{hash=4c02cbc53f53a2072070ee0e55153b43}{%
           family={Li},
           familyi={L\bibinitperiod},
           given={Shaoying},
           giveni={S\bibinitperiod}}}%
        {{hash=1703058ac1e82b63641879518d53a9de}{%
           family={Zhang},
           familyi={Z\bibinitperiod},
           given={Weihong},
           giveni={W\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{22eb3d18b5679a61696cb93168f6d540}
      \strng{fullhash}{e4cd621548b1c58127f9d20f2851620f}
      \strng{bibnamehash}{e4cd621548b1c58127f9d20f2851620f}
      \strng{authorbibnamehash}{e4cd621548b1c58127f9d20f2851620f}
      \strng{authornamehash}{22eb3d18b5679a61696cb93168f6d540}
      \strng{authorfullhash}{e4cd621548b1c58127f9d20f2851620f}
      \field{extraname}{2}
      \field{sortinit}{8}
      \field{sortinithash}{a231b008ebf0ecbe0b4d96dcc159445f}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{In this work, a novel design and modeling method is proposed to obtain hierarchical structures with non-uniform lattice microstructures based on density-based topology optimization. First of all, a parametric concept is proposed to generate a family of parameterized lattice microstructures that present similar topological features. In order to balance the structural performance and computational efficiency, we construct a Parameterized Interpolation for Lattice Material (PILM) model and the mathematical formulation incorporates two new design variables. At the macroscale, the relative density variable is applied to describe material volume fraction in the design domain, instead of using the pseudo-density in the Solid Isotropic Material with Penalization (SIMP) model. At the microscale, each macroelement is regarded as an individual microstructure controlled by an aspect ratio variable. The equivalent properties of parameterized lattice microstructures can be derived by interpolating the effective elastic matrixes of several typical microstructure unit cells, which avoid expensive iterative homogenization calculations during optimization procedure. Hence, the multiscale concurrent design method can optimize the macroscopic distribution and their spatially varying microstructural configurations simultaneously at an affordable computation cost. Several numerical examples are presented to demonstrate the effectiveness of the proposed approach. Furthermore, the obtained hierarchical structures with non-uniform lattice microstructures show good manufacturability and remarkably improved structural performance by means of the additive manufacturing and experimental testing, compared to the designs with uniform lattice microstructures.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{3}
      \field{number}{3}
      \field{title}{Concurrent design of hierarchical structures with three-dimensional parameterized lattice microstructures for additive manufacturing}
      \field{urlday}{12}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{61}
      \field{year}{2020}
      \field{urldateera}{ce}
      \field{pages}{869\bibrangedash 894}
      \range{pages}{26}
      \verb{doi}
      \verb 10.1007/s00158-019-02408-2
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\568KHYHP\\Wang et al. - 2020 - Concurrent design of hierarchical structures with .pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/s00158-019-02408-2
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s00158-019-02408-2
      \endverb
      \keyw{Topology optimization,Additive manufacturing,Concurrent design,Hierarchical structures,Lattice microstructures}
    \endentry
    \entry{rodrigues_hierarchical_2002}{article}{}
      \name{author}{3}{}{%
        {{hash=23ae4ab9501bf00f3c96e374a3e4caec}{%
           family={Rodrigues},
           familyi={R\bibinitperiod},
           given={H.},
           giveni={H\bibinitperiod}}}%
        {{hash=a46b64f3808c21131762bc2d0b5ba331}{%
           family={Guedes},
           familyi={G\bibinitperiod},
           given={J.M.},
           giveni={J\bibinitperiod}}}%
        {{hash=97d8fd057ddcb0a0d4253910c14e38e9}{%
           family={Bendsoe},
           familyi={B\bibinitperiod},
           given={M.P.},
           giveni={M\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{fb4f9df781da23ac3080e6046b3a14f7}
      \strng{fullhash}{fb4f9df781da23ac3080e6046b3a14f7}
      \strng{bibnamehash}{fb4f9df781da23ac3080e6046b3a14f7}
      \strng{authorbibnamehash}{fb4f9df781da23ac3080e6046b3a14f7}
      \strng{authornamehash}{fb4f9df781da23ac3080e6046b3a14f7}
      \strng{authorfullhash}{fb4f9df781da23ac3080e6046b3a14f7}
      \field{sortinit}{8}
      \field{sortinithash}{a231b008ebf0ecbe0b4d96dcc159445f}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This paper describes a hierarchical computational procedure for optimizing material distribution as well as the local material properties of mechanical elements. The local properties are designed using a topology design approach, leading to single scale microstructures, which may be restricted in various ways, based on design and manufacturing criteria. Implementation issues are also discussed and computational results illustrate the nature of the procedure.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{8}
      \field{number}{1}
      \field{title}{Hierarchical optimization of material and structure}
      \field{urlday}{12}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{24}
      \field{year}{2002}
      \field{urldateera}{ce}
      \field{pages}{1\bibrangedash 10}
      \range{pages}{10}
      \verb{doi}
      \verb 10.1007/s00158-002-0209-z
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\8LRHMF5A\\Rodrigues et al. - 2002 - Hierarchical optimization of material and structur.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/s00158-002-0209-z
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s00158-002-0209-z
      \endverb
      \keyw{Key words: optimization,topology,hierarchical,microstructure,material}
    \endentry
    \entry{pantz_post-treatment_2008}{article}{}
      \name{author}{2}{}{%
        {{hash=374ce21463f1753387a02b8b1b53c577}{%
           family={Pantz},
           familyi={P\bibinitperiod},
           given={O.},
           giveni={O\bibinitperiod}}}%
        {{hash=2cede8e9d80dcb76ff1c070c4c4b2555}{%
           family={Trabelsi},
           familyi={T\bibinitperiod},
           given={K.},
           giveni={K\bibinitperiod}}}%
      }
      \strng{namehash}{bee37b259d50e43e2be8fa547043a152}
      \strng{fullhash}{bee37b259d50e43e2be8fa547043a152}
      \strng{bibnamehash}{bee37b259d50e43e2be8fa547043a152}
      \strng{authorbibnamehash}{bee37b259d50e43e2be8fa547043a152}
      \strng{authornamehash}{bee37b259d50e43e2be8fa547043a152}
      \strng{authorfullhash}{bee37b259d50e43e2be8fa547043a152}
      \field{sortinit}{9}
      \field{sortinithash}{0a5ebc79d83c96b6579069544c73c7d4}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Following an idea of G. Nguetseng, the author defines a notion of “two-scale” convergence, which is aimed at a better description of sequences of oscillating functions. Bounded sequences in \$L{\textasciicircum}2 ({\textbackslash}Omega )\$ are proven to be relatively compact with respect to this new type of convergence. A corrector-type theorem (i.e., which permits, in some cases, replacing a sequence by its “two-scale” limit, up to a strongly convergent remainder in \$L{\textasciicircum}2 ({\textbackslash}Omega )\$) is also established. These results are especially useful for the homogenization of partial differential equations with periodically oscillating coefficients. In particular, a new method for proving the convergence of homogenization processes is proposed, which is an alternative to the so-called energy method of Tartar. The power and simplicity of the two-scale convergence method is demonstrated on several examples, including the homogenization of both linear and nonlinear second-order elliptic equations.}
      \field{issn}{0363-0129}
      \field{journaltitle}{SIAM Journal on Control and Optimization}
      \field{month}{1}
      \field{number}{3}
      \field{title}{A {Post}-{Treatment} of the {Homogenization} {Method} for {Shape} {Optimization}}
      \field{urlday}{12}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{47}
      \field{year}{2008}
      \field{urldateera}{ce}
      \field{pages}{1380\bibrangedash 1398}
      \range{pages}{19}
      \verb{doi}
      \verb 10.1137/070688900
      \endverb
      \verb{urlraw}
      \verb https://epubs.siam.org/doi/10.1137/070688900
      \endverb
      \verb{url}
      \verb https://epubs.siam.org/doi/10.1137/070688900
      \endverb
    \endentry
    \entry{groen_homogenization-based_2018}{article}{}
      \name{author}{2}{}{%
        {{hash=b3a28961a952de6972668feb8d306517}{%
           family={Groen},
           familyi={G\bibinitperiod},
           given={Jeroen\bibnamedelima P.},
           giveni={J\bibinitperiod\bibinitdelim P\bibinitperiod}}}%
        {{hash=d76f1c09e8d8d06e1b7c3c254efeae1a}{%
           family={Sigmund},
           familyi={S\bibinitperiod},
           given={Ole},
           giveni={O\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{994812b01771f6397b1e2119ee41a104}
      \strng{fullhash}{994812b01771f6397b1e2119ee41a104}
      \strng{bibnamehash}{994812b01771f6397b1e2119ee41a104}
      \strng{authorbibnamehash}{994812b01771f6397b1e2119ee41a104}
      \strng{authornamehash}{994812b01771f6397b1e2119ee41a104}
      \strng{authorfullhash}{994812b01771f6397b1e2119ee41a104}
      \field{sortinit}{9}
      \field{sortinithash}{0a5ebc79d83c96b6579069544c73c7d4}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This paper presents a projection method to obtain high-resolution, manufacturable structures from efficient and coarse-scale homogenization-based topology optimization results. The presented approach bridges coarse and fine scale, such that the complex periodic microstructures can be represented by a smooth and continuous lattice on the fine mesh. A heuristic methodology allows control of the projected topology, such that a minimum length scale on both solid and void features is ensured in the final result. Numerical examples show excellent behavior of the method, where performances of the projected designs are almost equal to the homogenization-based solutions. A significant reduction in computational cost is observed compared to conventional topology optimization approaches.}
      \field{issn}{1097-0207}
      \field{journaltitle}{International Journal for Numerical Methods in Engineering}
      \field{number}{8}
      \field{title}{Homogenization-based topology optimization for high-resolution manufacturable microstructures}
      \field{urlday}{12}
      \field{urlmonth}{10}
      \field{urlyear}{2020}
      \field{volume}{113}
      \field{year}{2018}
      \field{urldateera}{ce}
      \field{pages}{1148\bibrangedash 1163}
      \range{pages}{16}
      \verb{doi}
      \verb 10.1002/nme.5575
      \endverb
      \verb{file}
      \verb Groen et Sigmund - 2018 - Homogenization-based topology optimization for hig.pdf:D\:\\estragio\\Zotero\\storage\\DX2TUF6U\\Groen et Sigmund - 2018 - Homogenization-based topology optimization for hig.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.5575
      \endverb
      \verb{url}
      \verb https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.5575
      \endverb
      \keyw{high-resolution,homogenization,manufacturing constraints,topology optimization}
    \endentry
    \entry{guedes_preprocessing_1990}{article}{}
      \name{author}{2}{}{%
        {{hash=d3720e1ef069240782b4f9256b58ef90}{%
           family={Guedes},
           familyi={G\bibinitperiod},
           given={JoséMiranda},
           giveni={J\bibinitperiod}}}%
        {{hash=a76119010369dea475552b407ae8c3c0}{%
           family={Kikuchi},
           familyi={K\bibinitperiod},
           given={Noboru},
           giveni={N\bibinitperiod}}}%
      }
      \strng{namehash}{af51693957d372493f684ac2cc2c195d}
      \strng{fullhash}{af51693957d372493f684ac2cc2c195d}
      \strng{bibnamehash}{af51693957d372493f684ac2cc2c195d}
      \strng{authorbibnamehash}{af51693957d372493f684ac2cc2c195d}
      \strng{authornamehash}{af51693957d372493f684ac2cc2c195d}
      \strng{authorfullhash}{af51693957d372493f684ac2cc2c195d}
      \field{sortinit}{9}
      \field{sortinithash}{0a5ebc79d83c96b6579069544c73c7d4}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This paper discusses the homogenization method to determine the effective average elastic constants of linear elasticity of general composite materials by considering their microstructure. After giving a brief theory of the homogenization method, a finite element approximation is introduced with convergence study and corresponding error estimate. Applying these, computer programs PREMAT and POSTMAT are developed for preprocessing and postprocessing of material characterization of composite materials. Using these programs, the homogenized elastic constants for macroscopic stress analysis are obtained for typical composite materials to show their capability. Finally, the adaptive finite element method is introduced to improve the accuracy of the finite element approximation.}
      \field{issn}{0045-7825}
      \field{journaltitle}{Computer Methods in Applied Mechanics and Engineering}
      \field{month}{10}
      \field{number}{2}
      \field{title}{Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods}
      \field{urlday}{12}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{83}
      \field{year}{1990}
      \field{urldateera}{ce}
      \field{pages}{143\bibrangedash 198}
      \range{pages}{56}
      \verb{doi}
      \verb 10.1016/0045-7825(90)90148-F
      \endverb
      \verb{urlraw}
      \verb https://www.sciencedirect.com/science/article/pii/004578259090148F
      \endverb
      \verb{url}
      \verb https://www.sciencedirect.com/science/article/pii/004578259090148F
      \endverb
    \endentry
    \entry{cadman_design_2013}{article}{}
      \name{author}{4}{}{%
        {{hash=2c8ff2195b8f507c31f636bdc893839f}{%
           family={Cadman},
           familyi={C\bibinitperiod},
           given={Joseph\bibnamedelima E.},
           giveni={J\bibinitperiod\bibinitdelim E\bibinitperiod}}}%
        {{hash=ccb8cae1fb9a304a529e14b66f624e7d}{%
           family={Zhou},
           familyi={Z\bibinitperiod},
           given={Shiwei},
           giveni={S\bibinitperiod}}}%
        {{hash=2ccead0226705701db8d73c04598a2cd}{%
           family={Chen},
           familyi={C\bibinitperiod},
           given={Yuhang},
           giveni={Y\bibinitperiod}}}%
        {{hash=16a77262afb7cc9b0229c21f168bd098}{%
           family={Li},
           familyi={L\bibinitperiod},
           given={Qing},
           giveni={Q\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{6cd408aa9cacc2c90feb75880199834c}
      \strng{fullhash}{f8c50b1d3a791ffd640044b4526d1594}
      \strng{bibnamehash}{f8c50b1d3a791ffd640044b4526d1594}
      \strng{authorbibnamehash}{f8c50b1d3a791ffd640044b4526d1594}
      \strng{authornamehash}{6cd408aa9cacc2c90feb75880199834c}
      \strng{authorfullhash}{f8c50b1d3a791ffd640044b4526d1594}
      \field{sortinit}{9}
      \field{sortinithash}{0a5ebc79d83c96b6579069544c73c7d4}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{The design of periodic microstructural composite materials to achieve specific properties has been a major area of interest in material research. Tailoring different physical properties by modifying the microstructural architecture in unit cells is one of the main concerns in exploring and developing novel multi-functional cellular composites and has led to the development of a large variety of mathematical models, theories and methodologies for improving the performance of such materials. This paper provides a critical review on the state-of-the-art advances in the design of periodic microstructures of multi-functional materials for a range of physical properties, such as elastic stiffness, Poisson’s ratio, thermal expansion coefficient, conductivity, fluidic permeability, particle diffusivity, electrical permittivity and magnetic permeability, etc.}
      \field{issn}{1573-4803}
      \field{journaltitle}{Journal of Materials Science}
      \field{month}{1}
      \field{number}{1}
      \field{title}{On design of multi-functional microstructural materials}
      \field{urlday}{9}
      \field{urlmonth}{2}
      \field{urlyear}{2024}
      \field{volume}{48}
      \field{year}{2013}
      \field{urldateera}{ce}
      \field{pages}{51\bibrangedash 66}
      \range{pages}{16}
      \verb{doi}
      \verb 10.1007/s10853-012-6643-4
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\XBQN2MVE\\Cadman et al. - 2013 - On design of multi-functional microstructural mate.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/s10853-012-6643-4
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s10853-012-6643-4
      \endverb
      \keyw{Pareto Front,Solid Isotropic Material With Penalization,Topology Optimization,Topology Optimization Problem,Wall Shear Stress}
    \endentry
    \entry{alexandersen_topology_2015}{article}{}
      \name{author}{2}{}{%
        {{hash=a17f5df4246f7ceed2b474760fcbc96a}{%
           family={Alexandersen},
           familyi={A\bibinitperiod},
           given={Joe},
           giveni={J\bibinitperiod}}}%
        {{hash=7eac115f940766787d974635bdfc7da2}{%
           family={Lazarov},
           familyi={L\bibinitperiod},
           given={Boyan\bibnamedelima S.},
           giveni={B\bibinitperiod\bibinitdelim S\bibinitperiod}}}%
      }
      \strng{namehash}{e97a3fc953cccace86d7d46426439fa6}
      \strng{fullhash}{e97a3fc953cccace86d7d46426439fa6}
      \strng{bibnamehash}{e97a3fc953cccace86d7d46426439fa6}
      \strng{authorbibnamehash}{e97a3fc953cccace86d7d46426439fa6}
      \strng{authornamehash}{e97a3fc953cccace86d7d46426439fa6}
      \strng{authorfullhash}{e97a3fc953cccace86d7d46426439fa6}
      \field{sortinit}{9}
      \field{sortinithash}{0a5ebc79d83c96b6579069544c73c7d4}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This paper applies topology optimisation to the design of structures with periodic and layered microstructural details without length scale separation, i.e. considering the complete macroscopic structure and its response, while resolving all microstructural details, as compared to the often used homogenisation approach. The approach takes boundary conditions into account and ensures connected and macroscopically optimised microstructures regardless of the difference in micro- and macroscopic length scales. This results in microstructures tailored for specific applications rather than specific properties. Manufacturability is further ensured by the use of robust topology optimisation. Dealing with the complete macroscopic structure and its response is computationally challenging as very fine discretisations are needed in order to resolve all microstructural details. Therefore, this paper shows the benefits of applying a contrast-independent spectral preconditioner based on the multiscale finite element method (MsFEM) to large structures with fully-resolved microstructural details. It is shown that a single preconditioner can be reused for many design iterations and used for several design realisations, in turn leading to massive savings in computational cost. The density-based topology optimisation approach combined with a Heaviside projection filter and a stochastic robust formulation is used on various problems, with both periodic and layered microstructures. The presented approach is shown to allow for the topology optimisation of very large problems in Matlab, specifically a problem with 26 million displacement degrees of freedom in 26 hours using a single computational thread.}
      \field{issn}{0045-7825}
      \field{journaltitle}{Computer Methods in Applied Mechanics and Engineering}
      \field{month}{6}
      \field{title}{Topology optimisation of manufacturable microstructural details without length scale separation using a spectral coarse basis preconditioner}
      \field{urlday}{9}
      \field{urlmonth}{2}
      \field{urlyear}{2024}
      \field{volume}{290}
      \field{year}{2015}
      \field{urldateera}{ce}
      \field{pages}{156\bibrangedash 182}
      \range{pages}{27}
      \verb{doi}
      \verb 10.1016/j.cma.2015.02.028
      \endverb
      \verb{file}
      \verb Submitted Version:D\:\\estragio\\Zotero\\storage\\YZCDIRDQ\\Alexandersen and Lazarov - 2015 - Topology optimisation of manufacturable microstruc.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://www.sciencedirect.com/science/article/pii/S0045782515000924
      \endverb
      \verb{url}
      \verb https://www.sciencedirect.com/science/article/pii/S0045782515000924
      \endverb
      \keyw{Manufacturability,Microstructure,Multiscale design,Multiscale FEM,Spectral preconditioner,Topology optimisation}
    \endentry
    \entry{zhou_design_2008}{article}{}
      \name{author}{2}{}{%
        {{hash=ccb8cae1fb9a304a529e14b66f624e7d}{%
           family={Zhou},
           familyi={Z\bibinitperiod},
           given={Shiwei},
           giveni={S\bibinitperiod}}}%
        {{hash=16a77262afb7cc9b0229c21f168bd098}{%
           family={Li},
           familyi={L\bibinitperiod},
           given={Qing},
           giveni={Q\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{9210aa6e395d74ea41a58b98f2bcc7ac}
      \strng{fullhash}{9210aa6e395d74ea41a58b98f2bcc7ac}
      \strng{bibnamehash}{9210aa6e395d74ea41a58b98f2bcc7ac}
      \strng{authorbibnamehash}{9210aa6e395d74ea41a58b98f2bcc7ac}
      \strng{authornamehash}{9210aa6e395d74ea41a58b98f2bcc7ac}
      \strng{authorfullhash}{9210aa6e395d74ea41a58b98f2bcc7ac}
      \field{sortinit}{9}
      \field{sortinithash}{0a5ebc79d83c96b6579069544c73c7d4}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Being one of new generation of composites, functionally graded materials (FGMs) possess gradually changed physical properties due to their compositional and/or microstructural gradients. In literature, exhaustive studies have been carried out in compositional modeling and design, while limited reports are available for microstructural optimization. This article presents an inverse homogenization method for the design of two-phase (solid/void) FGM microstructures, whose periodic base cells (PBCs) vary in a direction parallel to the property gradient but periodically repeat themselves in the perpendicular direction. The effective elasticity tensor at each PBC is estimated in terms of the homogenization theory. The overall difference between the effective tensor and their target is minimized by seeking for an optimal PBC material topology. To preserve the connectivity between adjacent PBCs, three methods, namely connective constraint, pseudo load, and unified formulation with nonlinear diffusion are proposed herein. A number of two-dimensional examples possessing graded volume fraction and Young’s modulus but constant positive or negative Poisson’s ratios are presented to demonstrate this computational design procedure.}
      \field{issn}{1573-4803}
      \field{journaltitle}{Journal of Materials Science}
      \field{month}{8}
      \field{number}{15}
      \field{title}{Design of graded two-phase microstructures for tailored elasticity gradients}
      \field{urlday}{11}
      \field{urlmonth}{1}
      \field{urlyear}{2021}
      \field{volume}{43}
      \field{year}{2008}
      \field{urldateera}{ce}
      \field{pages}{5157\bibrangedash 5167}
      \range{pages}{11}
      \verb{doi}
      \verb 10.1007/s10853-008-2722-y
      \endverb
      \verb{file}
      \verb Springer Full Text PDF:D\:\\estragio\\Zotero\\storage\\ID6UJFGS\\Zhou et Li - 2008 - Design of graded two-phase microstructures for tai.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/s00158-020-02556-w
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s00158-020-02556-w
      \endverb
    \endentry
    \entry{allaire_topology_2019}{article}{}
      \name{author}{3}{}{%
        {{hash=e689b43ac5d3242f4613a353518abfb7}{%
           family={Allaire},
           familyi={A\bibinitperiod},
           given={Grégoire},
           giveni={G\bibinitperiod}}}%
        {{hash=21fa845a6088ad15722fab5d570f1259}{%
           family={Geoffroy-Donders},
           familyi={G\bibinithyphendelim D\bibinitperiod},
           given={Perle},
           giveni={P\bibinitperiod}}}%
        {{hash=45959b2759662f3fce2fb7bafd950559}{%
           family={Pantz},
           familyi={P\bibinitperiod},
           given={Olivier},
           giveni={O\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{3169344de921918d6d730d0523d7febf}
      \strng{fullhash}{3169344de921918d6d730d0523d7febf}
      \strng{bibnamehash}{3169344de921918d6d730d0523d7febf}
      \strng{authorbibnamehash}{3169344de921918d6d730d0523d7febf}
      \strng{authornamehash}{3169344de921918d6d730d0523d7febf}
      \strng{authorfullhash}{3169344de921918d6d730d0523d7febf}
      \field{sortinit}{9}
      \field{sortinithash}{0a5ebc79d83c96b6579069544c73c7d4}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This paper is concerned with the topology optimization of structures made of periodically perforated material, where the microscopic periodic cell can be macroscopically modulated and oriented. The main idea is to optimize the homogenized formulation of this problem, which is an easy task of parametric optimization, then to project the optimal microstructure at a desired lengthscale, which is a delicate issue, albeit computationally cheap. The main novelty of our work is, in a plane setting, the conformal treatment of the optimal orientation of the microstructure. In other words, although the periodicity cell has varying parameters and orientation throughout the computational domain, the angles between its members or bars are conserved. The main application of our work is the optimization of so-called lattice materials which are becoming increasingly popular in the context of additive manufacturing. Several numerical examples are presented for compliance minimization in 2-d.}
      \field{issn}{0898-1221}
      \field{journaltitle}{Computers \&amp; Mathematics with Applications}
      \field{month}{10}
      \field{number}{7}
      \field{series}{Simulation for {Additive} {Manufacturing}}
      \field{title}{Topology optimization of modulated and oriented periodic microstructures by the homogenization method}
      \field{urlday}{12}
      \field{urlmonth}{10}
      \field{urlyear}{2020}
      \field{volume}{78}
      \field{year}{2019}
      \field{urldateera}{ce}
      \field{pages}{2197\bibrangedash 2229}
      \range{pages}{33}
      \verb{doi}
      \verb 10.1016/j.camwa.2018.08.007
      \endverb
      \verb{file}
      \verb ScienceDirect Full Text PDF:D\:\\estragio\\Zotero\\storage\\ES44TYC2\\Allaire et al. - 2019 - Topology optimization of modulated and oriented pe.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb http://www.sciencedirect.com/science/article/pii/S0898122118304255
      \endverb
      \verb{url}
      \verb http://www.sciencedirect.com/science/article/pii/S0898122118304255
      \endverb
      \keyw{Lattice materials,Homogenization,Topology optimization}
    \endentry
    \entry{geoffroy-donders_3-d_2020}{article}{}
      \name{author}{3}{}{%
        {{hash=21fa845a6088ad15722fab5d570f1259}{%
           family={Geoffroy-Donders},
           familyi={G\bibinithyphendelim D\bibinitperiod},
           given={Perle},
           giveni={P\bibinitperiod}}}%
        {{hash=e689b43ac5d3242f4613a353518abfb7}{%
           family={Allaire},
           familyi={A\bibinitperiod},
           given={Grégoire},
           giveni={G\bibinitperiod}}}%
        {{hash=45959b2759662f3fce2fb7bafd950559}{%
           family={Pantz},
           familyi={P\bibinitperiod},
           given={Olivier},
           giveni={O\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{6b8f4c60a598bc9a899ea916d1876f0b}
      \strng{fullhash}{6b8f4c60a598bc9a899ea916d1876f0b}
      \strng{bibnamehash}{6b8f4c60a598bc9a899ea916d1876f0b}
      \strng{authorbibnamehash}{6b8f4c60a598bc9a899ea916d1876f0b}
      \strng{authornamehash}{6b8f4c60a598bc9a899ea916d1876f0b}
      \strng{authorfullhash}{6b8f4c60a598bc9a899ea916d1876f0b}
      \field{sortinit}{9}
      \field{sortinithash}{0a5ebc79d83c96b6579069544c73c7d4}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This paper is motivated by the optimization of so-called lattice materials which are becoming increasingly popular in the context of additive manufacturing. Generalizing our previous work in 2-d we propose a method for topology optimization of structures made of periodically perforated material, where the microscopic periodic cell can be macroscopically modulated and oriented. This method is made of three steps. The first step amounts to compute the homogenized properties of an adequately chosen parametrized microstructure (here, a cubic lattice with varying bar thicknesses). The second step optimizes the homogenized formulation of the problem, which is a classical problem of parametric optimization. The third, and most delicate, step projects the optimal oriented microstructure at a desired length scale. Compared to the 2-d case where rotations are parametrized by a single angle, to which a conformality constraint can be applied, the 3-d case is more involved and requires new ingredients. In particular, the full rotation matrix is regularized (instead of just one angle in 2-d) and the projection map which deforms the square periodic lattice is computed component by component. Several numerical examples are presented for compliance minimization in 3-d.}
      \field{issn}{0021-9991}
      \field{journaltitle}{Journal of Computational Physics}
      \field{month}{1}
      \field{title}{3-d topology optimization of modulated and oriented periodic microstructures by the homogenization method}
      \field{urlday}{12}
      \field{urlmonth}{10}
      \field{urlyear}{2020}
      \field{volume}{401}
      \field{year}{2020}
      \field{urldateera}{ce}
      \field{pages}{108994}
      \range{pages}{1}
      \verb{doi}
      \verb 10.1016/j.jcp.2019.108994
      \endverb
      \verb{file}
      \verb ScienceDirect Full Text PDF:D\:\\estragio\\Zotero\\storage\\8UY77UYE\\Geoffroy-Donders et al. - 2020 - 3-d topology optimization of modulated and oriente.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb http://www.sciencedirect.com/science/article/pii/S0021999119306990
      \endverb
      \verb{url}
      \verb http://www.sciencedirect.com/science/article/pii/S0021999119306990
      \endverb
      \keyw{Homogenization,Cellular structure,Lattice,Topology optimization}
    \endentry
    \entry{kumar_density-and-strain-based_2020}{article}{}
      \name{author}{2}{}{%
        {{hash=eeac0cf8b1966e521e7eadfaab69d771}{%
           family={Kumar},
           familyi={K\bibinitperiod},
           given={Tej},
           giveni={T\bibinitperiod}}}%
        {{hash=84c2102ad54186d7477842421e416280}{%
           family={Suresh},
           familyi={S\bibinitperiod},
           given={Krishnan},
           giveni={K\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{01e2e4205622d3fe717dc34952119abb}
      \strng{fullhash}{01e2e4205622d3fe717dc34952119abb}
      \strng{bibnamehash}{01e2e4205622d3fe717dc34952119abb}
      \strng{authorbibnamehash}{01e2e4205622d3fe717dc34952119abb}
      \strng{authornamehash}{01e2e4205622d3fe717dc34952119abb}
      \strng{authorfullhash}{01e2e4205622d3fe717dc34952119abb}
      \field{sortinit}{9}
      \field{sortinithash}{0a5ebc79d83c96b6579069544c73c7d4}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Microstructural topology optimization (MTO) is the simultaneous optimization of macroscale topology and microscale structure. MTO holds the promise of enhancing product-performance beyond what is possible today. Furthermore, with the advent of additive manufacturing, the resulting multiscale structures can be fabricated with relative ease. There are however two significant challenges associated with MTO: (1) high computational cost, and (2) potential loss of microstructural connectivity. In this paper, a novel density-and-strain-based K-means clustering method is proposed to reduce the computational cost of MTO. Further, a rotational degree of freedom is introduced to fully utilize the anisotropic nature of microstructures. Finally, the connectivity issue is addressed through auxiliary finite element fields. The proposed concepts are illustrated through several numerical examples applied to two-dimensional single-load problems.}
      \field{issn}{1615-147X, 1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{4}
      \field{number}{4}
      \field{title}{A density-and-strain-based {K}-clustering approach to microstructural topology optimization}
      \field{urlday}{18}
      \field{urlmonth}{11}
      \field{urlyear}{2021}
      \field{volume}{61}
      \field{year}{2020}
      \field{urldateera}{ce}
      \field{pages}{1399\bibrangedash 1415}
      \range{pages}{17}
      \verb{doi}
      \verb 10.1007/s00158-019-02422-4
      \endverb
      \verb{file}
      \verb s00158-019-02422-4.pdf:D\:\\estragio\\Zotero\\storage\\W29IGJZF\\s00158-019-02422-4.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb http://link.springer.com/10.1007/s00158-019-02422-4
      \endverb
      \verb{url}
      \verb http://link.springer.com/10.1007/s00158-019-02422-4
      \endverb
    \endentry
    \entry{xia_multiscale_2015}{article}{}
      \name{author}{2}{}{%
        {{hash=4abbbfdc11950e2124e4c9952b1fd20f}{%
           family={Xia},
           familyi={X\bibinitperiod},
           given={Liang},
           giveni={L\bibinitperiod}}}%
        {{hash=225ea9e43fc50791fa61c71b97f0015c}{%
           family={Breitkopf},
           familyi={B\bibinitperiod},
           given={Piotr},
           giveni={P\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{c3f35828ac72e3d6ee429477d9b1e8e0}
      \strng{fullhash}{c3f35828ac72e3d6ee429477d9b1e8e0}
      \strng{bibnamehash}{c3f35828ac72e3d6ee429477d9b1e8e0}
      \strng{authorbibnamehash}{c3f35828ac72e3d6ee429477d9b1e8e0}
      \strng{authornamehash}{c3f35828ac72e3d6ee429477d9b1e8e0}
      \strng{authorfullhash}{c3f35828ac72e3d6ee429477d9b1e8e0}
      \field{sortinit}{9}
      \field{sortinithash}{0a5ebc79d83c96b6579069544c73c7d4}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{issn}{00457825}
      \field{journaltitle}{Computer Methods in Applied Mechanics and Engineering}
      \field{month}{4}
      \field{title}{Multiscale structural topology optimization with an approximate constitutive model for local material microstructure}
      \field{urlday}{12}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{286}
      \field{year}{2015}
      \field{urldateera}{ce}
      \field{pages}{147\bibrangedash 167}
      \range{pages}{21}
      \verb{doi}
      \verb 10.1016/j.cma.2014.12.018
      \endverb
      \verb{urlraw}
      \verb https://linkinghub.elsevier.com/retrieve/pii/S0045782514004976
      \endverb
      \verb{url}
      \verb https://linkinghub.elsevier.com/retrieve/pii/S0045782514004976
      \endverb
    \endentry
    \entry{wang_concurrent_2018}{article}{}
      \name{author}{5}{}{%
        {{hash=5f314f633295db632e90990a3f8297a1}{%
           family={Wang},
           familyi={W\bibinitperiod},
           given={Chuang},
           giveni={C\bibinitperiod}}}%
        {{hash=c56130f772955f8030eb2f8d8a9fbf57}{%
           family={Zhu},
           familyi={Z\bibinitperiod},
           given={Ji\bibnamedelima Hong},
           giveni={J\bibinitperiod\bibinitdelim H\bibinitperiod}}}%
        {{hash=3ccecfd57d16b8a4e66bf1c013b1f964}{%
           family={Zhang},
           familyi={Z\bibinitperiod},
           given={Wei\bibnamedelima Hong},
           giveni={W\bibinitperiod\bibinitdelim H\bibinitperiod}}}%
        {{hash=16d7e2c21e89f14cfe7565b7b66e997b}{%
           family={Li},
           familyi={L\bibinitperiod},
           given={Shao\bibnamedelima Ying},
           giveni={S\bibinitperiod\bibinitdelim Y\bibinitperiod}}}%
        {{hash=59f8995b9b5201e3d55983556b74a198}{%
           family={Kong},
           familyi={K\bibinitperiod},
           given={Jie},
           giveni={J\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{22eb3d18b5679a61696cb93168f6d540}
      \strng{fullhash}{34768aa858b3ee562a4832ceaa513a5f}
      \strng{bibnamehash}{34768aa858b3ee562a4832ceaa513a5f}
      \strng{authorbibnamehash}{34768aa858b3ee562a4832ceaa513a5f}
      \strng{authornamehash}{22eb3d18b5679a61696cb93168f6d540}
      \strng{authorfullhash}{34768aa858b3ee562a4832ceaa513a5f}
      \field{extraname}{3}
      \field{sortinit}{9}
      \field{sortinithash}{0a5ebc79d83c96b6579069544c73c7d4}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This paper presents a novel concurrent topology optimization approach for finding the optimum topologies of macrostructures and their corresponding parameterized lattice microstructures in an integrated manner. Considering the manufacturability of the structure designs and computational efficiency, additional parameters are introduced to define the microstructure unit cell patterns and their non-uniform distribution, which avoids expensive iterative numerical homogenization calculations during topology optimization and results in an easier modelling of structure designs as well. It is worth mentioning that the equivalent properties of material microstructures serve as a link between the macro and the micro scale with the help of homogenization theory and the Porous Anisotropic Material with Penalization (PAMP) model. Besides, sensitivities of global structure compliance with respect to the pseudo-density variables and the microstructure parameter variables are derived, respectively. Moreover, several numerical examples are presented and reasonable solutions have been obtained to demonstrate the efficiency of the proposed method. Finally, mechanical testing is conducted to investigate the better performance of the optimized structure which is fabricated by 3D printing.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{7}
      \field{number}{1}
      \field{title}{Concurrent topology optimization design of structures and non-uniform parameterized lattice microstructures}
      \field{urlday}{12}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{58}
      \field{year}{2018}
      \field{urldateera}{ce}
      \field{pages}{35\bibrangedash 50}
      \range{pages}{16}
      \verb{doi}
      \verb 10.1007/s00158-018-2009-0
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\593R7BJ5\\Wang et al. - 2018 - Concurrent topology optimization design of structu.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/s00158-018-2009-0
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s00158-018-2009-0
      \endverb
      \keyw{Concurrent design,Homogenization,Multi-scale,Parameterized microstructures,Topology optimization}
    \endentry
    \entry{imediegwu_multiscale_2019}{article}{}
      \name{author}{4}{}{%
        {{hash=4a380ab918d6e62d83d646d0e52a67ba}{%
           family={Imediegwu},
           familyi={I\bibinitperiod},
           given={Chikwesiri},
           giveni={C\bibinitperiod}}}%
        {{hash=af42a6e4e2a78deec8b98c372a111c01}{%
           family={Murphy},
           familyi={M\bibinitperiod},
           given={Ryan},
           giveni={R\bibinitperiod}}}%
        {{hash=fccca068e7a379891e2f94f33dddcf81}{%
           family={Hewson},
           familyi={H\bibinitperiod},
           given={Robert},
           giveni={R\bibinitperiod}}}%
        {{hash=b614a548e4d41ef3709dd88ebfa60c39}{%
           family={Santer},
           familyi={S\bibinitperiod},
           given={Matthew},
           giveni={M\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{f6ce28ecc6fb692d68c9e4adaca79161}
      \strng{fullhash}{8c810bdee9650ad40322cf32c09576d7}
      \strng{bibnamehash}{8c810bdee9650ad40322cf32c09576d7}
      \strng{authorbibnamehash}{8c810bdee9650ad40322cf32c09576d7}
      \strng{authornamehash}{f6ce28ecc6fb692d68c9e4adaca79161}
      \strng{authorfullhash}{8c810bdee9650ad40322cf32c09576d7}
      \field{sortinit}{9}
      \field{sortinithash}{0a5ebc79d83c96b6579069544c73c7d4}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This paper develops a robust framework for the multiscale design of three-dimensional lattices with macroscopically tailored structural characteristics. The work exploits the high process flexibility and precision of additive manufacturing to the physical realization of complex microstructure of metamaterials by developing and implementing a multiscale approach. Structures derived from such metamaterials exhibit properties which differ from that of the constituent base material. A periodic microscale model is developed whose geometric parameterization enables smoothly changing properties and for which the connectivity of neighboring microstructures in the large-scale domain is guaranteed by slowly changing large-scale descriptions of the lattice parameters. A lattice-based functional grading of material is derived using the finite element method with sensitivities derived by the adjoint method. The novelty of the work lies in the use of multiple geometry-based small-scale design parameters for optimization problems in three-dimensional real space. The approach is demonstrated by solving a classical compliance minimization problem. The results show improved optimality compared to commonly implemented structural optimization algorithms.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{8}
      \field{number}{2}
      \field{title}{Multiscale structural optimization towards three-dimensional printable structures}
      \field{urlday}{12}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{60}
      \field{year}{2019}
      \field{urldateera}{ce}
      \field{pages}{513\bibrangedash 525}
      \range{pages}{13}
      \verb{doi}
      \verb 10.1007/s00158-019-02220-y
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\DCWH4P75\\Imediegwu et al. - 2019 - Multiscale structural optimization towards three-d.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/s00158-019-02220-y
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s00158-019-02220-y
      \endverb
      \keyw{Additive manufacturing,Heterogeneous multiscale methods,Homogenization,Lattice,Response surface model,Structural optimization}
    \endentry
    \entry{duriez_well_2021}{article}{}
      \name{author}{4}{}{%
        {{hash=25797b3c896ef58bac4c5bf67740e61c}{%
           family={Duriez},
           familyi={D\bibinitperiod},
           given={Edouard},
           giveni={E\bibinitperiod}}}%
        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
        {{hash=6562ac1f8239c50df0e604c9792fe4ef}{%
           family={Charlotte},
           familyi={C\bibinitperiod},
           given={Miguel},
           giveni={M\bibinitperiod}}}%
        {{hash=fed27bf5e0b1cedfe4dd9ff739ed0559}{%
           family={Azzaro-Pantel},
           familyi={A\bibinithyphendelim P\bibinitperiod},
           given={Catherine},
           giveni={C\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{58d2970fb8b7ccaeadabd03d1af1b724}
      \strng{fullhash}{6b9091e18b7380b556ee43381cb4905a}
      \strng{bibnamehash}{6b9091e18b7380b556ee43381cb4905a}
      \strng{authorbibnamehash}{6b9091e18b7380b556ee43381cb4905a}
      \strng{authornamehash}{58d2970fb8b7ccaeadabd03d1af1b724}
      \strng{authorfullhash}{6b9091e18b7380b556ee43381cb4905a}
      \field{extraname}{1}
      \field{sortinit}{9}
      \field{sortinithash}{0a5ebc79d83c96b6579069544c73c7d4}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Multi-scale topology optimization (a.k.a. micro-structural topology optimization, MTO) consists in optimizing macro-scale and micro-scale topology simultaneously. MTO could improve structural performance of products significantly. However, a few issues related to connectivity between micro-structures and high computational cost have to be addressed, without resulting in loss of performance. In this paper, a new efficient multi-scale topology optimization (EMTO) framework has been developed for this purpose. Connectivity is addressed through adaptive transmission zones which limit loss of performance. A pre-computed database of micro-structures is used to speed up the computing. Design variables have also been chosen carefully and include the orientation of the micro-structures to enhance performance. EMTO has been successfully tested on two-dimensional compliance optimization problems. The results show significant improvements compared to mono-scale methods (compliance value lower by up to 20\% on a simplistic case or 4\% on a more realistic case), and also demonstrate the versatility of EMTO.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{12}
      \field{number}{6}
      \field{title}{A well connected, locally-oriented and efficient multi-scale topology optimization ({EMTO}) strategy}
      \field{urlday}{12}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{64}
      \field{year}{2021}
      \field{urldateera}{ce}
      \field{pages}{3705\bibrangedash 3728}
      \range{pages}{24}
      \verb{doi}
      \verb 10.1007/s00158-021-03048-1
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\STI8XXRN\\Duriez et al. - 2021 - A well connected, locally-oriented and efficient m.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/s00158-021-03048-1
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s00158-021-03048-1
      \endverb
      \keyw{Material orientation,Metamodel,Micro-structure connectivity,Multi-scale topology optimization,Structural database}
    \endentry
    \entry{kim_machine_2021}{article}{}
      \name{author}{3}{}{%
        {{hash=8b67f2e15394dfa00be39910b0ced08a}{%
           family={Kim},
           familyi={K\bibinitperiod},
           given={Cheolwoong},
           giveni={C\bibinitperiod}}}%
        {{hash=ab7ed8d7d93e7aa6a5e98e6bd6e3041e}{%
           family={Lee},
           familyi={L\bibinitperiod},
           given={Jaewook},
           giveni={J\bibinitperiod}}}%
        {{hash=893342b9231a7535939e5174a39ae9f6}{%
           family={Yoo},
           familyi={Y\bibinitperiod},
           given={Jeonghoon},
           giveni={J\bibinitperiod}}}%
      }
      \strng{namehash}{9636fee4f5f92952ecbde42b667c6b60}
      \strng{fullhash}{9636fee4f5f92952ecbde42b667c6b60}
      \strng{bibnamehash}{9636fee4f5f92952ecbde42b667c6b60}
      \strng{authorbibnamehash}{9636fee4f5f92952ecbde42b667c6b60}
      \strng{authornamehash}{9636fee4f5f92952ecbde42b667c6b60}
      \strng{authorfullhash}{9636fee4f5f92952ecbde42b667c6b60}
      \field{sortinit}{9}
      \field{sortinithash}{0a5ebc79d83c96b6579069544c73c7d4}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This study presents new framework in which the representative volume element (RVE) method and machine learning (ML) model are used to construct continuous anisotropic effective material properties for simultaneous design of the overall topology configuration and local fiber material layout in functionally graded composite structures. It is an alternative to the asymptotic homogenization design method (AHDM) to obtain continuous effective material property functions. While the AHDM uses the asymptotic homogenization theory (AHT) and Legendre polynomials, the RVE method calculates anisotropic effective material properties having nonlinear behavior with respect to design variables of microstructures, and it is easier to implement than AHT given the governing equations and appropriate boundary conditions. More efficient and accurate than Legendre polynomials, ML is used to build a continuous model of the RVE results required for simultaneous design of the overall topology configuration and local fiber material layout. To show the convenience and expandability of the proposed method, a 3D RVE model is also proposed through the extension of the 2D model. The proposed method is verified through 2D and 3D numerical examples to minimize structural compliance and obtained results are compared with those from the application of AHDM.}
      \field{issn}{0045-7825}
      \field{journaltitle}{Computer Methods in Applied Mechanics and Engineering}
      \field{month}{12}
      \field{title}{Machine learning-combined topology optimization for functionary graded composite structure design}
      \field{urlday}{12}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{387}
      \field{year}{2021}
      \field{urldateera}{ce}
      \field{pages}{114158}
      \range{pages}{1}
      \verb{doi}
      \verb 10.1016/j.cma.2021.114158
      \endverb
      \verb{urlraw}
      \verb https://www.sciencedirect.com/science/article/pii/S0045782521004898
      \endverb
      \verb{url}
      \verb https://www.sciencedirect.com/science/article/pii/S0045782521004898
      \endverb
      \keyw{Anisotropic effective material property,Functionally graded composite structure,Machine learning,Representative volume element method,Topology optimization}
    \endentry
    \entry{white_multiscale_2019}{article}{}
      \name{author}{4}{}{%
        {{hash=4215597d2c71e616e31751f6b8ed0e31}{%
           family={White},
           familyi={W\bibinitperiod},
           given={Daniel\bibnamedelima A.},
           giveni={D\bibinitperiod\bibinitdelim A\bibinitperiod}}}%
        {{hash=778e078a8365e381faabfb9b7517227a}{%
           family={Arrighi},
           familyi={A\bibinitperiod},
           given={William\bibnamedelima J.},
           giveni={W\bibinitperiod\bibinitdelim J\bibinitperiod}}}%
        {{hash=60d0e334c4a514fc59970c0ae5e62c3f}{%
           family={Kudo},
           familyi={K\bibinitperiod},
           given={Jun},
           giveni={J\bibinitperiod}}}%
        {{hash=88a5d4e50898d8564f00213fb8528171}{%
           family={Watts},
           familyi={W\bibinitperiod},
           given={Seth\bibnamedelima E.},
           giveni={S\bibinitperiod\bibinitdelim E\bibinitperiod}}}%
      }
      \strng{namehash}{5e766dcc5049101497b4e8141a05157f}
      \strng{fullhash}{e4237a57fcbe708281c36a5f8ab9b6c9}
      \strng{bibnamehash}{e4237a57fcbe708281c36a5f8ab9b6c9}
      \strng{authorbibnamehash}{e4237a57fcbe708281c36a5f8ab9b6c9}
      \strng{authornamehash}{5e766dcc5049101497b4e8141a05157f}
      \strng{authorfullhash}{e4237a57fcbe708281c36a5f8ab9b6c9}
      \field{sortinit}{9}
      \field{sortinithash}{0a5ebc79d83c96b6579069544c73c7d4}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{We are concerned with optimization of macroscale elastic structures that are designed utilizing spatially varying microscale metamaterials. The macroscale optimization is accomplished using gradient-based nonlinear topological optimization. But instead of using density as the optimization decision variable, the decision variables are the multiple parameters that define the local microscale metamaterial. This is accomplished using single layer feedforward Gaussian basis function networks as a surrogate models of the elastic response of the microscale metamaterial. The surrogate models are trained using highly resolved continuum finite element simulations of the microscale metamaterials and hence are significantly more accurate than analytical models e.g. classical beam theory. Because the derivative of the surrogate model is important for sensitivity analysis of the macroscale topology optimization, a neural network training procedure based on the Sobolev norm is described. Since the SIMP method is not appropriate for spatially varying lattices, an alternative method is developed to enable creation of void regions. The efficacy of this approach is demonstrated via several examples in which the optimal graded metamaterial outperforms a traditional solid structure.}
      \field{issn}{0045-7825}
      \field{journaltitle}{Computer Methods in Applied Mechanics and Engineering}
      \field{month}{4}
      \field{title}{Multiscale topology optimization using neural network surrogate models}
      \field{urlday}{12}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{346}
      \field{year}{2019}
      \field{urldateera}{ce}
      \field{pages}{1118\bibrangedash 1135}
      \range{pages}{18}
      \verb{doi}
      \verb 10.1016/j.cma.2018.09.007
      \endverb
      \verb{urlraw}
      \verb https://www.sciencedirect.com/science/article/pii/S004578251830450X
      \endverb
      \verb{url}
      \verb https://www.sciencedirect.com/science/article/pii/S004578251830450X
      \endverb
      \keyw{Material models,Multiscale analysis,Neural networks,Topology optimization}
    \endentry
    \entry{chandrasekhar_multi-material_2021}{article}{}
      \name{author}{2}{}{%
        {{hash=e2ded8f3849a7ea87edc9347ae2ea3a8}{%
           family={Chandrasekhar},
           familyi={C\bibinitperiod},
           given={Aaditya},
           giveni={A\bibinitperiod}}}%
        {{hash=84c2102ad54186d7477842421e416280}{%
           family={Suresh},
           familyi={S\bibinitperiod},
           given={Krishnan},
           giveni={K\bibinitperiod}}}%
      }
      \strng{namehash}{4ae8e84ba5fda890223894e624f29ac9}
      \strng{fullhash}{4ae8e84ba5fda890223894e624f29ac9}
      \strng{bibnamehash}{4ae8e84ba5fda890223894e624f29ac9}
      \strng{authorbibnamehash}{4ae8e84ba5fda890223894e624f29ac9}
      \strng{authornamehash}{4ae8e84ba5fda890223894e624f29ac9}
      \strng{authorfullhash}{4ae8e84ba5fda890223894e624f29ac9}
      \field{sortinit}{9}
      \field{sortinithash}{0a5ebc79d83c96b6579069544c73c7d4}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{The focus of this paper is on multi-material topology optimization (MMTO), where the objective is to not only compute the optimal topology, but also the distribution of two or more materials within the topology. In the popular density-based MMTO, the underlying pseudo-density fields are typically represented using an underlying mesh. While mesh-based MMTO ties in well with mesh-based finite element analysis, there are inherent challenges, namely the extraction of thin features, and the computation of the gradients of the density fields. The objective of this paper is to present a neural network (NN) based MMTO method where the density fields are represented in a mesh-independent manner, using the NN’s activation functions, with the weights and biases associated with the NN serving as the design variables. Then, by relying on the NN’s built-in optimization routines, and a conventional finite element solver, the MMTO problem is solved. The salient features of the proposed method include: (1) thin features can be extracted through a simple post-processing step, (2) gradients and sensitivities can be computed accurately through back-propagation, (3) the NN construction implicitly guarantees the partition of unity between constituent materials, (4) the NN designs often exhibit better performance than mesh-based designs, and (5) the number of design variables is relatively small. Finally, the proposed framework is simple to implement, and is illustrated through several examples.}
      \field{issn}{0010-4485}
      \field{journaltitle}{Computer-Aided Design}
      \field{month}{7}
      \field{title}{Multi-{Material} {Topology} {Optimization} {Using} {Neural} {Networks}}
      \field{urlday}{12}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{136}
      \field{year}{2021}
      \field{urldateera}{ce}
      \field{pages}{103017}
      \range{pages}{1}
      \verb{doi}
      \verb 10.1016/j.cad.2021.103017
      \endverb
      \verb{urlraw}
      \verb https://www.sciencedirect.com/science/article/pii/S0010448521000282
      \endverb
      \verb{url}
      \verb https://www.sciencedirect.com/science/article/pii/S0010448521000282
      \endverb
      \keyw{Multi-material,Neural networks,SIMP,Thin features,Topology optimization}
    \endentry
    \entry{sigmund_benchmarking_2022}{article}{}
      \name{author}{1}{}{%
        {{hash=d76f1c09e8d8d06e1b7c3c254efeae1a}{%
           family={Sigmund},
           familyi={S\bibinitperiod},
           given={Ole},
           giveni={O\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{fullhash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{bibnamehash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{authorbibnamehash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{authornamehash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \strng{authorfullhash}{d76f1c09e8d8d06e1b7c3c254efeae1a}
      \field{extraname}{8}
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      \field{sortinithash}{0a5ebc79d83c96b6579069544c73c7d4}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Topology optimization has developed tremendously and new approaches, algorithms and applications are appearing on a daily basis. However, how to fairly evaluate and compare new concepts and ideas to existing ones is an open question due to the broadness of modelling approaches, geometry parameterizations and physical applications. Ideally, the community should define common benchmark examples but again, how to define benchmarks that are generally applicable? In the lack or impracticality of common benchmarks, the responsibility of fair evaluation of contributions is up to authors but the literature shows multiple examples where this seems to be challenging. This note lists a number of recommendations, tools and concepts that papers in the field of topology optimization (and possibly other fields) should consider to represent good scientific practise.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{10}
      \field{number}{11}
      \field{title}{On benchmarking and good scientific practise in topology optimization}
      \field{urlday}{17}
      \field{urlmonth}{11}
      \field{urlyear}{2022}
      \field{volume}{65}
      \field{year}{2022}
      \field{urldateera}{ce}
      \field{pages}{315}
      \range{pages}{1}
      \verb{doi}
      \verb 10.1007/s00158-022-03427-2
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\BWKY8YPI\\Sigmund - 2022 - On benchmarking and good scientific practise in to.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/s00158-022-03427-2
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s00158-022-03427-2
      \endverb
      \keyw{Topology optimization,Benchmarking,Scientific practise}
    \endentry
    \entry{cheng_functionally_2019}{article}{}
      \name{author}{3}{}{%
        {{hash=b6821df5befbb13e494f84d9b04a49c2}{%
           family={Cheng},
           familyi={C\bibinitperiod},
           given={Lin},
           giveni={L\bibinitperiod}}}%
        {{hash=2d852398379089743760671f87b52b44}{%
           family={Bai},
           familyi={B\bibinitperiod},
           given={Jiaxi},
           giveni={J\bibinitperiod}}}%
        {{hash=3593935608ee9a16d2edcba9b6b826d1}{%
           family={To},
           familyi={T\bibinitperiod},
           given={Albert\bibnamedelima C.},
           giveni={A\bibinitperiod\bibinitdelim C\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{962ad98721e655dc7d3b7f61e84c0dce}
      \strng{fullhash}{962ad98721e655dc7d3b7f61e84c0dce}
      \strng{bibnamehash}{962ad98721e655dc7d3b7f61e84c0dce}
      \strng{authorbibnamehash}{962ad98721e655dc7d3b7f61e84c0dce}
      \strng{authornamehash}{962ad98721e655dc7d3b7f61e84c0dce}
      \strng{authorfullhash}{962ad98721e655dc7d3b7f61e84c0dce}
      \field{sortinit}{9}
      \field{sortinithash}{0a5ebc79d83c96b6579069544c73c7d4}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{issn}{0045-7825}
      \field{journaltitle}{Computer Methods in Applied Mechanics and Engineering}
      \field{month}{2}
      \field{title}{Functionally graded lattice structure topology optimization for the design of additive manufactured components with stress constraints}
      \field{urlday}{7}
      \field{urlmonth}{5}
      \field{urlyear}{2021}
      \field{volume}{344}
      \field{year}{2019}
      \field{urldateera}{ce}
      \field{pages}{334\bibrangedash 359}
      \range{pages}{26}
      \verb{doi}
      \verb 10.1016/j.cma.2018.10.010
      \endverb
      \verb{urlraw}
      \verb https://www.sciencedirect.com/science/article/pii/S0045782518305061
      \endverb
      \verb{url}
      \verb https://www.sciencedirect.com/science/article/pii/S0045782518305061
      \endverb
      \keyw{Homogenization,Additive manufacturing,Lattice structure topology optimization,Stress constraint}
    \endentry
    \entry{wu_infill_2018}{article}{}
      \name{author}{4}{}{%
        {{hash=aaf4818e3816b53809f264b2c1b2ecae}{%
           family={Wu},
           familyi={W\bibinitperiod},
           given={Jun},
           giveni={J\bibinitperiod}}}%
        {{hash=fa5a136030c946f96655797e3220c1bb}{%
           family={Aage},
           familyi={A\bibinitperiod},
           given={Niels},
           giveni={N\bibinitperiod}}}%
        {{hash=c00f68e0027a0118ca2aa59ae43124c6}{%
           family={Westermann},
           familyi={W\bibinitperiod},
           given={Rüdiger},
           giveni={R\bibinitperiod}}}%
        {{hash=d76f1c09e8d8d06e1b7c3c254efeae1a}{%
           family={Sigmund},
           familyi={S\bibinitperiod},
           given={Ole},
           giveni={O\bibinitperiod}}}%
      }
      \strng{namehash}{24485726fb023b68e63d57d174e325bc}
      \strng{fullhash}{ab0b7d57ec927a9d0478a38afad23b30}
      \strng{bibnamehash}{ab0b7d57ec927a9d0478a38afad23b30}
      \strng{authorbibnamehash}{ab0b7d57ec927a9d0478a38afad23b30}
      \strng{authornamehash}{24485726fb023b68e63d57d174e325bc}
      \strng{authorfullhash}{ab0b7d57ec927a9d0478a38afad23b30}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Porous structures such as trabecular bone are widely seen in nature. These structures are lightweight and exhibit strong mechanical properties. In this paper, we present a method to generate bone-like porous structures as lightweight infill for additive manufacturing. Our method builds upon and extends voxel-wise topology optimization. In particular, for the purpose of generating sparse yet stable structures distributed in the interior of a given shape, we propose upper bounds on the localized material volume in the proximity of each voxel in the design domain. We then aggregate the local per-voxel constraints by their p-norm into an equivalent global constraint, in order to facilitate an efficient optimization process. Implemented on a high-resolution topology optimization framework, our results demonstrate mechanically optimized, detailed porous structures which mimic those found in nature. We further show variants of the optimized structures subject to different design specifications, and we analyze the optimality and robustness of the obtained structures.}
      \field{issn}{1941-0506}
      \field{journaltitle}{IEEE Transactions on Visualization and Computer Graphics}
      \field{month}{2}
      \field{number}{2}
      \field{title}{Infill {Optimization} for {Additive} {Manufacturing}—{Approaching} {Bone}-{Like} {Porous} {Structures}}
      \field{volume}{24}
      \field{year}{2018}
      \field{pages}{1127\bibrangedash 1140}
      \range{pages}{14}
      \verb{doi}
      \verb 10.1109/TVCG.2017.2655523
      \endverb
      \verb{file}
      \verb IEEE Xplore Full Text PDF:D\:\\estragio\\Zotero\\storage\\IGT5AQCL\\Wu et al. - 2018 - Infill Optimization for Additive Manufacturing—App.pdf:application/pdf
      \endverb
      \keyw{additive manufacturing,Bones,Infill,Mechanical factors,Optimization,porous structures,Shape,Solids,Three-dimensional printing,Topology,topology optimization,trabecular bone}
    \endentry
    \entry{huang_optimal_2008}{article}{}
      \name{author}{2}{}{%
        {{hash=bf1afb45a50313a87b61c9f7a08f8989}{%
           family={Huang},
           familyi={H\bibinitperiod},
           given={X.},
           giveni={X\bibinitperiod}}}%
        {{hash=dfa4794abf731bd58660a4dae45c4dad}{%
           family={Xie},
           familyi={X\bibinitperiod},
           given={Y.\bibnamedelimi M.},
           giveni={Y\bibinitperiod\bibinitdelim M\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{f1809a42bd21c36e991b1f4575c82577}
      \strng{fullhash}{f1809a42bd21c36e991b1f4575c82577}
      \strng{bibnamehash}{f1809a42bd21c36e991b1f4575c82577}
      \strng{authorbibnamehash}{f1809a42bd21c36e991b1f4575c82577}
      \strng{authornamehash}{f1809a42bd21c36e991b1f4575c82577}
      \strng{authorfullhash}{f1809a42bd21c36e991b1f4575c82577}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This paper presents a method for topology optimization of periodic structures using the bi-directional evolutionary structural optimization (BESO) technique. To satisfy the periodic constraint, the designable domain is divided into a certain number of identical unit cells. The optimal topology of the unit cell is determined by gradually removing and adding material based on a sensitivity analysis. Sensitivity numbers that consider the periodic constraint for the repetitive elements are developed. To demonstrate the capability and effectiveness of the proposed approach, topology design problems of 2D and 3D periodic structures are investigated. The results indicate that the optimal topology depends, to a great extent, on the defined unit cells and on the relative strength of other non-designable part, such as the skins of sandwich structures.}
      \field{issn}{1615-147X, 1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{11}
      \field{number}{6}
      \field{title}{Optimal design of periodic structures using evolutionary topology optimization}
      \field{urlday}{28}
      \field{urlmonth}{10}
      \field{urlyear}{2021}
      \field{volume}{36}
      \field{year}{2008}
      \field{urldateera}{ce}
      \field{pages}{597\bibrangedash 606}
      \range{pages}{10}
      \verb{doi}
      \verb 10.1007/s00158-007-0196-1
      \endverb
      \verb{file}
      \verb Huang and Xie - 2008 - Optimal design of periodic structures using evolut.pdf:D\:\\estragio\\Zotero\\storage\\BB2LWXGG\\Huang and Xie - 2008 - Optimal design of periodic structures using evolut.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb http://link.springer.com/10.1007/s00158-007-0196-1
      \endverb
      \verb{url}
      \verb http://link.springer.com/10.1007/s00158-007-0196-1
      \endverb
    \endentry
    \entry{tugilimana_integrated_2019}{article}{}
      \name{author}{3}{}{%
        {{hash=1aa69159af81958758aafc93b4a2a4d0}{%
           family={Tugilimana},
           familyi={T\bibinitperiod},
           given={Alexis},
           giveni={A\bibinitperiod}}}%
        {{hash=c959890c39060ae8bbd6c5dce99754f7}{%
           family={Coelho},
           familyi={C\bibinitperiod},
           given={Rajan\bibnamedelima Filomeno},
           giveni={R\bibinitperiod\bibinitdelim F\bibinitperiod}}}%
        {{hash=48da781e19224718578086f3f02cafad}{%
           family={Thrall},
           familyi={T\bibinitperiod},
           given={Ashley\bibnamedelima P.},
           giveni={A\bibinitperiod\bibinitdelim P\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{fe0b2709c1d7b46a4a4902cd39171770}
      \strng{fullhash}{fe0b2709c1d7b46a4a4902cd39171770}
      \strng{bibnamehash}{fe0b2709c1d7b46a4a4902cd39171770}
      \strng{authorbibnamehash}{fe0b2709c1d7b46a4a4902cd39171770}
      \strng{authornamehash}{fe0b2709c1d7b46a4a4902cd39171770}
      \strng{authorfullhash}{fe0b2709c1d7b46a4a4902cd39171770}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Modularity, a design philosophy in which a structure is comprised of identical components called modules, offers economical advantages as the modules can be mass produced in high quality controlled facilities. Prior research investigated structural optimization as a means of improving modular design, focusing on optimizing separately (i) the module topology and the module spatial orientation or (ii) the dynamic grouping into families of different topologies. This research did not include stability despite its considerable importance during preliminary design. In this paper, a novel integrated strategy is proposed for the preliminary design of modular trusses, unifying module topology, spatial orientation, and grouping optimization, as well as stability considerations to define meaningful solutions for real-life case studies. This is addressed by formulating an appropriate mixed-variable minimum volume problem in elastic design, including multiple load cases with self-weight and stress limitations in tension and compression. Global stability is considered through a linear prebuckling constraint, and a local buckling constraint is formulated by considering Euler buckling with standard profiles obtained from commercial catalogues. The practical applicability of this contribution is demonstrated on a benchmark modular bridge and a three-dimensional modular vault structure. The importance of stability considerations is also investigated, where the redundancy introduced by modularity is shown to contribute to the global resistance of the entire structure.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{8}
      \field{number}{2}
      \field{title}{An integrated design methodology for modular trusses including dynamic grouping, module spatial orientation, and topology optimization}
      \field{urlday}{24}
      \field{urlmonth}{3}
      \field{urlyear}{2023}
      \field{volume}{60}
      \field{year}{2019}
      \field{urldateera}{ce}
      \field{pages}{613\bibrangedash 638}
      \range{pages}{26}
      \verb{doi}
      \verb 10.1007/s00158-019-02230-w
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\SYLSHWPE\\Tugilimana et al. - 2019 - An integrated design methodology for modular truss.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/s00158-019-02230-w
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s00158-019-02230-w
      \endverb
      \keyw{Truss topology optimization,Mixed-variable optimization problem,Modular trusses,Simulated annealing}
    \endentry
    \entry{bakker_simultaneous_2021}{article}{}
      \name{author}{4}{}{%
        {{hash=9ed40ce9609fbecc530d3a1ae9a2122a}{%
           family={Bakker},
           familyi={B\bibinitperiod},
           given={Coen},
           giveni={C\bibinitperiod}}}%
        {{hash=bb8be7b4ded9506bc5fbf1b332a8c693}{%
           family={Zhang},
           familyi={Z\bibinitperiod},
           given={Lidan},
           giveni={L\bibinitperiod}}}%
        {{hash=a0a790c8a2103e63158b60b025824f37}{%
           family={Higginson},
           familyi={H\bibinitperiod},
           given={Kristie},
           giveni={K\bibinitperiod}}}%
        {{hash=fced7f35e3ed00611970d9aa7179fda2}{%
           family={Keulen},
           familyi={K\bibinitperiod},
           given={Fred\bibnamedelima van},
           giveni={F\bibinitperiod\bibinitdelim v\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{c34848e186e0f4277d28885c63c6c0fd}
      \strng{fullhash}{f35f484e012b0f812b1320eb42fbe04a}
      \strng{bibnamehash}{f35f484e012b0f812b1320eb42fbe04a}
      \strng{authorbibnamehash}{f35f484e012b0f812b1320eb42fbe04a}
      \strng{authornamehash}{c34848e186e0f4277d28885c63c6c0fd}
      \strng{authorfullhash}{f35f484e012b0f812b1320eb42fbe04a}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Stiffened shells and plates are widely used in engineering. Their performance is highly influenced by the arrangement, or layout, of stiffeners on the base shell or plate and the geometric features, or topology, of these stiffeners. Moreover, modular design is beneficial, since it allows for increased quality control and mass production. In this work, a method is developed that simultaneously optimizes the topology of stiffeners and their layout on a base shell or plate. This is accomplished by introducing a fixed number of modular stiffeners, which are subject to density-based topology optimization and a mapping of these modules to a ground structure. To illustrate potential applications, several stiffened plates and shell examples are presented. All examples demonstrated that the proposed method is able to generate clear topologies for any number of modules and a distinct layout of the stiffeners on the base shell or plate.}
      \field{issn}{1615-147X, 1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{11}
      \field{number}{5}
      \field{title}{Simultaneous optimization of topology and layout of modular stiffeners on shells and plates}
      \field{urlday}{15}
      \field{urlmonth}{3}
      \field{urlyear}{2023}
      \field{volume}{64}
      \field{year}{2021}
      \field{urldateera}{ce}
      \field{pages}{3147\bibrangedash 3161}
      \range{pages}{15}
      \verb{doi}
      \verb 10.1007/s00158-021-03081-0
      \endverb
      \verb{file}
      \verb Bakker et al. - 2021 - Simultaneous optimization of topology and layout o.pdf:D\:\\estragio\\Zotero\\storage\\AHC7UEG9\\Bakker et al. - 2021 - Simultaneous optimization of topology and layout o.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://link.springer.com/10.1007/s00158-021-03081-0
      \endverb
      \verb{url}
      \verb https://link.springer.com/10.1007/s00158-021-03081-0
      \endverb
    \endentry
    \entry{tugilimana_spatial_2017}{article}{}
      \name{author}{4}{}{%
        {{hash=1aa69159af81958758aafc93b4a2a4d0}{%
           family={Tugilimana},
           familyi={T\bibinitperiod},
           given={Alexis},
           giveni={A\bibinitperiod}}}%
        {{hash=48da781e19224718578086f3f02cafad}{%
           family={Thrall},
           familyi={T\bibinitperiod},
           given={Ashley\bibnamedelima P.},
           giveni={A\bibinitperiod\bibinitdelim P\bibinitperiod}}}%
        {{hash=a867726c6de8cbbc5b38459f1179c726}{%
           family={Descamps},
           familyi={D\bibinitperiod},
           given={Benoît},
           giveni={B\bibinitperiod}}}%
        {{hash=c959890c39060ae8bbd6c5dce99754f7}{%
           family={Coelho},
           familyi={C\bibinitperiod},
           given={Rajan\bibnamedelima Filomeno},
           giveni={R\bibinitperiod\bibinitdelim F\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{53e3c8df6a70262859a48df26c70d8e6}
      \strng{fullhash}{2aac681fc39c1e827dcfa0eee03b3b7a}
      \strng{bibnamehash}{2aac681fc39c1e827dcfa0eee03b3b7a}
      \strng{authorbibnamehash}{2aac681fc39c1e827dcfa0eee03b3b7a}
      \strng{authornamehash}{53e3c8df6a70262859a48df26c70d8e6}
      \strng{authorfullhash}{2aac681fc39c1e827dcfa0eee03b3b7a}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Modularity in structural engineering offers significant cost advantages since identical components can be mass-produced in high quality-controlled facilities. While prior research has investigated the optimization of modular structures, this work is limited to the module topology periodicity, leading to solutions where some structure parts remain inefficiently used. This paper proposes a continuum-based formulation for optimizing simultaneously the module topology and spatial orientation in modular trusses. The numerical difficulties associated with the module rotations in the optimization formulation are identified, and properly handled by a novel topology-based rotation representation using group theory. A relaxation strategy based on complementary constraints enables the continuous integration of the module rotations in a lower-bound plastic design formulation (or fully stressed design). Case studies involving high density ground structures demonstrate that it is able in the worst case to retrieve the results obtained by imposing the module orientation a priori, and to improve the optimized design when freedom on the rotations is considered.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{2}
      \field{number}{2}
      \field{title}{Spatial orientation and topology optimization of modular trusses}
      \field{urlday}{24}
      \field{urlmonth}{3}
      \field{urlyear}{2023}
      \field{volume}{55}
      \field{year}{2017}
      \field{urldateera}{ce}
      \field{pages}{459\bibrangedash 476}
      \range{pages}{18}
      \verb{doi}
      \verb 10.1007/s00158-016-1501-7
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\MV66JJ27\\Tugilimana et al. - 2017 - Spatial orientation and topology optimization of m.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/s00158-016-1501-7
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s00158-016-1501-7
      \endverb
      \keyw{Plastic design,Group theory,Modular structures,Rotation optimization,Truss topology optimization}
    \endentry
    \entry{thomas_finite_2021}{article}{}
      \name{author}{3}{}{%
        {{hash=464f4e389b93f6c64353eed7bbc9b5b7}{%
           family={Thomas},
           familyi={T\bibinitperiod},
           given={Simon},
           giveni={S\bibinitperiod}}}%
        {{hash=16a77262afb7cc9b0229c21f168bd098}{%
           family={Li},
           familyi={L\bibinitperiod},
           given={Qing},
           giveni={Q\bibinitperiod}}}%
        {{hash=1082db87b763bcb5f84eb0f56fc9ee1d}{%
           family={Steven},
           familyi={S\bibinitperiod},
           given={Grant},
           giveni={G\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{0e39530550189c086e80909823ed1c6a}
      \strng{fullhash}{0e39530550189c086e80909823ed1c6a}
      \strng{bibnamehash}{0e39530550189c086e80909823ed1c6a}
      \strng{authorbibnamehash}{0e39530550189c086e80909823ed1c6a}
      \strng{authornamehash}{0e39530550189c086e80909823ed1c6a}
      \strng{authorfullhash}{0e39530550189c086e80909823ed1c6a}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Periodic topology optimization has been suggested as an effective means to design efficient structures which address a range of practical constraints, such as manufacturability, transportability, replaceability and ease of assembly. This study proposes a new approach for design of finite periodic structures by allowing variable orientation states of individual unit-cells. In some design instances of periodic structures, the unit-cell may exhibit certain geometric features allowing multiple possible assembly orientations (e.g. facing up or down). For the first time, this work incorporates such assembly flexibility within the periodic topology optimization, which enables to greatly expand the conventional periodic design space and take more advantage of structural periodicity. Given its broad applications, a methodology for the design of more efficient periodic structures while maintaining the same degree of periodic constraint may be of significant benefit to engineering practice. In this study, several numerical examples are presented to demonstrate the effectiveness of this new approach for both static and vibratory criteria. Brute force analysis is also utilized to compare all possible assembly configurations for several periodic structures with a small number of unit-cells. A heuristic approach is suggested for selecting more beneficially oriented configurations in periodic structures with a large number of unit-cells for which an exhaustive search may be computationally infeasible. It is found that in all the presented cases, the oriented periodic structures outperform the conventional non-oriented (or namely translational) periodic counterparts. Finally, an educational MATLAB code is provided for replication of the design results in this paper.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{10}
      \field{number}{4}
      \field{title}{Finite periodic topology optimization with oriented unit-cells}
      \field{urlday}{28}
      \field{urlmonth}{10}
      \field{urlyear}{2021}
      \field{volume}{64}
      \field{year}{2021}
      \field{urldateera}{ce}
      \field{pages}{1765\bibrangedash 1779}
      \range{pages}{15}
      \verb{doi}
      \verb 10.1007/s00158-021-03045-4
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      \verb{file}
      \verb Springer Full Text PDF:D\:\\estragio\\Zotero\\storage\\RAFZ88IY\\Thomas et al. - 2021 - Finite periodic topology optimization with oriente.pdf:application/pdf
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      \verb{urlraw}
      \verb https://doi.org/10.1007/s00158-021-03045-4
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s00158-021-03045-4
      \endverb
    \endentry
    \entry{liu_layout_2023}{article}{}
      \name{author}{6}{}{%
        {{hash=2ed68a56bfd902e0756e8c08e314a25c}{%
           family={Liu},
           familyi={L\bibinitperiod},
           given={Yufeng},
           giveni={Y\bibinitperiod}}}%
        {{hash=d23f8780b31a9738eb2ec5f9c954bcb4}{%
           family={Wang},
           familyi={W\bibinitperiod},
           given={Zhen},
           giveni={Z\bibinitperiod}}}%
        {{hash=ff82f455a06b3c34786ab4e11bbec2c2}{%
           family={Lu},
           familyi={L\bibinitperiod},
           given={Hongjia},
           giveni={H\bibinitperiod}}}%
        {{hash=3737d32939a3f1581e3cba8bf0eb0adc}{%
           family={Ye},
           familyi={Y\bibinitperiod},
           given={Jun},
           giveni={J\bibinitperiod}}}%
        {{hash=f0e7d180081df6c4c59c600f7c044474}{%
           family={Zhao},
           familyi={Z\bibinitperiod},
           given={Yang},
           giveni={Y\bibinitperiod}}}%
        {{hash=e9329c0d246f8f167e8b5c2dd7d3c974}{%
           family={Min\bibnamedelima Xie},
           familyi={M\bibinitperiod\bibinitdelim X\bibinitperiod},
           given={Yi},
           giveni={Y\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{ffd9ce6df6d4c05f97fcd2d53f29bee8}
      \strng{fullhash}{89d28e3bc84925dbc3417faa1aca7ef7}
      \strng{bibnamehash}{89d28e3bc84925dbc3417faa1aca7ef7}
      \strng{authorbibnamehash}{89d28e3bc84925dbc3417faa1aca7ef7}
      \strng{authornamehash}{ffd9ce6df6d4c05f97fcd2d53f29bee8}
      \strng{authorfullhash}{89d28e3bc84925dbc3417faa1aca7ef7}
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      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Truss layout optimization is a well-established technique for designing efficient structures, but the optimized structures are often complex and associated with high manufacturing costs. To address this problem, repetitive modules are often used. However, relying solely on a single type of module may negatively impact the structural efficiency. To mitigate this trade-off, this study presents a novel approach for designing truss structures that incorporates multiple types of modules. Additionally, both the module arrangement and module structures are determined by the optimization approach. To achieve this, a novel mixed-integer linear programming problem is developed, and a heuristic method is proposed to enhance computational efficiency. The proposed approach is validated through several numerical examples, which demonstrate its ability to produce truss designs with low manufacturing costs and high structural efficiency.}
      \field{issn}{2352-0124}
      \field{journaltitle}{Structures}
      \field{month}{9}
      \field{title}{Layout optimization of truss structures with modular constraints}
      \field{urlday}{5}
      \field{urlmonth}{7}
      \field{urlyear}{2023}
      \field{volume}{55}
      \field{year}{2023}
      \field{urldateera}{ce}
      \field{pages}{1460\bibrangedash 1469}
      \range{pages}{10}
      \verb{doi}
      \verb 10.1016/j.istruc.2023.06.071
      \endverb
      \verb{file}
      \verb ScienceDirect Full Text PDF:D\:\\estragio\\Zotero\\storage\\FCMC7FB2\\Liu et al. - 2023 - Layout optimization of truss structures with modul.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://www.sciencedirect.com/science/article/pii/S2352012423008305
      \endverb
      \verb{url}
      \verb https://www.sciencedirect.com/science/article/pii/S2352012423008305
      \endverb
      \keyw{Truss layout optimization,Mixed integer linear programming,Modular constraints,Structure optimization}
    \endentry
    \entry{stromberg_application_2011}{article}{}
      \name{author}{4}{}{%
        {{hash=13f49aed5bca84d0f93c8e22b8142f40}{%
           family={Stromberg},
           familyi={S\bibinitperiod},
           given={Lauren\bibnamedelima L.},
           giveni={L\bibinitperiod\bibinitdelim L\bibinitperiod}}}%
        {{hash=60b8d0ade8e2531f2adea6e53fc9f416}{%
           family={Beghini},
           familyi={B\bibinitperiod},
           given={Alessandro},
           giveni={A\bibinitperiod}}}%
        {{hash=a732cc0c5d33a4f870b8857cb58cd6b7}{%
           family={Baker},
           familyi={B\bibinitperiod},
           given={William\bibnamedelima F.},
           giveni={W\bibinitperiod\bibinitdelim F\bibinitperiod}}}%
        {{hash=d23667ac0203644c62a6179e0cd9673d}{%
           family={Paulino},
           familyi={P\bibinitperiod},
           given={Glaucio\bibnamedelima H.},
           giveni={G\bibinitperiod\bibinitdelim H\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{4632c80f8149e49b56d3ac1fa605c630}
      \strng{fullhash}{a70537cb08acbfbeb202f29a9ef3d8e9}
      \strng{bibnamehash}{a70537cb08acbfbeb202f29a9ef3d8e9}
      \strng{authorbibnamehash}{a70537cb08acbfbeb202f29a9ef3d8e9}
      \strng{authornamehash}{4632c80f8149e49b56d3ac1fa605c630}
      \strng{authorfullhash}{a70537cb08acbfbeb202f29a9ef3d8e9}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This paper explores the use of manufacturingtype constraints, in particular pattern gradation and repetition, in the context of building layout optimization. By placing constraints on the design domain in terms of number and variable size of repeating patterns along any direction, the conceptual design for buildings is facilitated. To substantiate the potential future applications of this work, examples within the context of high-rise building design are presented. Successful development of such ideas can contribute to practical engineering solutions, especially during the building design process. Examples are given to illustrate the ideas developed both in two-dimensional and three-dimensional building configurations.}
      \field{issn}{1615-147X, 1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{2}
      \field{number}{2}
      \field{title}{Application of layout and topology optimization using pattern gradation for the conceptual design of buildings}
      \field{urlday}{24}
      \field{urlmonth}{9}
      \field{urlyear}{2021}
      \field{volume}{43}
      \field{year}{2011}
      \field{urldateera}{ce}
      \field{pages}{165\bibrangedash 180}
      \range{pages}{16}
      \verb{doi}
      \verb 10.1007/s00158-010-0563-1
      \endverb
      \verb{file}
      \verb Stromberg et al. - 2011 - Application of layout and topology optimization us.pdf:D\:\\estragio\\Zotero\\storage\\9HLJAWKW\\Stromberg et al. - 2011 - Application of layout and topology optimization us.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb http://link.springer.com/10.1007/s00158-010-0563-1
      \endverb
      \verb{url}
      \verb http://link.springer.com/10.1007/s00158-010-0563-1
      \endverb
    \endentry
    \entry{wu_system_2016}{article}{}
      \name{author}{3}{}{%
        {{hash=aaf4818e3816b53809f264b2c1b2ecae}{%
           family={Wu},
           familyi={W\bibinitperiod},
           given={Jun},
           giveni={J\bibinitperiod}}}%
        {{hash=a22d6a7210969575471d46eba0df827c}{%
           family={Dick},
           familyi={D\bibinitperiod},
           given={Christian},
           giveni={C\bibinitperiod}}}%
        {{hash=c00f68e0027a0118ca2aa59ae43124c6}{%
           family={Westermann},
           familyi={W\bibinitperiod},
           given={Rüdiger},
           giveni={R\bibinitperiod}}}%
      }
      \strng{namehash}{fd6b712d4db2d86e9e06c93f8ebe40e4}
      \strng{fullhash}{fd6b712d4db2d86e9e06c93f8ebe40e4}
      \strng{bibnamehash}{fd6b712d4db2d86e9e06c93f8ebe40e4}
      \strng{authorbibnamehash}{fd6b712d4db2d86e9e06c93f8ebe40e4}
      \strng{authornamehash}{fd6b712d4db2d86e9e06c93f8ebe40e4}
      \strng{authorfullhash}{fd6b712d4db2d86e9e06c93f8ebe40e4}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
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      \field{labeltitlesource}{title}
      \field{abstract}{A key requirement in 3D fabrication is to generate objects with individual exterior shapes and their interior being optimized to application-specific force constraints and low material consumption. Accomplishing this task is challenging on desktop computers, due to the extreme model resolutions that are required to accurately predict the physical shape properties, requiring memory and computational capacities going beyond what is currently available. Moreover, fabrication-specific constraints need to be considered to enable printability. To address these challenges, we present a scalable system for generating 3D objects using topology optimization, which allows to efficiently evolve the topology of high-resolution solids towards printable and light-weight-high-resistance structures. To achieve this, the system is equipped with a high-performance GPU solver which can efficiently handle models comprising several millions of elements. A minimum thickness constraint is built into the optimization process to automatically enforce printability of the resulting shapes. We further shed light on the question how to incorporate geometric shape constraints, such as symmetry and pattern repetition, in the optimization process. We analyze the performance of the system and demonstrate its potential by a variety of different shapes such as interior structures within closed surfaces, exposed support structures, and surface models.}
      \field{issn}{1941-0506}
      \field{journaltitle}{IEEE Transactions on Visualization and Computer Graphics}
      \field{month}{3}
      \field{number}{3}
      \field{title}{A {System} for {High}-{Resolution} {Topology} {Optimization}}
      \field{urlday}{11}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{22}
      \field{year}{2016}
      \field{urldateera}{ce}
      \field{pages}{1195\bibrangedash 1208}
      \range{pages}{14}
      \verb{doi}
      \verb 10.1109/TVCG.2015.2502588
      \endverb
      \verb{urlraw}
      \verb https://ieeexplore.ieee.org/document/7332965
      \endverb
      \verb{url}
      \verb https://ieeexplore.ieee.org/document/7332965
      \endverb
    \endentry
    \entry{stragiotti_towards_2021}{inproceedings}{}
      \name{author}{4}{}{%
        {{hash=6c4965d3ad73fb11f44136afa897bb91}{%
           family={Stragiotti},
           familyi={S\bibinitperiod},
           given={Enrico},
           giveni={E\bibinitperiod}}}%
        {{hash=6ffe413a21f4954b0aac85ca037c7876}{%
           family={Irisarri},
           familyi={I\bibinitperiod},
           given={François-Xavier},
           giveni={F\bibinithyphendelim X\bibinitperiod}}}%
        {{hash=d9c42bf5ce7591763a45d8334a00d4e1}{%
           family={Julien},
           familyi={J\bibinitperiod},
           given={Cédric},
           giveni={C\bibinitperiod}}}%
        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
      }
      \list{location}{1}{%
        {Lisbon, Portugal}%
      }
      \list{publisher}{1}{%
        {ECCOMAS}%
      }
      \strng{namehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{fullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{bibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authorbibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authornamehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{authorfullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
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      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{shorttitle}
      \field{booktitle}{{AeroBest} 2021 {International} {Conference} on {Multidisciplinary} {Design} {Optimization} of {Aerospace} {Systems}. {Book} of proceedings}
      \field{month}{7}
      \field{shorttitle}{Towards manufactured lattice structures}
      \field{title}{Towards manufactured lattice structures: a comparison between layout and topology optimization}
      \field{urlday}{22}
      \field{urlmonth}{10}
      \field{urlyear}{2021}
      \field{year}{2021}
      \field{urldateera}{ce}
      \field{pages}{229\bibrangedash 244}
      \range{pages}{16}
      \verb{file}
      \verb HAL PDF Full Text:D\:\\estragio\\Zotero\\storage\\LTHX869B\\Stragiotti et al. - 2021 - Towards manufactured lattice structures a compari.pdf:application/pdf
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      \verb{urlraw}
      \verb https://hal.archives-ouvertes.fr/hal-03384893
      \endverb
      \verb{url}
      \verb https://hal.archives-ouvertes.fr/hal-03384893
      \endverb
      \keyw{Structural Optimization,Lattice Structures,Layout Optimization,Optimisation avec contraintes de stress,Optimisation des structures,Optimisation du Layout,Optimisation Topologique,Stress-Constrained Optimization,Structures Lattice,Topology Optimization,own}
    \endentry
    \entry{achtziger_mathematical_2008}{article}{}
      \name{author}{2}{}{%
        {{hash=be14cd2ace252d6ec45e16ea92c74e0f}{%
           family={Achtziger},
           familyi={A\bibinitperiod},
           given={Wolfgang},
           giveni={W\bibinitperiod}}}%
        {{hash=97d2e434223bd2d37723183cbed5e8df}{%
           family={Kanzow},
           familyi={K\bibinitperiod},
           given={Christian},
           giveni={C\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{9196a90280f9f19b16c3cbb96251e7a6}
      \strng{fullhash}{9196a90280f9f19b16c3cbb96251e7a6}
      \strng{bibnamehash}{9196a90280f9f19b16c3cbb96251e7a6}
      \strng{authorbibnamehash}{9196a90280f9f19b16c3cbb96251e7a6}
      \strng{authornamehash}{9196a90280f9f19b16c3cbb96251e7a6}
      \strng{authorfullhash}{9196a90280f9f19b16c3cbb96251e7a6}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{shorttitle}
      \field{journaltitle}{Mathematical Programming}
      \field{month}{7}
      \field{number}{1}
      \field{shorttitle}{Mathematical programs with vanishing constraints}
      \field{title}{Mathematical programs with vanishing constraints: optimality conditions and constraint qualifications}
      \field{urlday}{23}
      \field{urlmonth}{3}
      \field{urlyear}{2021}
      \field{volume}{114}
      \field{year}{2008}
      \field{urldateera}{ce}
      \field{pages}{69\bibrangedash 99}
      \range{pages}{31}
      \verb{doi}
      \verb 10.1007/s10107-006-0083-3
      \endverb
    \endentry
    \entry{cheng_study_1992}{article}{}
      \name{author}{2}{}{%
        {{hash=5fba7de724fe01e2541f05efe522b531}{%
           family={Cheng},
           familyi={C\bibinitperiod},
           given={Gengdong},
           giveni={G\bibinitperiod}}}%
        {{hash=e9848eb537eccb742ec1403babebb7d2}{%
           family={Jiang},
           familyi={J\bibinitperiod},
           given={Zheng},
           giveni={Z\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{b480503eac99a715174c302554837635}
      \strng{fullhash}{b480503eac99a715174c302554837635}
      \strng{bibnamehash}{b480503eac99a715174c302554837635}
      \strng{authorbibnamehash}{b480503eac99a715174c302554837635}
      \strng{authornamehash}{b480503eac99a715174c302554837635}
      \strng{authorfullhash}{b480503eac99a715174c302554837635}
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      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{journaltitle}{Engineering Optimization}
      \field{month}{11}
      \field{number}{2}
      \field{title}{Study on {Topology} {Optimization} with {Stress} {Constraints}}
      \field{urlday}{23}
      \field{urlmonth}{6}
      \field{urlyear}{2021}
      \field{volume}{20}
      \field{year}{1992}
      \field{urldateera}{ce}
      \field{pages}{129\bibrangedash 148}
      \range{pages}{20}
      \verb{doi}
      \verb 10.1080/03052159208941276
      \endverb
    \endentry
    \entry{verbart_unified_2017}{article}{}
      \name{author}{3}{}{%
        {{hash=8e862bb73f0719127baabf8cd7eea5c3}{%
           family={Verbart},
           familyi={V\bibinitperiod},
           given={Alexander},
           giveni={A\bibinitperiod}}}%
        {{hash=252f12ad906deceed3132e4839bf0aba}{%
           family={Langelaar},
           familyi={L\bibinitperiod},
           given={Matthijs},
           giveni={M\bibinitperiod}}}%
        {{hash=fced7f35e3ed00611970d9aa7179fda2}{%
           family={Keulen},
           familyi={K\bibinitperiod},
           given={Fred\bibnamedelima van},
           giveni={F\bibinitperiod\bibinitdelim v\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{8ae7d135b945e4a7f6a5e0dae651bc6a}
      \strng{fullhash}{8ae7d135b945e4a7f6a5e0dae651bc6a}
      \strng{bibnamehash}{8ae7d135b945e4a7f6a5e0dae651bc6a}
      \strng{authorbibnamehash}{8ae7d135b945e4a7f6a5e0dae651bc6a}
      \strng{authornamehash}{8ae7d135b945e4a7f6a5e0dae651bc6a}
      \strng{authorfullhash}{8ae7d135b945e4a7f6a5e0dae651bc6a}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{In this paper, we propose a unified aggregation and relaxation approach for topology optimization with stress constraints. Following this approach, we first reformulate the original optimization problem with a design-dependent set of constraints into an equivalent optimization problem with a fixed design-independent set of constraints. The next step is to perform constraint aggregation over the reformulated local constraints using a lower bound aggregation function. We demonstrate that this approach concurrently aggregates the constraints and relaxes the feasible domain, thereby making singular optima accessible. The main advantage is that no separate constraint relaxation techniques are necessary, which reduces the parameter dependence of the problem. Furthermore, there is a clear relationship between the original feasible domain and the perturbed feasible domain via this aggregation parameter.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{2}
      \field{number}{2}
      \field{title}{A unified aggregation and relaxation approach for stress-constrained topology optimization}
      \field{urlday}{25}
      \field{urlmonth}{3}
      \field{urlyear}{2021}
      \field{volume}{55}
      \field{year}{2017}
      \field{urldateera}{ce}
      \field{pages}{663\bibrangedash 679}
      \range{pages}{17}
      \verb{doi}
      \verb 10.1007/s00158-016-1524-0
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      \verb{file}
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      \verb{urlraw}
      \verb https://doi.org/10.1007/s00158-016-1524-0
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s00158-016-1524-0
      \endverb
    \endentry
    \entry{duysinx_topology_1998}{article}{}
      \name{author}{2}{}{%
        {{hash=b1ed7d234fa596fdf5e7b44ba01e7c30}{%
           family={Duysinx},
           familyi={D\bibinitperiod},
           given={P.},
           giveni={P\bibinitperiod}}}%
        {{hash=193e92bb57a8aeb7a8a809f2e4f7221f}{%
           family={Bendsøe},
           familyi={B\bibinitperiod},
           given={M.\bibnamedelimi P.},
           giveni={M\bibinitperiod\bibinitdelim P\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{e32944e7bdb38addf1165b1334c1f251}
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      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{We introduce an extension of current technologies for topology optimization of continuum structures which allows for treating local stress criteria. We first consider relevant stress criteria for porous composite materials, initially by studying the stress states of the so-called rank 2 layered materials. Then, on the basis of the theoretical study of the rank 2 microstructures, we propose an empirical model that extends the power penalized stiffness model (also called SIMP for Solid Isotropic Microstructure with Penalization for inter-mediate densities). In a second part, solution aspects of topology problems are considered. To deal with the so-called ‘singularity’ phenomenon of stress constraints in topology design, an ϵ-constraint relaxation of the stress constraints is used. We describe the mathematical programming approach that is used to solve the numerical optimization problems, and show results for a number of example applications. © 1998 John Wiley \&amp; Sons, Ltd.}
      \field{issn}{1097-0207}
      \field{journaltitle}{International Journal for Numerical Methods in Engineering}
      \field{number}{8}
      \field{title}{Topology optimization of continuum structures with local stress constraints}
      \field{urlday}{23}
      \field{urlmonth}{6}
      \field{urlyear}{2021}
      \field{volume}{43}
      \field{year}{1998}
      \field{urldateera}{ce}
      \field{pages}{1453\bibrangedash 1478}
      \range{pages}{26}
      \verb{doi}
      \verb 10.1002/(SICI)1097-0207(19981230)43:8&lt;1453::AID-NME480&gt;3.0.CO;2-2
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\WR64FMTM\\Duysinx and Bendsøe - 1998 - Topology optimization of continuum structures with.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://onlinelibrary.wiley.com/doi/abs/10.1002/%28SICI%291097-0207%2819981230%2943%3A8%3C1453%3A%3AAID-NME480%3E3.0.CO%3B2-2
      \endverb
      \verb{url}
      \verb https://onlinelibrary.wiley.com/doi/abs/10.1002/%28SICI%291097-0207%2819981230%2943%3A8%3C1453%3A%3AAID-NME480%3E3.0.CO%3B2-2
      \endverb
      \keyw{topology optimization,stress constraints,continua}
    \endentry
    \entry{le_stress-based_2010}{article}{}
      \name{author}{5}{}{%
        {{hash=4c29a40368ae4798216557c9fb04cab4}{%
           family={Le},
           familyi={L\bibinitperiod},
           given={Chau},
           giveni={C\bibinitperiod}}}%
        {{hash=ab3e6d42ded9f4fe23a33e44db433f9e}{%
           family={Norato},
           familyi={N\bibinitperiod},
           given={Julian},
           giveni={J\bibinitperiod}}}%
        {{hash=2559d4f414b2f656b0eaf647be2f36e7}{%
           family={Bruns},
           familyi={B\bibinitperiod},
           given={Tyler},
           giveni={T\bibinitperiod}}}%
        {{hash=9c346d89aa70f3bf08f4963d3af4c75a}{%
           family={Ha},
           familyi={H\bibinitperiod},
           given={Christopher},
           giveni={C\bibinitperiod}}}%
        {{hash=5b4c682f8ad091b7cf3101b8bf56350a}{%
           family={Tortorelli},
           familyi={T\bibinitperiod},
           given={Daniel},
           giveni={D\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{c62850260484cff936e5048b34713f08}
      \strng{fullhash}{495bf2c7c0d02fa6bebee2cbaa73c8d9}
      \strng{bibnamehash}{495bf2c7c0d02fa6bebee2cbaa73c8d9}
      \strng{authorbibnamehash}{495bf2c7c0d02fa6bebee2cbaa73c8d9}
      \strng{authornamehash}{c62850260484cff936e5048b34713f08}
      \strng{authorfullhash}{495bf2c7c0d02fa6bebee2cbaa73c8d9}
      \field{sortinit}{1}
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      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{We propose an effective algorithm to resolve the stress-constrained topology optimization problem. Our procedure combines a density ﬁlter for length scale control, the solid isotropic material with penalization (SIMP) to generate black-and-white designs, a SIMP-motivated stress deﬁnition to resolve the stress singularity phenomenon, and a global/regional stress measure combined with an adaptive normalization scheme to control the local stress level.}
      \field{issn}{1615-147X, 1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{4}
      \field{number}{4}
      \field{title}{Stress-based topology optimization for continua}
      \field{urlday}{23}
      \field{urlmonth}{6}
      \field{urlyear}{2021}
      \field{volume}{41}
      \field{year}{2010}
      \field{urldateera}{ce}
      \field{pages}{605\bibrangedash 620}
      \range{pages}{16}
      \verb{doi}
      \verb 10.1007/s00158-009-0440-y
      \endverb
      \verb{file}
      \verb Le et al. - 2010 - Stress-based topology optimization for continua.pdf:D\:\\estragio\\Zotero\\storage\\HK6G4IST\\Le et al. - 2010 - Stress-based topology optimization for continua.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb http://link.springer.com/10.1007/s00158-009-0440-y
      \endverb
      \verb{url}
      \verb http://link.springer.com/10.1007/s00158-009-0440-y
      \endverb
    \endentry
    \entry{holmberg_stress_2013}{article}{}
      \name{author}{3}{}{%
        {{hash=1c863ccd6d20cab37c5bf301bea34669}{%
           family={Holmberg},
           familyi={H\bibinitperiod},
           given={Erik},
           giveni={E\bibinitperiod}}}%
        {{hash=ca37f74b84a88500bfea47d9a4caed22}{%
           family={Torstenfelt},
           familyi={T\bibinitperiod},
           given={Bo},
           giveni={B\bibinitperiod}}}%
        {{hash=653e1123d26b5e95243c1eba80065a66}{%
           family={Klarbring},
           familyi={K\bibinitperiod},
           given={Anders},
           giveni={A\bibinitperiod}}}%
      }
      \strng{namehash}{dcfbf2ef22e396ed8c5fccd258db3346}
      \strng{fullhash}{dcfbf2ef22e396ed8c5fccd258db3346}
      \strng{bibnamehash}{dcfbf2ef22e396ed8c5fccd258db3346}
      \strng{authorbibnamehash}{dcfbf2ef22e396ed8c5fccd258db3346}
      \strng{authornamehash}{dcfbf2ef22e396ed8c5fccd258db3346}
      \strng{authorfullhash}{dcfbf2ef22e396ed8c5fccd258db3346}
      \field{sortinit}{1}
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      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This paper develops and evaluates a method for handling stress constraints in topology optimization. The stress constraints are used together with an objective function that minimizes mass or maximizes stiffness, and in addition, the traditional stiffness based formulation is discussed for comparison. We use a clustering technique, where stresses for several stress evaluation points are clustered into groups using a modified P-norm to decrease the number of stress constraints and thus the computational cost. We give a detailed description of the formulations and the sensitivity analysis. This is done in a general manner, so that different element types and 2D as well as 3D structures can be treated. However, we restrict the numerical examples to 2D structures with bilinear quadrilateral elements. The three formulations and different approaches to stress constraints are compared using two well known test examples in topology optimization: the L-shaped beam and the MBB-beam. In contrast to some other papers on stress constrained topology optimization, we find that our formulation gives topologies that are significantly different from traditionally optimized designs, in that it actually manage to avoid stress concentrations. It can therefore be used to generate conceptual designs for industrial applications.}
      \field{issn}{1615-147X}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{number}{1}
      \field{title}{Stress constrained topology optimization}
      \field{urlday}{30}
      \field{urlmonth}{8}
      \field{urlyear}{2023}
      \field{volume}{48}
      \field{year}{2013}
      \field{urldateera}{ce}
      \field{pages}{33\bibrangedash 47}
      \range{pages}{15}
      \verb{doi}
      \verb 10.1007/s00158-012-0880-7
      \endverb
      \verb{file}
      \verb Submitted Version:D\:\\estragio\\Zotero\\storage\\TNMAU4KW\\Holmberg et al. - 2013 - Stress constrained topology optimization.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/s00158-012-0880-7
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s00158-012-0880-7
      \endverb
      \keyw{Clusters,MMA,SIMP,Stress constraints,Topology optimization}
    \endentry
    \entry{da_silva_stress-constrained_2019}{article}{}
      \name{author}{3}{}{%
        {{hash=b8a94b8fc55213cefb82db0ccc4a44af}{%
           family={Silva},
           familyi={S\bibinitperiod},
           given={Gustavo\bibnamedelima Assis},
           giveni={G\bibinitperiod\bibinitdelim A\bibinitperiod},
           prefix={da},
           prefixi={d\bibinitperiod}}}%
        {{hash=6246559c30f5c20668706f0cd8651634}{%
           family={Beck},
           familyi={B\bibinitperiod},
           given={André\bibnamedelima Teófilo},
           giveni={A\bibinitperiod\bibinitdelim T\bibinitperiod}}}%
        {{hash=d76f1c09e8d8d06e1b7c3c254efeae1a}{%
           family={Sigmund},
           familyi={S\bibinitperiod},
           given={Ole},
           giveni={O\bibinitperiod}}}%
      }
      \strng{namehash}{b137bea409a40c60669bce5023ea28f0}
      \strng{fullhash}{b137bea409a40c60669bce5023ea28f0}
      \strng{bibnamehash}{b137bea409a40c60669bce5023ea28f0}
      \strng{authorbibnamehash}{b137bea409a40c60669bce5023ea28f0}
      \strng{authornamehash}{b137bea409a40c60669bce5023ea28f0}
      \strng{authorfullhash}{b137bea409a40c60669bce5023ea28f0}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This paper proposes a robust design approach, based on eroded, intermediate and dilated projections, to handle uniform manufacturing uncertainties in stress-constrained topology optimization. In addition, a simple scheme is proposed to increase accuracy of stress evaluation at jagged edges, based on limiting sharpness of the projections to intentionally allow a thin layer of intermediate material between solid and void phases. A reference problem is analyzed through voxel-based finite element models, demonstrating that, in association with a proper choice of stiffness and stress interpolation functions, the proposed scheme can ensure consistent stress magnitude and smooth stress behavior for uniform boundary variation. Optimization problems are solved and post-processing with body-fitted meshes is performed over optimized solutions, demonstrating that: (1) stresses evaluated with voxel-based meshes containing thin soft transition boundaries are consistent with stresses evaluated with body-fitted meshes; and (2) optimized structures are robust with respect to uniform boundary variations.}
      \field{issn}{0045-7825}
      \field{journaltitle}{Computer Methods in Applied Mechanics and Engineering}
      \field{month}{2}
      \field{title}{Stress-constrained topology optimization considering uniform manufacturing uncertainties}
      \field{urlday}{30}
      \field{urlmonth}{8}
      \field{urlyear}{2023}
      \field{volume}{344}
      \field{year}{2019}
      \field{urldateera}{ce}
      \field{pages}{512\bibrangedash 537}
      \range{pages}{26}
      \verb{doi}
      \verb 10.1016/j.cma.2018.10.020
      \endverb
      \verb{file}
      \verb ScienceDirect Full Text PDF:D\:\\estragio\\Zotero\\storage\\CGEBVEZR\\da Silva et al. - 2019 - Stress-constrained topology optimization consideri.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://www.sciencedirect.com/science/article/pii/S0045782518305231
      \endverb
      \verb{url}
      \verb https://www.sciencedirect.com/science/article/pii/S0045782518305231
      \endverb
      \keyw{Topology optimization,Stress constraints,Manufacturing uncertainties,Robust design}
    \endentry
    \entry{stolpe_models_2003}{thesis}{}
      \name{author}{1}{}{%
        {{hash=2ac977bc03dde1f3d4061cda61ab9795}{%
           family={Stolpe},
           familyi={S\bibinitperiod},
           given={Mathias},
           giveni={M\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {eng}%
      }
      \strng{namehash}{2ac977bc03dde1f3d4061cda61ab9795}
      \strng{fullhash}{2ac977bc03dde1f3d4061cda61ab9795}
      \strng{bibnamehash}{2ac977bc03dde1f3d4061cda61ab9795}
      \strng{authorbibnamehash}{2ac977bc03dde1f3d4061cda61ab9795}
      \strng{authornamehash}{2ac977bc03dde1f3d4061cda61ab9795}
      \strng{authorfullhash}{2ac977bc03dde1f3d4061cda61ab9795}
      \field{extraname}{3}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{title}{On {Models} and {Methods} for {Global} {Optimization} of {Structural} {Topology}}
      \field{type}{phdthesis}
      \field{urlday}{25}
      \field{urlmonth}{3}
      \field{urlyear}{2021}
      \field{year}{2003}
      \field{urldateera}{ce}
      \verb{urlraw}
      \verb http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3478
      \endverb
      \verb{url}
      \verb http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3478
      \endverb
    \endentry
    \entry{sved_structural_1968}{article}{}
      \name{author}{2}{}{%
        {{hash=f2221d47cce5ac2ac3fd4d1c332980d0}{%
           family={Sved},
           familyi={S\bibinitperiod},
           given={G.},
           giveni={G\bibinitperiod}}}%
        {{hash=f08a245e8a015e2279883d1610f7fc4b}{%
           family={Ginos},
           familyi={G\bibinitperiod},
           given={Z.},
           giveni={Z\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{360d3249060f35926f15baad821aee05}
      \strng{fullhash}{360d3249060f35926f15baad821aee05}
      \strng{bibnamehash}{360d3249060f35926f15baad821aee05}
      \strng{authorbibnamehash}{360d3249060f35926f15baad821aee05}
      \strng{authornamehash}{360d3249060f35926f15baad821aee05}
      \strng{authorfullhash}{360d3249060f35926f15baad821aee05}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{journaltitle}{International Journal of Mechanical Sciences}
      \field{month}{10}
      \field{number}{10}
      \field{title}{Structural optimization under multiple loading}
      \field{urlday}{23}
      \field{urlmonth}{6}
      \field{urlyear}{2021}
      \field{volume}{10}
      \field{year}{1968}
      \field{urldateera}{ce}
      \field{pages}{803\bibrangedash 805}
      \range{pages}{3}
      \verb{doi}
      \verb 10.1016/0020-7403(68)90021-0
      \endverb
    \endentry
    \entry{da_silva_local_2021}{article}{}
      \name{author}{4}{}{%
        {{hash=b8a94b8fc55213cefb82db0ccc4a44af}{%
           family={Silva},
           familyi={S\bibinitperiod},
           given={Gustavo\bibnamedelima Assis},
           giveni={G\bibinitperiod\bibinitdelim A\bibinitperiod},
           prefix={da},
           prefixi={d\bibinitperiod}}}%
        {{hash=fa5a136030c946f96655797e3220c1bb}{%
           family={Aage},
           familyi={A\bibinitperiod},
           given={Niels},
           giveni={N\bibinitperiod}}}%
        {{hash=6246559c30f5c20668706f0cd8651634}{%
           family={Beck},
           familyi={B\bibinitperiod},
           given={André\bibnamedelima Teófilo},
           giveni={A\bibinitperiod\bibinitdelim T\bibinitperiod}}}%
        {{hash=d76f1c09e8d8d06e1b7c3c254efeae1a}{%
           family={Sigmund},
           familyi={S\bibinitperiod},
           given={Ole},
           giveni={O\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{cd0010b0b7e6f555dd016af38edea5a7}
      \strng{fullhash}{35ad91d750fcdde377e4b6cf0045e1a4}
      \strng{bibnamehash}{35ad91d750fcdde377e4b6cf0045e1a4}
      \strng{authorbibnamehash}{35ad91d750fcdde377e4b6cf0045e1a4}
      \strng{authornamehash}{cd0010b0b7e6f555dd016af38edea5a7}
      \strng{authorfullhash}{35ad91d750fcdde377e4b6cf0045e1a4}
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      \field{labelnamesource}{author}
      \field{labeltitlesource}{shorttitle}
      \field{abstract}{Stress-constrained topology optimization requires techniques for handling thousands to millions of stress constraints. This work presents a comprehensive numerical study comparing local and global stress constraint strategies in topology optimization. Four local and four global solution strategies are presented and investigated. The local strategies are based on either the augmented Lagrangian or the pure exterior penalty method, whereas the global strategies are based on the P-mean aggregation function. Extensive parametric studies are carried out on the L-shaped design problem to identify the most promising parameters for each solution strategy. It is found that (1) the local strategies are less sensitive to the continuation procedure employed in standard density-based topology optimization, allowing achievement of better quality results using less iterations when compared with the global strategies; (2) the global strategies become competitive when P values larger than 100 are employed, but for this to be possible a very slow continuation procedure should be used; (3) the local strategies based on the augmented Lagrangian method provide the best compromise between computational cost and performance, being able to achieve optimized topologies at the level of a pure P-continuation global strategy with P=300, but using less iterations.}
      \field{issn}{1097-0207}
      \field{journaltitle}{International Journal for Numerical Methods in Engineering}
      \field{number}{21}
      \field{shorttitle}{Local versus global stress constraint strategies in topology optimization}
      \field{title}{Local versus global stress constraint strategies in topology optimization: {A} comparative study}
      \field{urlday}{31}
      \field{urlmonth}{8}
      \field{urlyear}{2023}
      \field{volume}{122}
      \field{year}{2021}
      \field{urldateera}{ce}
      \field{pages}{6003\bibrangedash 6036}
      \range{pages}{34}
      \verb{doi}
      \verb 10.1002/nme.6781
      \endverb
      \verb{file}
      \verb Full Text:D\:\\estragio\\Zotero\\storage\\XKFNV4QM\\da Silva et al. - 2021 - Local versus global stress constraint strategies i.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.6781
      \endverb
      \verb{url}
      \verb https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.6781
      \endverb
      \keyw{augmented Lagrangian,global stress constraint,local stress constraints,stress aggregation function,topology optimization}
    \endentry
    \entry{kreisselmeier_systematic_1979}{article}{}
      \name{author}{2}{}{%
        {{hash=2df8c0d19b6d7e4b9a673cb47db3ce46}{%
           family={Kreisselmeier},
           familyi={K\bibinitperiod},
           given={G.},
           giveni={G\bibinitperiod}}}%
        {{hash=8ba9577c5f057b3f8ffe26fdbbc155bd}{%
           family={Steinhauser},
           familyi={S\bibinitperiod},
           given={R.},
           giveni={R\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{f5a184712a4d2fc83113c18dd3f68667}
      \strng{fullhash}{f5a184712a4d2fc83113c18dd3f68667}
      \strng{bibnamehash}{f5a184712a4d2fc83113c18dd3f68667}
      \strng{authorbibnamehash}{f5a184712a4d2fc83113c18dd3f68667}
      \strng{authornamehash}{f5a184712a4d2fc83113c18dd3f68667}
      \strng{authorfullhash}{f5a184712a4d2fc83113c18dd3f68667}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{journaltitle}{IFAC Proceedings Volumes}
      \field{month}{9}
      \field{number}{7}
      \field{series}{{IFAC} {Symposium} on computer {Aided} {Design} of {Control} {Systems}, {Zurich}, {Switzerland}, 29-31 {August}}
      \field{title}{Systematic {Control} {Design} by {Optimizing} a {Vector} {Performance} {Index}}
      \field{urlday}{14}
      \field{urlmonth}{4}
      \field{urlyear}{2021}
      \field{volume}{12}
      \field{year}{1979}
      \field{urldateera}{ce}
      \field{pages}{113\bibrangedash 117}
      \range{pages}{5}
      \verb{doi}
      \verb 10.1016/S1474-6670(17)65584-8
      \endverb
      \keyw{Computer aided design,vector performance index}
    \endentry
    \entry{watts_simple_2019}{article}{}
      \name{author}{5}{}{%
        {{hash=71baf31625fa1536b2c32e1e2c07e97d}{%
           family={Watts},
           familyi={W\bibinitperiod},
           given={Seth},
           giveni={S\bibinitperiod}}}%
        {{hash=f09774962ebba4d0026a48cf2109df81}{%
           family={Arrighi},
           familyi={A\bibinitperiod},
           given={William},
           giveni={W\bibinitperiod}}}%
        {{hash=60d0e334c4a514fc59970c0ae5e62c3f}{%
           family={Kudo},
           familyi={K\bibinitperiod},
           given={Jun},
           giveni={J\bibinitperiod}}}%
        {{hash=2dc94736fafc9292d9d5fe6bbacf2606}{%
           family={Tortorelli},
           familyi={T\bibinitperiod},
           given={Daniel\bibnamedelima A.},
           giveni={D\bibinitperiod\bibinitdelim A\bibinitperiod}}}%
        {{hash=4215597d2c71e616e31751f6b8ed0e31}{%
           family={White},
           familyi={W\bibinitperiod},
           given={Daniel\bibnamedelima A.},
           giveni={D\bibinitperiod\bibinitdelim A\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{a5e426b96d7e6c3c5ee5569f2a045ca2}
      \strng{fullhash}{ea681b2d1cea0ead3ec69409cf164740}
      \strng{bibnamehash}{ea681b2d1cea0ead3ec69409cf164740}
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      \strng{authorfullhash}{ea681b2d1cea0ead3ec69409cf164740}
      \field{sortinit}{1}
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      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Elastic meta-materials are those whose unique properties come from their micro-architecture, rather than, e.g., from their chemistry. The introduction of such architecture, which is increasingly able to be fabricated due to advances in additive manufacturing, expands the design domain and enables improved design, from the most complex multi-physics design problems to the simple compliance design problem that is our focus. Unfortunately, concurrent design of both the micro-scale and the macroscale is computationally very expensive when the former can vary spatially, particularly in three dimensions. Instead, we provide simple, accurate surrogate models of the homogenized linear elastic response of the isotruss, the octet truss, and the ORC truss based on high-fidelity continuum finite element analyses. These surrogate models are relatively accurate over the full range of relative densities, in contrast to analytical models in the literature, which we show lose accuracy as relative density increases. The surrogate models are also simple to implement, which we demonstrate by modifying Sigmund’s 99-line code to solve a three-dimensional, multiscale compliance design problem with spatially varying relative density. We use this code to generate examples in both two and three dimensions that illustrate the advantage of elastic meta-materials over structures with a single length scale, i.e., those without micro-architectures.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{11}
      \field{number}{5}
      \field{title}{Simple, accurate surrogate models of the elastic response of three-dimensional open truss micro-architectures with applications to multiscale topology design}
      \field{urlday}{16}
      \field{urlmonth}{12}
      \field{urlyear}{2020}
      \field{volume}{60}
      \field{year}{2019}
      \field{urldateera}{ce}
      \field{pages}{1887\bibrangedash 1920}
      \range{pages}{34}
      \verb{doi}
      \verb 10.1007/s00158-019-02297-5
      \endverb
      \verb{file}
      \verb Springer Full Text PDF:D\:\\estragio\\Zotero\\storage\\3QL6FSVV\\Watts et al. - 2019 - Simple, accurate surrogate models of the elastic r.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/s00158-019-02297-5
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s00158-019-02297-5
      \endverb
    \endentry
    \entry{NLopt_2007}{misc}{}
      \name{author}{1}{}{%
        {{hash=f271cef1e5ae0aff0d07deccf21fd368}{%
           family={Johnson},
           familyi={J\bibinitperiod},
           given={Steven\bibnamedelima G.},
           giveni={S\bibinitperiod\bibinitdelim G\bibinitperiod}}}%
      }
      \strng{namehash}{f271cef1e5ae0aff0d07deccf21fd368}
      \strng{fullhash}{f271cef1e5ae0aff0d07deccf21fd368}
      \strng{bibnamehash}{f271cef1e5ae0aff0d07deccf21fd368}
      \strng{authorbibnamehash}{f271cef1e5ae0aff0d07deccf21fd368}
      \strng{authornamehash}{f271cef1e5ae0aff0d07deccf21fd368}
      \strng{authorfullhash}{f271cef1e5ae0aff0d07deccf21fd368}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{howpublished}{\url{https://github.com/stevengj/nlopt}}
      \field{title}{The {NLopt} nonlinear-optimization package}
      \field{year}{2007}
    \endentry
    \entry{diamond_cvxpy_2016}{misc}{}
      \name{author}{2}{}{%
        {{hash=d50bdcda78beb231a5057a4372dac2fd}{%
           family={Diamond},
           familyi={D\bibinitperiod},
           given={Steven},
           giveni={S\bibinitperiod}}}%
        {{hash=ec94d94cc487dd71939a90cbeaaf47d0}{%
           family={Boyd},
           familyi={B\bibinitperiod},
           given={Stephen},
           giveni={S\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{7cce040882870150496852f2140da7fb}
      \strng{fullhash}{7cce040882870150496852f2140da7fb}
      \strng{bibnamehash}{7cce040882870150496852f2140da7fb}
      \strng{authorbibnamehash}{7cce040882870150496852f2140da7fb}
      \strng{authornamehash}{7cce040882870150496852f2140da7fb}
      \strng{authorfullhash}{7cce040882870150496852f2140da7fb}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{title}{{CVXPY}: {A} {Python}-{Embedded} {Modeling} {Language} for {Convex} {Optimization}}
      \field{year}{2016}
      \field{pages}{5}
      \range{pages}{1}
    \endentry
    \entry{domahidi_ecos_2013}{inproceedings}{}
      \name{author}{3}{}{%
        {{hash=65509ad17c3ebe7d343fc93576249e6c}{%
           family={Domahidi},
           familyi={D\bibinitperiod},
           given={Alexander},
           giveni={A\bibinitperiod}}}%
        {{hash=a9b44e6e637f2b45f96e1c9c60803c93}{%
           family={Chu},
           familyi={C\bibinitperiod},
           given={Eric},
           giveni={E\bibinitperiod}}}%
        {{hash=ec94d94cc487dd71939a90cbeaaf47d0}{%
           family={Boyd},
           familyi={B\bibinitperiod},
           given={Stephen},
           giveni={S\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \list{location}{1}{%
        {Zurich}%
      }
      \list{publisher}{1}{%
        {IEEE}%
      }
      \strng{namehash}{b18d5df085a5b31c591b33eaffa01215}
      \strng{fullhash}{b18d5df085a5b31c591b33eaffa01215}
      \strng{bibnamehash}{b18d5df085a5b31c591b33eaffa01215}
      \strng{authorbibnamehash}{b18d5df085a5b31c591b33eaffa01215}
      \strng{authornamehash}{b18d5df085a5b31c591b33eaffa01215}
      \strng{authorfullhash}{b18d5df085a5b31c591b33eaffa01215}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{In this paper, we describe the embedded conic solver (ECOS), an interior-point solver for second-order cone programming (SOCP) designed speciﬁcally for embedded applications. ECOS is written in low footprint, single-threaded, library-free ANSI-C and so runs on most embedded platforms. The main interior-point algorithm is a standard primal-dual Mehrotra predictor-corrector method with Nesterov-Todd scaling and self-dual embedding, with search directions found via a symmetric indeﬁnite KKT system, chosen to allow stable factorization with a ﬁxed pivoting order. The indeﬁnite system is solved using Davis’ SparseLDL package, which we modify by adding dynamic regularization and iterative reﬁnement for stability and reliability, as is done in the CVXGEN code generation system, allowing us to avoid all numerical pivoting; the elimination ordering is found entirely symbolically. This keeps the solver simple, only 750 lines of code, with virtually no variation in run time. For small problems, ECOS is faster than most existing SOCP solvers; it is still competitive for mediumsized problems up to tens of thousands of variables.}
      \field{booktitle}{2013 {European} {Control} {Conference} ({ECC})}
      \field{isbn}{978-3-033-03962-9}
      \field{month}{7}
      \field{title}{{ECOS}: {An} {SOCP} solver for embedded systems}
      \field{urlday}{17}
      \field{urlmonth}{1}
      \field{urlyear}{2023}
      \field{year}{2013}
      \field{urldateera}{ce}
      \field{pages}{3071\bibrangedash 3076}
      \range{pages}{6}
      \verb{doi}
      \verb 10.23919/ECC.2013.6669541
      \endverb
      \verb{file}
      \verb Domahidi et al. - 2013 - ECOS An SOCP solver for embedded systems.pdf:D\:\\estragio\\Zotero\\storage\\L69QPGKJ\\Domahidi et al. - 2013 - ECOS An SOCP solver for embedded systems.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://ieeexplore.ieee.org/document/6669541/
      \endverb
      \verb{url}
      \verb https://ieeexplore.ieee.org/document/6669541/
      \endverb
    \endentry
    \entry{lewinski_extended_1994}{article}{}
      \name{author}{3}{}{%
        {{hash=417b620beb41937e6ad39fabaaed560f}{%
           family={Lewiński},
           familyi={L\bibinitperiod},
           given={T.},
           giveni={T\bibinitperiod}}}%
        {{hash=3edb51e096c6e1b022984c9159c4df2d}{%
           family={Zhou},
           familyi={Z\bibinitperiod},
           given={M.},
           giveni={M\bibinitperiod}}}%
        {{hash=2dd717bb9ecafd6aa2723e522b7aa056}{%
           family={Rozvany},
           familyi={R\bibinitperiod},
           given={G.\bibnamedelimi I.\bibnamedelimi N.},
           giveni={G\bibinitperiod\bibinitdelim I\bibinitperiod\bibinitdelim N\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{ed2c491ed02bf15f6b8a278441395d58}
      \strng{fullhash}{ed2c491ed02bf15f6b8a278441395d58}
      \strng{bibnamehash}{ed2c491ed02bf15f6b8a278441395d58}
      \strng{authorbibnamehash}{ed2c491ed02bf15f6b8a278441395d58}
      \strng{authornamehash}{ed2c491ed02bf15f6b8a278441395d58}
      \strng{authorfullhash}{ed2c491ed02bf15f6b8a278441395d58}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{shorttitle}
      \field{abstract}{The paper deals with new applications of Michell's theory for determining the layout of least-weight trusses under a single load condition and the same permissible stress for all bars. Considering cantilever trusses with a horizontal axis of symmetry, the optimal layout was derived in a closed analytical form by A. S. L. Chan and H. S. Y. Chan for a limited length: height ratio. Solutions beyond the above ratio are investigated in this paper. The results will be extended to non-symmetric cantilever trusses in Part II of this study. In both parts, a novel method is used for deriving adjoint displacements. The results are also confirmed by comparisons with discretized solutions for trusses and perforated plates.}
      \field{issn}{0020-7403}
      \field{journaltitle}{International Journal of Mechanical Sciences}
      \field{number}{5}
      \field{shorttitle}{Extended exact solutions for least-weight truss layouts—{Part} {I}}
      \field{title}{Extended exact solutions for least-weight truss layouts—{Part} {I}: {Cantilever} with a horizontal axis of symmetry}
      \field{urlday}{9}
      \field{urlmonth}{2}
      \field{urlyear}{2022}
      \field{volume}{36}
      \field{year}{1994}
      \field{urldateera}{ce}
      \field{pages}{375\bibrangedash 398}
      \range{pages}{24}
      \verb{doi}
      \verb 10.1016/0020-7403(94)90043-4
      \endverb
      \verb{file}
      \verb ScienceDirect Full Text PDF:D\:\\estragio\\Zotero\\storage\\8Q2Q9AQS\\Lewiński et al. - 1994 - Extended exact solutions for least-weight truss la.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://www.sciencedirect.com/science/article/pii/0020740394900434
      \endverb
      \verb{url}
      \verb https://www.sciencedirect.com/science/article/pii/0020740394900434
      \endverb
    \endentry
    \entry{munro_local_2017}{article}{}
      \name{author}{2}{}{%
        {{hash=86d57f1424c871d9cee9a456c6cac101}{%
           family={Munro},
           familyi={M\bibinitperiod},
           given={Dirk},
           giveni={D\bibinitperiod}}}%
        {{hash=b09157e6ec926e08ed399f5defc663f0}{%
           family={Groenwold},
           familyi={G\bibinitperiod},
           given={Albert},
           giveni={A\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{fd89c93293974cfecabe0bf494cf0d2e}
      \strng{fullhash}{fd89c93293974cfecabe0bf494cf0d2e}
      \strng{bibnamehash}{fd89c93293974cfecabe0bf494cf0d2e}
      \strng{authorbibnamehash}{fd89c93293974cfecabe0bf494cf0d2e}
      \strng{authornamehash}{fd89c93293974cfecabe0bf494cf0d2e}
      \strng{authorfullhash}{fd89c93293974cfecabe0bf494cf0d2e}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{shorttitle}
      \field{issn}{00295981}
      \field{journaltitle}{International Journal for Numerical Methods in Engineering}
      \field{month}{5}
      \field{number}{5}
      \field{shorttitle}{Local stress-constrained and slope-constrained {SAND} topology optimisation}
      \field{title}{Local stress-constrained and slope-constrained {SAND} topology optimisation}
      \field{urlday}{18}
      \field{urlmonth}{2}
      \field{urlyear}{2022}
      \field{volume}{110}
      \field{year}{2017}
      \field{urldateera}{ce}
      \field{pages}{420\bibrangedash 439}
      \range{pages}{20}
      \verb{doi}
      \verb 10.1002/nme.5360
      \endverb
      \verb{file}
      \verb Numerical Meth Engineering - 2016 - Munro - Local stress‐constrained and slope‐constrained SAND topology optimisation.pdf:D\:\\estragio\\Zotero\\storage\\9I666R5Q\\Numerical Meth Engineering - 2016 - Munro - Local stress‐constrained and slope‐constrained SAND topology optimisation.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://onlinelibrary.wiley.com/doi/10.1002/nme.5360
      \endverb
      \verb{url}
      \verb https://onlinelibrary.wiley.com/doi/10.1002/nme.5360
      \endverb
    \endentry
    \entry{bruggi_topology_2012}{article}{}
      \name{author}{2}{}{%
        {{hash=a59dab04e567acdb5c9d56e5f573819f}{%
           family={Bruggi},
           familyi={B\bibinitperiod},
           given={Matteo},
           giveni={M\bibinitperiod}}}%
        {{hash=55bbf59917324962aed0534c9e5595b5}{%
           family={Duysinx},
           familyi={D\bibinitperiod},
           given={Pierre},
           giveni={P\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{7692f8ed7491b619414e8112f69b6e8b}
      \strng{fullhash}{7692f8ed7491b619414e8112f69b6e8b}
      \strng{bibnamehash}{7692f8ed7491b619414e8112f69b6e8b}
      \strng{authorbibnamehash}{7692f8ed7491b619414e8112f69b6e8b}
      \strng{authornamehash}{7692f8ed7491b619414e8112f69b6e8b}
      \strng{authorfullhash}{7692f8ed7491b619414e8112f69b6e8b}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{The paper deals with a formulation for the topology optimization of elastic structures that aims at minimizing the structural weight subject to compliance and local stress constraints. The global constraint provides the expected stiffness to the optimal design while a selected set of local enforcements require feasibility with respect to the assigned strength of material. The Drucker–Prager failure criterion is implemented to handle materials with either equal or unequal behavior in tension and compression. A suitable relaxation of the equivalent stress measure is implemented to overcome the difficulties related to the singularity problem. Numerical examples are presented to discuss the features of the achieved optimal designs along with performances of the adopted procedure. Comparisons with pure compliance–based or pure stress–based strategies are also provided to point out differences arising in the optimal design with respect to conventional approaches, depending on the assumed material behavior.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{9}
      \field{number}{3}
      \field{title}{Topology optimization for minimum weight with compliance and stress constraints}
      \field{urlday}{15}
      \field{urlmonth}{9}
      \field{urlyear}{2023}
      \field{volume}{46}
      \field{year}{2012}
      \field{urldateera}{ce}
      \field{pages}{369\bibrangedash 384}
      \range{pages}{16}
      \verb{doi}
      \verb 10.1007/s00158-012-0759-7
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\2R38SI97\\Bruggi and Duysinx - 2012 - Topology optimization for minimum weight with comp.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/s00158-012-0759-7
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s00158-012-0759-7
      \endverb
      \keyw{Compliance constraint,Drucker–Prager failure criterion,Singularity problem,Stress constraints,Topology optimization}
    \endentry
    \entry{paris_block_2010}{article}{}
      \name{author}{4}{}{%
        {{hash=d5358f941b9ce3b868ad60b0b25d313f}{%
           family={París},
           familyi={P\bibinitperiod},
           given={J.},
           giveni={J\bibinitperiod}}}%
        {{hash=bd604f402c50664e2d14ddc89fbc6359}{%
           family={Navarrina},
           familyi={N\bibinitperiod},
           given={F.},
           giveni={F\bibinitperiod}}}%
        {{hash=e9c7d9afdc5ae7d037a0d57750df1044}{%
           family={Colominas},
           familyi={C\bibinitperiod},
           given={I.},
           giveni={I\bibinitperiod}}}%
        {{hash=f47b7cc888194e51521c9000aa87546a}{%
           family={Casteleiro},
           familyi={C\bibinitperiod},
           given={M.},
           giveni={M\bibinitperiod}}}%
      }
      \strng{namehash}{3c10530b8e6c27884ec21425903e726a}
      \strng{fullhash}{c47c3d885eca2002a428255daa62a4aa}
      \strng{bibnamehash}{c47c3d885eca2002a428255daa62a4aa}
      \strng{authorbibnamehash}{c47c3d885eca2002a428255daa62a4aa}
      \strng{authornamehash}{3c10530b8e6c27884ec21425903e726a}
      \strng{authorfullhash}{c47c3d885eca2002a428255daa62a4aa}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Structural topology optimization problems have been traditionally stated and solved by means of maximum stiffness formulations. On the other hand, some effort has been devoted to stating and solving this kind of problems by means of minimum weight formulations with stress (and/or displacement) constraints. It seems clear that the latter approach is closer to the engineering point of view, but it also leads to more complicated optimization problems, since a large number of highly non-linear (local) constraints must be taken into account to limit the maximum stress (and/or displacement) at the element level. In this paper, we explore the feasibility of defining a so-called global constraint, which basic aim is to limit the maximum stress (and/or displacement) simultaneously within all the structure by means of one single inequality. Should this global constraint perform adequately, the complexity of the underlying mathematical programming problem would be drastically reduced. However, a certain weakening of the feasibility conditions is expected to occur when a large number of local constraints are lumped into one single inequality. With the aim of mitigating this undesirable collateral effect, we group the elements into blocks. Then, the local constraints corresponding to all the elements within each block can be combined to produce a single aggregated constraint per block. Finally, we compare the performance of these three approaches (local, global and block aggregated constraints) by solving several topology optimization problems.}
      \field{issn}{0965-9978}
      \field{journaltitle}{Advances in Engineering Software}
      \field{month}{3}
      \field{number}{3}
      \field{series}{Advances in optimum engineering design}
      \field{title}{Block aggregation of stress constraints in topology optimization of structures}
      \field{urlday}{15}
      \field{urlmonth}{9}
      \field{urlyear}{2023}
      \field{volume}{41}
      \field{year}{2010}
      \field{urldateera}{ce}
      \field{pages}{433\bibrangedash 441}
      \range{pages}{9}
      \verb{doi}
      \verb 10.1016/j.advengsoft.2009.03.006
      \endverb
      \verb{file}
      \verb ScienceDirect Full Text PDF:D\:\\estragio\\Zotero\\storage\\EYHU43NS\\París et al. - 2010 - Block aggregation of stress constraints in topolog.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://www.sciencedirect.com/science/article/pii/S0965997809000568
      \endverb
      \verb{url}
      \verb https://www.sciencedirect.com/science/article/pii/S0965997809000568
      \endverb
      \keyw{Block aggregated constraints,FEM,Global constraints,Local constraints,Minimum weight,Stress constraints,Structural topology optimization}
    \endentry
    \entry{norato_maximum-rectifier-function_2022}{article}{}
      \name{author}{4}{}{%
        {{hash=1707fd6c8a20694afeda449ef30c7b5f}{%
           family={Norato},
           familyi={N\bibinitperiod},
           given={Julián\bibnamedelima A.},
           giveni={J\bibinitperiod\bibinitdelim A\bibinitperiod}}}%
        {{hash=cac315242fa5563f0f2cb2471f87983a}{%
           family={Smith},
           familyi={S\bibinitperiod},
           given={Hollis\bibnamedelima A.},
           giveni={H\bibinitperiod\bibinitdelim A\bibinitperiod}}}%
        {{hash=ec86e4aa7ab8383da34f05060fed48a7}{%
           family={Deaton},
           familyi={D\bibinitperiod},
           given={Joshua\bibnamedelima D.},
           giveni={J\bibinitperiod\bibinitdelim D\bibinitperiod}}}%
        {{hash=4900e507a4a31bf76075ee3258a5b5f8}{%
           family={Kolonay},
           familyi={K\bibinitperiod},
           given={Raymond\bibnamedelima M.},
           giveni={R\bibinitperiod\bibinitdelim M\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{28f219a86dad6b996901d1e339f792c7}
      \strng{fullhash}{e810072abc997706d26b00b697d90bc1}
      \strng{bibnamehash}{e810072abc997706d26b00b697d90bc1}
      \strng{authorbibnamehash}{e810072abc997706d26b00b697d90bc1}
      \strng{authornamehash}{28f219a86dad6b996901d1e339f792c7}
      \strng{authorfullhash}{e810072abc997706d26b00b697d90bc1}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This paper introduces a novel method for stress-constrained topology optimization in which the stress constraint is a differentiable approximation of the maximum element stress violation in the structure. The element stress violation is given by a differentiable rectifier function. A key feature of the proposed method is its ability to render designs that satisfy the stress limit without renormalization of the constraint, as in some existing aggregation approaches. Numerical experiments demonstrate that the proposed technique exhibits better convergence and is less sensitive to the aggregation parameter than aggregation methods that employ renormalization. The effectiveness of the proposed method is demonstrated by several examples.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{9}
      \field{number}{10}
      \field{title}{A maximum-rectifier-function approach to stress-constrained topology optimization}
      \field{urlday}{15}
      \field{urlmonth}{9}
      \field{urlyear}{2023}
      \field{volume}{65}
      \field{year}{2022}
      \field{urldateera}{ce}
      \field{pages}{286}
      \range{pages}{1}
      \verb{doi}
      \verb 10.1007/s00158-022-03357-z
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\R4GWDGM9\\Norato et al. - 2022 - A maximum-rectifier-function approach to stress-co.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/s00158-022-03357-z
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s00158-022-03357-z
      \endverb
      \keyw{Aggregation functions,Constraint scaling,Stress constraints}
    \endentry
    \entry{stragiotti_efficient_2024}{article}{}
      \name{author}{4}{}{%
        {{hash=6c4965d3ad73fb11f44136afa897bb91}{%
           family={Stragiotti},
           familyi={S\bibinitperiod},
           given={Enrico},
           giveni={E\bibinitperiod}}}%
        {{hash=6ffe413a21f4954b0aac85ca037c7876}{%
           family={Irisarri},
           familyi={I\bibinitperiod},
           given={François-Xavier},
           giveni={F\bibinithyphendelim X\bibinitperiod}}}%
        {{hash=d9c42bf5ce7591763a45d8334a00d4e1}{%
           family={Julien},
           familyi={J\bibinitperiod},
           given={Cédric},
           giveni={C\bibinitperiod}}}%
        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{fullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{bibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authorbibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authornamehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{authorfullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \field{extraname}{2}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{1}
      \field{title}{Efficient 3D truss topology optimization for aeronautical structures (in press)}
      \field{year}{2024}
      \verb{doi}
      \verb 10.1007/s00158-024-03739-5
      \endverb
      \keyw{art}
    \endentry
    \entry{reinschmidt_applications_1974}{article}{}
      \name{author}{2}{}{%
        {{hash=1f198aca397687835f030d6b23778983}{%
           family={Reinschmidt},
           familyi={R\bibinitperiod},
           given={Kenneth\bibnamedelima F.},
           giveni={K\bibinitperiod\bibinitdelim F\bibinitperiod}}}%
        {{hash=f966287080a3461f7c43c3ebf6bd172f}{%
           family={Russell},
           familyi={R\bibinitperiod},
           given={Alan\bibnamedelima D.},
           giveni={A\bibinitperiod\bibinitdelim D\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{a4270879922700fa375acf0dddba76e0}
      \strng{fullhash}{a4270879922700fa375acf0dddba76e0}
      \strng{bibnamehash}{a4270879922700fa375acf0dddba76e0}
      \strng{authorbibnamehash}{a4270879922700fa375acf0dddba76e0}
      \strng{authornamehash}{a4270879922700fa375acf0dddba76e0}
      \strng{authorfullhash}{a4270879922700fa375acf0dddba76e0}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Various computer methods have been developed for the optimal design of indeterminate structures, but it is not possible to guarantee that the result of any method will be a global optimum, rather than merely a local optimum. By temporarily neglecting the conditions of elastic compatibility and formulating a mathematical optimization problem based on the equilibrium conditions and the stress constraints, it is possible to obtain an approximate design which avoids merely local optima. In the cases examined, this design is close to the exact global optimum obtained by enforcing the compatibility conditions and is therefore a good starting point for an optimizing procedure. Examples include a graphical solution of a simple grillage known to have multiple local optima, and a sequence of planar trusses under alternate loading conditions. Linear programming is used to find the minimum weight truss designs satisfying equilibrium; this method eliminates extraneous members and leads to better indeterminate truss configurations than does a stress-ratio type algorithm.}
      \field{issn}{0045-7949}
      \field{journaltitle}{Computers \&amp; Structures}
      \field{month}{8}
      \field{number}{4}
      \field{title}{Applications of linear programming in structural layout and optimization}
      \field{urlday}{21}
      \field{urlmonth}{10}
      \field{urlyear}{2021}
      \field{volume}{4}
      \field{year}{1974}
      \field{urldateera}{ce}
      \field{pages}{855\bibrangedash 869}
      \range{pages}{15}
      \verb{doi}
      \verb 10.1016/0045-7949(74)90049-2
      \endverb
    \endentry
    \entry{oberndorfer_two_1996}{article}{}
      \name{author}{3}{}{%
        {{hash=b6cde8f18dd4c07bdc70812d5a53d0ff}{%
           family={Oberndorfer},
           familyi={O\bibinitperiod},
           given={J.\bibnamedelimi M.},
           giveni={J\bibinitperiod\bibinitdelim M\bibinitperiod}}}%
        {{hash=453fe478aaef8cda186519d42b21f6c3}{%
           family={Achtziger},
           familyi={A\bibinitperiod},
           given={W.},
           giveni={W\bibinitperiod}}}%
        {{hash=2d8c95419dc782572dd2b0d875123e75}{%
           family={Hornlein},
           familyi={H\bibinitperiod},
           given={H.\bibnamedelimi R.\bibnamedelimi E.\bibnamedelimi M.},
           giveni={H\bibinitperiod\bibinitdelim R\bibinitperiod\bibinitdelim E\bibinitperiod\bibinitdelim M\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{ff5329539e22525fcb41bb9f998b1f05}
      \strng{fullhash}{ff5329539e22525fcb41bb9f998b1f05}
      \strng{bibnamehash}{ff5329539e22525fcb41bb9f998b1f05}
      \strng{authorbibnamehash}{ff5329539e22525fcb41bb9f998b1f05}
      \strng{authornamehash}{ff5329539e22525fcb41bb9f998b1f05}
      \strng{authorfullhash}{ff5329539e22525fcb41bb9f998b1f05}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{shorttitle}
      \field{issn}{0934-4373, 1615-1488}
      \field{journaltitle}{Structural Optimization}
      \field{month}{6}
      \field{number}{3-4}
      \field{shorttitle}{Two approaches for truss topology optimization}
      \field{title}{Two approaches for truss topology optimization: a comparison for practical use}
      \field{urlday}{16}
      \field{urlmonth}{4}
      \field{urlyear}{2021}
      \field{volume}{11}
      \field{year}{1996}
      \field{urldateera}{ce}
      \field{pages}{137\bibrangedash 144}
      \range{pages}{8}
      \verb{doi}
      \verb 10.1007/BF01197027
      \endverb
      \verb{file}
      \verb Oberndorfer et al. - 1996 - Two approaches for truss topology optimization a .pdf:D\:\\estragio\\Zotero\\storage\\QKBQ3IZK\\Oberndorfer et al. - 1996 - Two approaches for truss topology optimization a .pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb http://link.springer.com/10.1007/BF01197027
      \endverb
      \verb{url}
      \verb http://link.springer.com/10.1007/BF01197027
      \endverb
    \endentry
    \entry{silva_smith_topology_1997}{article}{}
      \name{author}{1}{}{%
        {{hash=d9dd5036eb8fcf856c3eee452e152c49}{%
           family={Silva\bibnamedelima Smith},
           familyi={S\bibinitperiod\bibinitdelim S\bibinitperiod},
           given={O.},
           giveni={O\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{d9dd5036eb8fcf856c3eee452e152c49}
      \strng{fullhash}{d9dd5036eb8fcf856c3eee452e152c49}
      \strng{bibnamehash}{d9dd5036eb8fcf856c3eee452e152c49}
      \strng{authorbibnamehash}{d9dd5036eb8fcf856c3eee452e152c49}
      \strng{authornamehash}{d9dd5036eb8fcf856c3eee452e152c49}
      \strng{authorfullhash}{d9dd5036eb8fcf856c3eee452e152c49}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{shorttitle}
      \field{issn}{0934-4373, 1615-1488}
      \field{journaltitle}{Structural Optimization}
      \field{month}{4}
      \field{number}{2-3}
      \field{shorttitle}{Topology optimization of trusses with local stability constraints and multiple loading conditions?}
      \field{title}{Topology optimization of trusses with local stability constraints and multiple loading conditions?a heuristic approach}
      \field{urlday}{14}
      \field{urlmonth}{2}
      \field{urlyear}{2023}
      \field{volume}{13}
      \field{year}{1997}
      \field{urldateera}{ce}
      \field{pages}{155\bibrangedash 166}
      \range{pages}{12}
      \verb{doi}
      \verb 10.1007/BF01199235
      \endverb
    \endentry
    \entry{achtziger_local_1999b}{article}{}
      \name{author}{1}{}{%
        {{hash=453fe478aaef8cda186519d42b21f6c3}{%
           family={Achtziger},
           familyi={A\bibinitperiod},
           given={W.},
           giveni={W\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{453fe478aaef8cda186519d42b21f6c3}
      \strng{fullhash}{453fe478aaef8cda186519d42b21f6c3}
      \strng{bibnamehash}{453fe478aaef8cda186519d42b21f6c3}
      \strng{authorbibnamehash}{453fe478aaef8cda186519d42b21f6c3}
      \strng{authornamehash}{453fe478aaef8cda186519d42b21f6c3}
      \strng{authorfullhash}{453fe478aaef8cda186519d42b21f6c3}
      \field{extraname}{3}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{shorttitle}
      \field{abstract}{The paper considers the problem of optimal truss topology design with respect to stress, slenderness, and local buckling constraints. An exact problem formulation is used dealing with the inherent difficulty that the local buckling constraints are discontinuous functions in the bar areas due to the topology aspect. This exact problem formulation has been derived in Part I. In this paper, a numerical approach to this nonconvex and largescale problem is proposed. First, discontinuity of constraints is erased by providing an equivalent formulation in standard form of nonlinear programming. Then a linearization concept is proposed partly preserving the given problem structure. It is proved that the resulting sequential linear programming algorithm is a descent method generating truss designs feasible for the original problem. A numerical test on a nontrivial example shows that the exact treatment of the problem leads to different designs than the usual local buckling constraints neglecting the difficulties induced by the topology aspect.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural optimization}
      \field{month}{12}
      \field{number}{4}
      \field{shorttitle}{Local stability of trusses in the context of topology optimization {Part} {II}}
      \field{title}{Local stability of trusses in the context of topology optimization {Part} {II}: {A} numerical approach}
      \field{urlday}{2}
      \field{urlmonth}{2}
      \field{urlyear}{2022}
      \field{volume}{17}
      \field{year}{1999}
      \field{urldateera}{ce}
      \field{pages}{247\bibrangedash 258}
      \range{pages}{12}
      \verb{doi}
      \verb 10.1007/BF01207000
      \endverb
    \endentry
    \entry{pritchard_plastic_2005}{article}{}
      \name{author}{3}{}{%
        {{hash=8e9e80475353517ef156ba40e086ea45}{%
           family={Pritchard},
           familyi={P\bibinitperiod},
           given={T.},
           giveni={T\bibinitperiod}}}%
        {{hash=c187b1075ee4dfc79e5c9154527f9040}{%
           family={Gilbert},
           familyi={G\bibinitperiod},
           given={Matthew},
           giveni={M\bibinitperiod}}}%
        {{hash=b36ef59d73d5b8a68c1b2dec068985de}{%
           family={Tyas},
           familyi={T\bibinitperiod},
           given={Andrew},
           giveni={A\bibinitperiod}}}%
      }
      \strng{namehash}{851255826398263aff1d42d870de66d6}
      \strng{fullhash}{851255826398263aff1d42d870de66d6}
      \strng{bibnamehash}{851255826398263aff1d42d870de66d6}
      \strng{authorbibnamehash}{851255826398263aff1d42d870de66d6}
      \strng{authornamehash}{851255826398263aff1d42d870de66d6}
      \strng{authorfullhash}{851255826398263aff1d42d870de66d6}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{1. Abstract In the past few decades plastic layout optimization methods have been largely ignored in favour of those based upon elastic design principles. However, when multiple load cases are present elastic methods are generally computationally expensive and/or are prone to finding local optima. Therefore, they may not at present provide a suitable basis for practical truss layout optimization software, capable of treating real-world scale problems. In fact long computation times have impeded the development of truss layout optimization tools, both plastic and elastic. This is because, when using a fully connected ground structure, problem size quickly increases with increasing numbers of nodes in the design domain. Hence available memory can quickly become exhausted, preventing optimization even when using comparatively simple plastic problem formulations. Recently the authors presented a technique that allows large-scale plastic layout optimization to be performed on a typical desktop PC. Through the use of an iterative 'member-adding' algorithm, CPU times and memory requirements may be dramatically reduced, allowing problems containing up to approx. 1,000,000,000 potential members to be tackled. This paper extends the method so as to be capable of treating 3D problems with multiple load cases. Furthermore, in order to provide more realistic optimum structures, member self-weight and joint length penalties can also be included. Example problems demonstrate that the new algorithm is capable of optimizing structures with many millions of potential members, whilst still providing provably optimum}
      \field{month}{1}
      \field{title}{Plastic {Layout} {Optimization} of {Large}-{Scale} {Frameworks} {Subject} to {Multiple} {Load} {Cases}, {Member} {Self}-{Weight} and with {Joint} {Length} {Penalties}}
      \field{year}{2005}
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\3RMCQMMN\\Pritchard et al. - 2005 - Plastic Layout Optimization of Large-Scale Framewo.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://www.semanticscholar.org/paper/Plastic-Layout-Optimization-of-Large-Scale-Subject-Pritchard-Gilbert/580c2596f655b50e516ffe9f1324b10e1c0da0e0
      \endverb
      \verb{url}
      \verb https://www.semanticscholar.org/paper/Plastic-Layout-Optimization-of-Large-Scale-Subject-Pritchard-Gilbert/580c2596f655b50e516ffe9f1324b10e1c0da0e0
      \endverb
    \endentry
    \entry{tyas_practical_2006}{article}{}
      \name{author}{3}{}{%
        {{hash=f3439e006e1e87eac065ef83ee82c1b9}{%
           family={Tyas},
           familyi={T\bibinitperiod},
           given={A.},
           giveni={A\bibinitperiod}}}%
        {{hash=9d7322a84f0f9b0b90e0e094b8c4ccdd}{%
           family={Gilbert},
           familyi={G\bibinitperiod},
           given={M.},
           giveni={M\bibinitperiod}}}%
        {{hash=8e9e80475353517ef156ba40e086ea45}{%
           family={Pritchard},
           familyi={P\bibinitperiod},
           given={T.},
           giveni={T\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{6f8a8842f7abaa4020b98290226d40c9}
      \strng{fullhash}{6f8a8842f7abaa4020b98290226d40c9}
      \strng{bibnamehash}{6f8a8842f7abaa4020b98290226d40c9}
      \strng{authorbibnamehash}{6f8a8842f7abaa4020b98290226d40c9}
      \strng{authornamehash}{6f8a8842f7abaa4020b98290226d40c9}
      \strng{authorfullhash}{6f8a8842f7abaa4020b98290226d40c9}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Frequently the topologies generated using conventional discrete structural layout optimization methods may be shown to be in unstable equilibrium with the specified applied loading. Previously proposed methods to overcome this problem have tended to suffer from either a lack of rigour in identifying unstable solutions, a failure to properly consider all means of ensuring the stability of a framework, or are likely to be very computationally expensive. This paper discusses the drawbacks of current methods and introduces a conceptually simple approach that incorporates nominal lateral force load cases in a plastic linear programming problem formulation. Examples of stable solutions identified by this approach are discussed along with future developments to increase the practicality and efficiency of the method.}
      \field{issn}{0045-7949}
      \field{journaltitle}{Computers \&amp; Structures}
      \field{month}{1}
      \field{number}{3}
      \field{title}{Practical plastic layout optimization of trusses incorporating stability considerations}
      \field{urlday}{5}
      \field{urlmonth}{10}
      \field{urlyear}{2021}
      \field{volume}{84}
      \field{year}{2006}
      \field{urldateera}{ce}
      \field{pages}{115\bibrangedash 126}
      \range{pages}{12}
      \verb{doi}
      \verb 10.1016/j.compstruc.2005.09.032
      \endverb
      \keyw{Structural optimization,Truss,Buckling,Linear programming,Plastic,Stability}
    \endentry
    \entry{descamps_nominal_2014}{article}{}
      \name{author}{2}{}{%
        {{hash=a867726c6de8cbbc5b38459f1179c726}{%
           family={Descamps},
           familyi={D\bibinitperiod},
           given={Benoît},
           giveni={B\bibinitperiod}}}%
        {{hash=1462acafce6f777c7120022f3f81fcff}{%
           family={Filomeno\bibnamedelima Coelho},
           familyi={F\bibinitperiod\bibinitdelim C\bibinitperiod},
           given={Rajan},
           giveni={R\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{b9c8eaf45dc9f4fd7d05c4f4af3eeb22}
      \strng{fullhash}{b9c8eaf45dc9f4fd7d05c4f4af3eeb22}
      \strng{bibnamehash}{b9c8eaf45dc9f4fd7d05c4f4af3eeb22}
      \strng{authorbibnamehash}{b9c8eaf45dc9f4fd7d05c4f4af3eeb22}
      \strng{authornamehash}{b9c8eaf45dc9f4fd7d05c4f4af3eeb22}
      \strng{authorfullhash}{b9c8eaf45dc9f4fd7d05c4f4af3eeb22}
      \field{extraname}{2}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This paper presents a computationally efficient method for truss layout optimization with stability constraints. Previously proposed approaches that ensure stability of optimal frameworks are first reviewed, showing that existing studies are generally restricted to topology optimization. The present contribution aims to generalize the approach to simultaneous geometry and topology optimization. A lower-bound plastic design formulation under multiple loading will serve as basis for this purpose. The numerical difficulties associated with geometrical variations are identified and the parametrization is adapted accordingly. To avoid nodal instability, the nominal force method is adopted, which introduces artificial loading cases to simulate the effect of geometric imperfections. Hence, the truss systems with unstable nodes are eliminated from the set of optimal solutions. At the same time, the local stability of structural members is ensured via a consistent local buckling criterion. This novel formulation leads to optimal configurations that can be practically used for the preliminary design of structural frameworks. Four applications illustrate the impact of stability constraints on the solution. The importance of geometry optimization is also pointed out by comparing with results that would be unattainable by topology optimization only.}
      \field{issn}{0020-7683}
      \field{journaltitle}{International Journal of Solids and Structures}
      \field{month}{6}
      \field{number}{13}
      \field{title}{The nominal force method for truss geometry and topology optimization incorporating stability considerations}
      \field{urlday}{21}
      \field{urlmonth}{1}
      \field{urlyear}{2021}
      \field{volume}{51}
      \field{year}{2014}
      \field{urldateera}{ce}
      \field{pages}{2390\bibrangedash 2399}
      \range{pages}{10}
      \verb{doi}
      \verb 10.1016/j.ijsolstr.2014.03.003
      \endverb
      \verb{file}
      \verb ScienceDirect Full Text PDF:D\:\\estragio\\Zotero\\storage\\76WP4QQ3\\Descamps and Filomeno Coelho - 2014 - The nominal force method for truss geometry and to.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb http://www.sciencedirect.com/science/article/pii/S002076831400095X
      \endverb
      \verb{url}
      \verb http://www.sciencedirect.com/science/article/pii/S002076831400095X
      \endverb
      \keyw{Topology optimization,Geometry optimization,Local buckling,Nodal stability,Nominal force,Plastic design,Truss layout optimization}
    \endentry
    \entry{schwarz_efficient_2018}{article}{}
      \name{author}{4}{}{%
        {{hash=2f120127ecf36cc930cd929c3b226d0c}{%
           family={Schwarz},
           familyi={S\bibinitperiod},
           given={Jonas},
           giveni={J\bibinitperiod}}}%
        {{hash=d52d5021e1175b35d7f7627593afa5ce}{%
           family={Chen},
           familyi={C\bibinitperiod},
           given={Tian},
           giveni={T\bibinitperiod}}}%
        {{hash=a0ebf28d3f3be731c050dbc3d66795c0}{%
           family={Shea},
           familyi={S\bibinitperiod},
           given={Kristina},
           giveni={K\bibinitperiod}}}%
        {{hash=ef625fb812a6a03e25d6b74a382cd30c}{%
           family={Stanković},
           familyi={S\bibinitperiod},
           given={Tino},
           giveni={T\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{a0e02a6fc27e3965a148f34090c94c2c}
      \strng{fullhash}{b70f4a8369d7d44a81692fe2ef91ecfe}
      \strng{bibnamehash}{b70f4a8369d7d44a81692fe2ef91ecfe}
      \strng{authorbibnamehash}{b70f4a8369d7d44a81692fe2ef91ecfe}
      \strng{authornamehash}{a0e02a6fc27e3965a148f34090c94c2c}
      \strng{authorfullhash}{b70f4a8369d7d44a81692fe2ef91ecfe}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{The advance in digital fabrication technologies and additive manufacturing allows for the fabrication of complex truss structure designs but at the same time posing challenging structural optimization problems to capitalize on this new design freedom. In response to this, an iterative approach in which Sequential Linear Programming (SLP) is used to simultaneously solve a size and shape optimization sub-problem subject to local stress and Euler buckling constraints is proposed in this work. To accomplish this, a first order Taylor expansion for the nodal movement and the buckling constraint is derived to conform to the SLP problem formulation. At each iteration a post-processing step is initiated to map a design vector to the exact buckling constraint boundary in order to facilitate the overall efficiency. The method is verified against an exact non-linear optimization problem formulation on a range of benchmark examples obtained from the literature. The results show that the proposed method produces optimized designs that are either close or identical to the solutions obtained by the non-linear problem formulation while significantly decreasing the computational time. This enables more efficient size and shape optimization of truss structures considering practical engineering constraints.}
      \field{issn}{1615-147X, 1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{7}
      \field{number}{1}
      \field{title}{Efficient size and shape optimization of truss structures subject to stress and local buckling constraints using sequential linear programming}
      \field{urlday}{18}
      \field{urlmonth}{10}
      \field{urlyear}{2021}
      \field{volume}{58}
      \field{year}{2018}
      \field{urldateera}{ce}
      \field{pages}{171\bibrangedash 184}
      \range{pages}{14}
      \verb{doi}
      \verb 10.1007/s00158-017-1885-z
      \endverb
    \endentry
    \entry{cai_topology_2022}{article}{}
      \name{author}{3}{}{%
        {{hash=b61037ab06c0a5cf95a4c3f0d6202516}{%
           family={Cai},
           familyi={C\bibinitperiod},
           given={Qi},
           giveni={Q\bibinitperiod}}}%
        {{hash=6e42f927cea5f3037dc91c1bcee91bb7}{%
           family={Feng},
           familyi={F\bibinitperiod},
           given={Ruoqiang},
           giveni={R\bibinitperiod}}}%
        {{hash=fc81944ae7b189dae8d4cfe2673b07b8}{%
           family={Zhang},
           familyi={Z\bibinitperiod},
           given={Zhijie},
           giveni={Z\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{ba5738bdde02678d9ec5044504869922}
      \strng{fullhash}{ba5738bdde02678d9ec5044504869922}
      \strng{bibnamehash}{ba5738bdde02678d9ec5044504869922}
      \strng{authorbibnamehash}{ba5738bdde02678d9ec5044504869922}
      \strng{authornamehash}{ba5738bdde02678d9ec5044504869922}
      \strng{authorfullhash}{ba5738bdde02678d9ec5044504869922}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{For the practical application of optimized truss structures, the local stability of the bar must be considered to obtain stable and realistic structures. However, in the practical design of structures, the initial crookedness of the bars and residual stresses that remain in the bar after the manufacturing process should be taken into account, which makes the buckling strength highly non-connected and non-convex in terms of the cross-sectional properties. Therefore, most conventional truss optimization formulations include only local buckling constraints based on the Euler buckling criterion, while local buckling constraints based on design specifications are rarely incorporated. To treat these problems, a novel topology optimization model for trusses is proposed, where the critical buckling strength is calculated according to the practical design code GB5007-2017. In addition, a linearized iterative allowable stress method is used to solve the optimization model. Since the allowable stresses are calculated at each iteration based on the critical buckling strength, other types of design codes can also be incorporated into the proposed truss topology optimization model. The proposed computational model shows, through several numerical examples, the remarkable effect of including local buckling stability in the optimal design of trusses, while demonstrating that the optimized topology depends on whether the local buckling constraints are derived from the Euler buckling criterion or from actual structural design codes.}
      \field{issn}{2352-0124}
      \field{journaltitle}{Structures}
      \field{month}{7}
      \field{title}{Topology optimization of trusses incorporating practical local buckling stability considerations}
      \field{urlday}{10}
      \field{urlmonth}{6}
      \field{urlyear}{2022}
      \field{volume}{41}
      \field{year}{2022}
      \field{urldateera}{ce}
      \field{pages}{1710\bibrangedash 1718}
      \range{pages}{9}
      \verb{doi}
      \verb 10.1016/j.istruc.2022.05.109
      \endverb
      \verb{urlraw}
      \verb https://www.sciencedirect.com/science/article/pii/S2352012422004714
      \endverb
      \verb{url}
      \verb https://www.sciencedirect.com/science/article/pii/S2352012422004714
      \endverb
      \keyw{Topology optimization,Truss,Local buckling,Practical design code}
    \endentry
    \entry{guo_new_2001}{article}{}
      \name{author}{3}{}{%
        {{hash=d1cf3b5875e193af09fb48f09d5f8c55}{%
           family={Guo},
           familyi={G\bibinitperiod},
           given={X.},
           giveni={X\bibinitperiod}}}%
        {{hash=112f6df29c44bf60dd57629dca6325c7}{%
           family={Cheng},
           familyi={C\bibinitperiod},
           given={G.},
           giveni={G\bibinitperiod}}}%
        {{hash=5820606881b5579e27ce19d5f6f34724}{%
           family={Yamazaki},
           familyi={Y\bibinitperiod},
           given={K.},
           giveni={K\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{cd642c0be54d9d9f316618b4f8c99dc6}
      \strng{fullhash}{cd642c0be54d9d9f316618b4f8c99dc6}
      \strng{bibnamehash}{cd642c0be54d9d9f316618b4f8c99dc6}
      \strng{authorbibnamehash}{cd642c0be54d9d9f316618b4f8c99dc6}
      \strng{authornamehash}{cd642c0be54d9d9f316618b4f8c99dc6}
      \strng{authorfullhash}{cd642c0be54d9d9f316618b4f8c99dc6}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{The present paper investigates problems of truss topology optimization under local buckling constraints. A new approach for the solution of singular problems caused by stress and local buckling constraints is proposed. At ﬁrst, a second order smooth-extended technique is used to make the disjoint feasible domains connect, then the so-called ε-relaxed method is applied to eliminate the singular optima from problem formulation. By means of this approach, the singular optimum of the original problem caused by stress and local buckling constraints can be searched approximately by employing the algorithms developed for sizing optimization problems with high accuracy. Therefore, the numerical problem resulting from stress and local buckling constraints can be solved in an elegant way. The applications of the proposed approach and its eﬀectiveness are illustrated with several numerical examples.}
      \field{issn}{1615-147X, 1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{12}
      \field{number}{5}
      \field{title}{A new approach for the solution of singular optima in truss topology optimization with stress and local buckling constraints}
      \field{urlday}{16}
      \field{urlmonth}{6}
      \field{urlyear}{2022}
      \field{volume}{22}
      \field{year}{2001}
      \field{urldateera}{ce}
      \field{pages}{364\bibrangedash 373}
      \range{pages}{10}
      \verb{doi}
      \verb 10.1007/s00158-001-0156-0
      \endverb
    \endentry
    \entry{stolpe_note_2003}{article}{}
      \name{author}{2}{}{%
        {{hash=9bad1d1c66b6ba268b1b0102bf0ab5ad}{%
           family={Stolpe},
           familyi={S\bibinitperiod},
           given={M.},
           giveni={M\bibinitperiod}}}%
        {{hash=350e8570c519473f8a9f62854e7ef0a1}{%
           family={Svanberg},
           familyi={S\bibinitperiod},
           given={K.},
           giveni={K\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{efe1cb231b5b208e463f0508f00cd1fc}
      \strng{fullhash}{efe1cb231b5b208e463f0508f00cd1fc}
      \strng{bibnamehash}{efe1cb231b5b208e463f0508f00cd1fc}
      \strng{authorbibnamehash}{efe1cb231b5b208e463f0508f00cd1fc}
      \strng{authornamehash}{efe1cb231b5b208e463f0508f00cd1fc}
      \strng{authorfullhash}{efe1cb231b5b208e463f0508f00cd1fc}
      \field{extraname}{2}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{The purpose of this brief note is to demonstrate that general-purpose optimization methods and codes should not be discarded when dealing with stressconstrained truss topology optimization. By using a disaggregated formulation of the considered problem, such methods may ﬁnd also “singular optima”, without using perturbation techniques like the ε-relaxed approach.}
      \field{issn}{1615-147X, 1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{3}
      \field{number}{1}
      \field{title}{A note on stress-constrained truss topology optimization}
      \field{urlday}{25}
      \field{urlmonth}{3}
      \field{urlyear}{2021}
      \field{volume}{25}
      \field{year}{2003}
      \field{urldateera}{ce}
      \field{pages}{62\bibrangedash 64}
      \range{pages}{3}
      \verb{doi}
      \verb 10.1007/s00158-002-0273-4
      \endverb
    \endentry
    \entry{zhou_difficulties_1996}{article}{}
      \name{author}{1}{}{%
        {{hash=3edb51e096c6e1b022984c9159c4df2d}{%
           family={Zhou},
           familyi={Z\bibinitperiod},
           given={M.},
           giveni={M\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{3edb51e096c6e1b022984c9159c4df2d}
      \strng{fullhash}{3edb51e096c6e1b022984c9159c4df2d}
      \strng{bibnamehash}{3edb51e096c6e1b022984c9159c4df2d}
      \strng{authorbibnamehash}{3edb51e096c6e1b022984c9159c4df2d}
      \strng{authornamehash}{3edb51e096c6e1b022984c9159c4df2d}
      \strng{authorfullhash}{3edb51e096c6e1b022984c9159c4df2d}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{The aim of this note is to discuss problems associated with local buckling constraints in the context of topology optimization. It is shown that serious difficulties are encountered unless additional measures are introduced.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural optimization}
      \field{month}{4}
      \field{number}{2}
      \field{title}{Difficulties in truss topology optimization with stress and local buckling constraints}
      \field{volume}{11}
      \field{year}{1996}
      \field{pages}{134\bibrangedash 136}
      \range{pages}{3}
      \verb{doi}
      \verb 10.1007/BF01376857
      \endverb
      \keyw{Additional Measure,Civil Engineer,Topology Optimization,Truss Topology,Truss Topology Optimization}
    \endentry
    \entry{rozvany_difficulties_1996}{article}{}
      \name{author}{1}{}{%
        {{hash=2dd717bb9ecafd6aa2723e522b7aa056}{%
           family={Rozvany},
           familyi={R\bibinitperiod},
           given={G.\bibnamedelimi I.\bibnamedelimi N.},
           giveni={G\bibinitperiod\bibinitdelim I\bibinitperiod\bibinitdelim N\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{2dd717bb9ecafd6aa2723e522b7aa056}
      \strng{fullhash}{2dd717bb9ecafd6aa2723e522b7aa056}
      \strng{bibnamehash}{2dd717bb9ecafd6aa2723e522b7aa056}
      \strng{authorbibnamehash}{2dd717bb9ecafd6aa2723e522b7aa056}
      \strng{authornamehash}{2dd717bb9ecafd6aa2723e522b7aa056}
      \strng{authorfullhash}{2dd717bb9ecafd6aa2723e522b7aa056}
      \field{extraname}{3}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{A serlous difficulty in topology optimization with only stress andlocal buckling constraints was pointed out recently by Zhou (1996a). Possibilities for avoiding this pitfall are (i) inclusion of system stability constraints and (ii) application of imperfections in the ground structure. However, it is shown in this study that the above modified procedures may also lead to erroneous solutions which cannot be avoided without changing the ground structure.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural optimization}
      \field{month}{6}
      \field{number}{3}
      \field{title}{Difficulties in truss topology optimization with stress, local buckling and system stability constraints}
      \field{volume}{11}
      \field{year}{1996}
      \field{pages}{213\bibrangedash 217}
      \range{pages}{5}
      \verb{doi}
      \verb 10.1007/BF01197036
      \endverb
    \endentry
    \entry{ben-tal_optimal_2000}{article}{}
      \name{author}{5}{}{%
        {{hash=b4f10717c86d56d33bf7c4dadf066084}{%
           family={Ben-Tal},
           familyi={B\bibinithyphendelim T\bibinitperiod},
           given={Aharon},
           giveni={A\bibinitperiod}}}%
        {{hash=e750cfbe16c2bc31d2cd5348971f9a0c}{%
           family={Jarre},
           familyi={J\bibinitperiod},
           given={Florian},
           giveni={F\bibinitperiod}}}%
        {{hash=605986314dedbdb5fdcce5d179e265c4}{%
           family={Kočvara},
           familyi={K\bibinitperiod},
           given={Michal},
           giveni={M\bibinitperiod}}}%
        {{hash=b7bb695716d8b9e139e5d51d5dfd3567}{%
           family={Nemirovski},
           familyi={N\bibinitperiod},
           given={Arkadi},
           giveni={A\bibinitperiod}}}%
        {{hash=dca63935e750832e22eaac8aee840e04}{%
           family={Zowe},
           familyi={Z\bibinitperiod},
           given={Jochem},
           giveni={J\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{b012d2c62a79d648ce0209d21908132c}
      \strng{fullhash}{8ceb6ff9d410a1f4a158963fd3850192}
      \strng{bibnamehash}{8ceb6ff9d410a1f4a158963fd3850192}
      \strng{authorbibnamehash}{8ceb6ff9d410a1f4a158963fd3850192}
      \strng{authornamehash}{b012d2c62a79d648ce0209d21908132c}
      \strng{authorfullhash}{8ceb6ff9d410a1f4a158963fd3850192}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{We propose a novel formulation of a truss design problem involving a constraint on the global stability of the structure due to the linear buckling phenomenon. The optimization problem is modelled as a nonconvex semidefinite programming problem. We propose two techniques for the numerical solution of the problem and apply them to a series of numerical examples.}
      \field{issn}{1573-2924}
      \field{journaltitle}{Optimization and Engineering}
      \field{month}{7}
      \field{number}{2}
      \field{title}{Optimal {Design} of {Trusses} {Under} a {Nonconvex} {Global} {Buckling} {Constraint}}
      \field{volume}{1}
      \field{year}{2000}
      \field{pages}{189\bibrangedash 213}
      \range{pages}{25}
      \verb{doi}
      \verb 10.1023/A:1010091831812
      \endverb
      \keyw{buckling,nonconvex semidefinite programming,truss design}
    \endentry
    \entry{kocvara_modelling_2002}{article}{}
      \name{author}{1}{}{%
        {{hash=eb4b6bcb33a343efa9f6bda1cbf9e061}{%
           family={Kočvara},
           familyi={K\bibinitperiod},
           given={M.},
           giveni={M\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{eb4b6bcb33a343efa9f6bda1cbf9e061}
      \strng{fullhash}{eb4b6bcb33a343efa9f6bda1cbf9e061}
      \strng{bibnamehash}{eb4b6bcb33a343efa9f6bda1cbf9e061}
      \strng{authorbibnamehash}{eb4b6bcb33a343efa9f6bda1cbf9e061}
      \strng{authornamehash}{eb4b6bcb33a343efa9f6bda1cbf9e061}
      \strng{authorfullhash}{eb4b6bcb33a343efa9f6bda1cbf9e061}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{The goal of this paper is to ﬁnd a computationally tractable formulation of the optimum truss design problem involving a constraint on the global stability of the structure. The stability constraint is based on the linear buckling phenomenon. We formulate the problem as a nonconvex semideﬁnite programming problem and brieﬂy discuss an interior point technique for the numerical solution of this problem. We further discuss relation to other models. The paper is concluded by a series of numerical examples.}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{4}
      \field{number}{3}
      \field{title}{On the modelling and solving of the truss design problem with global stability constraints}
      \field{volume}{23}
      \field{year}{2002}
      \field{pages}{189\bibrangedash 203}
      \range{pages}{15}
      \verb{doi}
      \verb 10.1007/s00158-002-0177-3
      \endverb
    \endentry
    \entry{neves_generalized_1995}{article}{}
      \name{author}{3}{}{%
        {{hash=475be29ef14e2c12886fb87a2a9340f0}{%
           family={Neves},
           familyi={N\bibinitperiod},
           given={M.\bibnamedelimi M.},
           giveni={M\bibinitperiod\bibinitdelim M\bibinitperiod}}}%
        {{hash=23ae4ab9501bf00f3c96e374a3e4caec}{%
           family={Rodrigues},
           familyi={R\bibinitperiod},
           given={H.},
           giveni={H\bibinitperiod}}}%
        {{hash=a46b64f3808c21131762bc2d0b5ba331}{%
           family={Guedes},
           familyi={G\bibinitperiod},
           given={J.\bibnamedelimi M.},
           giveni={J\bibinitperiod\bibinitdelim M\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{6c737a0ca85be9ed933241bf215b4fc8}
      \strng{fullhash}{6c737a0ca85be9ed933241bf215b4fc8}
      \strng{bibnamehash}{6c737a0ca85be9ed933241bf215b4fc8}
      \strng{authorbibnamehash}{6c737a0ca85be9ed933241bf215b4fc8}
      \strng{authornamehash}{6c737a0ca85be9ed933241bf215b4fc8}
      \strng{authorfullhash}{6c737a0ca85be9ed933241bf215b4fc8}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Material based models for topology optimization of linear elastic solids with a low volume constraint generate very slender structures composed mainly of bars and beam elements. For this type of structure the value of the buckling critical load becomes one of the most important design criteria and so its control is very important for meaningful practical designs. This paper tries to address this problem, presenting an approach to introduce the possibility of critical load control into the topology optimization model.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural optimization}
      \field{month}{10}
      \field{number}{2}
      \field{title}{Generalized topology design of structures with a buckling load criterion}
      \field{urlday}{6}
      \field{urlmonth}{5}
      \field{urlyear}{2022}
      \field{volume}{10}
      \field{year}{1995}
      \field{urldateera}{ce}
      \field{pages}{71\bibrangedash 78}
      \range{pages}{8}
      \verb{doi}
      \verb 10.1007/BF01743533
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\TFLV4YJG\\Neves et al. - 1995 - Generalized topology design of structures with a b.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/BF01743533
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/BF01743533
      \endverb
      \keyw{Topology Optimization,Beam Element,Critical Load,Effective Property,Instability Mode}
    \endentry
    \entry{ferrari_topology_2021}{article}{}
      \name{author}{3}{}{%
        {{hash=8ea05860eca5cf81174a397fc54c388e}{%
           family={Ferrari},
           familyi={F\bibinitperiod},
           given={Federico},
           giveni={F\bibinitperiod}}}%
        {{hash=d76f1c09e8d8d06e1b7c3c254efeae1a}{%
           family={Sigmund},
           familyi={S\bibinitperiod},
           given={Ole},
           giveni={O\bibinitperiod}}}%
        {{hash=6dd049bc1a7f372ad642fba8a231fdfb}{%
           family={Guest},
           familyi={G\bibinitperiod},
           given={James\bibnamedelima K.},
           giveni={J\bibinitperiod\bibinitdelim K\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{e8dbb7b7ceaed94061236d2219cefef5}
      \strng{fullhash}{e8dbb7b7ceaed94061236d2219cefef5}
      \strng{bibnamehash}{e8dbb7b7ceaed94061236d2219cefef5}
      \strng{authorbibnamehash}{e8dbb7b7ceaed94061236d2219cefef5}
      \strng{authornamehash}{e8dbb7b7ceaed94061236d2219cefef5}
      \strng{authorfullhash}{e8dbb7b7ceaed94061236d2219cefef5}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{We present a 250-line Matlab code for topology optimization for linearized buckling criteria. The code is conceived to handle stiffness, volume and buckling load factors (BLFs) either as the objective function or as constraints. We use the Kreisselmeier-Steinhauser aggregation function in order to reduce multiple objectives (viz. constraints) to a single, differentiable one. Then, the problem is sequentially approximated by using MMA-like expansions and an OC-like scheme is tailored to update the variables. The inspection of the stress stiffness matrix leads to a vectorized implementation for its efficient construction and for the sensitivity analysis of the BLFs. This, coupled with the efficiency improvements already presented by Ferrari and Sigmund (Struct Multidiscip Optim 62:2211–2228, 2020a), cuts all the computational bottlenecks associated with setting up the buckling analysis and allows buckling topology optimization problems of an interesting size to be solved on a laptop. The efficiency and flexibility of the code are demonstrated over a few structural design examples and some ideas are given for possible extensions.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{6}
      \field{number}{6}
      \field{title}{Topology optimization with linearized buckling criteria in 250 lines of {Matlab}}
      \field{urlday}{23}
      \field{urlmonth}{10}
      \field{urlyear}{2023}
      \field{volume}{63}
      \field{year}{2021}
      \field{urldateera}{ce}
      \field{pages}{3045\bibrangedash 3066}
      \range{pages}{22}
      \verb{doi}
      \verb 10.1007/s00158-021-02854-x
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\MM8X29QG\\Ferrari et al. - 2021 - Topology optimization with linearized buckling cri.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/s00158-021-02854-x
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s00158-021-02854-x
      \endverb
      \keyw{Aggregation functions,Buckling optimization,Matlab,Optimality criteria,Topology optimization}
    \endentry
    \entry{mela_resolving_2014}{article}{}
      \name{author}{1}{}{%
        {{hash=58f07ca48443e971859245fe2c6f78b5}{%
           family={Mela},
           familyi={M\bibinitperiod},
           given={Kristo},
           giveni={K\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{58f07ca48443e971859245fe2c6f78b5}
      \strng{fullhash}{58f07ca48443e971859245fe2c6f78b5}
      \strng{bibnamehash}{58f07ca48443e971859245fe2c6f78b5}
      \strng{authorbibnamehash}{58f07ca48443e971859245fe2c6f78b5}
      \strng{authornamehash}{58f07ca48443e971859245fe2c6f78b5}
      \strng{authorfullhash}{58f07ca48443e971859245fe2c6f78b5}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{In this paper, several issues related to member buckling in truss topology optimization are treated. In the conventional formulations, where cross-sectional areas of ground structure members are the design variables, member buckling constraints are known to be very difficult to handle, both numerically and theoretically. Buckling constraints produce a feasible set that is non-connected and non-convex. Furthermore, the so-called jump in the buckling length phenomenon introduces severe difficulties for determining the correct buckling strength of parallel consecutive compression members. These issues are handled in the paper by employing a mixed variable formulation of truss topology optimization problems. In this formulation, member buckling constraints become linear. Parallel consecutive members of the ground structure are identified as chains, and overlapping members are added to the ground structure between each pair of nodes of a chain. Buckling constraints are written for every member, and linear constraints on the binary member existence variables disallow impractical topologies. In the proposed approach, Euler buckling as well as buckling according to various design codes, can be incorporated. Numerical examples demonstrate that the optimum topology depends on whether the buckling constraints are derived from Euler’s theory or from design codes.}
      \field{issn}{1615-147X, 1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{12}
      \field{number}{6}
      \field{title}{Resolving issues with member buckling in truss topology optimization using a mixed variable approach}
      \field{urlday}{18}
      \field{urlmonth}{2}
      \field{urlyear}{2022}
      \field{volume}{50}
      \field{year}{2014}
      \field{urldateera}{ce}
      \field{pages}{1037\bibrangedash 1049}
      \range{pages}{13}
      \verb{doi}
      \verb 10.1007/s00158-014-1095-x
      \endverb
    \endentry
    \entry{kirsch_effect_1989}{article}{}
      \name{author}{1}{}{%
        {{hash=effe3f1738f379672a1034006b971c63}{%
           family={Kirsch},
           familyi={K\bibinitperiod},
           given={Uri},
           giveni={U\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {EN}%
      }
      \strng{namehash}{effe3f1738f379672a1034006b971c63}
      \strng{fullhash}{effe3f1738f379672a1034006b971c63}
      \strng{bibnamehash}{effe3f1738f379672a1034006b971c63}
      \strng{authorbibnamehash}{effe3f1738f379672a1034006b971c63}
      \strng{authornamehash}{effe3f1738f379672a1034006b971c63}
      \strng{authorfullhash}{effe3f1738f379672a1034006b971c63}
      \field{extraname}{3}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Assuming force method analysis formulation, the effect of compatibility conditions on optimal design of trusses is studied. Neglecting the latter conditions, a linear programming (LP) formulation is obtained. The possibility of applying prestressing forces by “lack of fit” to maintain compatibility at the LP optimum is demonstrated. It has been shown that for structures subjected to a single loading condition, the LP lower‐bound solution is the final optimum. Prestressing might be required to maintain compatibility in cases where the optimal solution represents a statically indeterminate structure. The various possible solutions for structures subjected to multiple loading conditions are discussed. It is shown that under certain circumstances, compatibility conditions can be satisfied at the LP optimum only by applying different sets of prestressing forces for the various loadings. For certain geometries, the LP solution represents multiple optimal topologies, part of them being statically determinate structures. In such cases, the LP lower‐bound solution is the final optimum, and no prestressing is required to maintain compatibility. In cases where compatibility conditions considerably affect the solution, prestressing by lack of fit might significantly improve the final optimum.}
      \field{issn}{0733-9445}
      \field{journaltitle}{Journal of Structural Engineering}
      \field{month}{3}
      \field{number}{3}
      \field{title}{Effect of {Compatibility} and {Prestressing} on {Optimized} {Trusses}}
      \field{urlday}{22}
      \field{urlmonth}{10}
      \field{urlyear}{2021}
      \field{volume}{115}
      \field{year}{1989}
      \field{urldateera}{ce}
      \field{pages}{724\bibrangedash 737}
      \range{pages}{14}
      \verb{doi}
      \verb 10.1061/(ASCE)0733-9445(1989)115:3(724)
      \endverb
      \keyw{Design,Prestressing,Trusses}
    \endentry
    \entry{Moore_Mechmotum}{misc}{}
      \name{author}{2}{}{%
        {{hash=e34341172d9f9982d03250508ab44826}{%
           family={Moore},
           familyi={M\bibinitperiod},
           given={Jason;\bibnamedelima K.},
           giveni={J\bibinitperiod\bibinitdelim K\bibinitperiod}}}%
        {{hash=308ff4b0e8eed65b6e5bd44f526dba49}{%
           family={Mechmotum},
           familyi={M\bibinitperiod}}}%
      }
      \strng{namehash}{5c3e427269c05136c40df05c0097cd6d}
      \strng{fullhash}{5c3e427269c05136c40df05c0097cd6d}
      \strng{bibnamehash}{5c3e427269c05136c40df05c0097cd6d}
      \strng{authorbibnamehash}{5c3e427269c05136c40df05c0097cd6d}
      \strng{authornamehash}{5c3e427269c05136c40df05c0097cd6d}
      \strng{authorfullhash}{5c3e427269c05136c40df05c0097cd6d}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{journaltitle}{GitHub}
      \field{title}{cyipopt: Cython interface for the interior point optimzer IPOPT}
      \field{year}{2018}
      \verb{urlraw}
      \verb https://github.com/mechmotum/cyipopt
      \endverb
      \verb{url}
      \verb https://github.com/mechmotum/cyipopt
      \endverb
    \endentry
    \entry{alappat_recursive_2020}{article}{}
      \name{author}{8}{}{%
        {{hash=c6a08cc6454e9ac9f8884d84a16450f0}{%
           family={Alappat},
           familyi={A\bibinitperiod},
           given={Christie},
           giveni={C\bibinitperiod}}}%
        {{hash=089967122dd60507de492b1a82148146}{%
           family={Basermann},
           familyi={B\bibinitperiod},
           given={Achim},
           giveni={A\bibinitperiod}}}%
        {{hash=9e5c799ec99245ee2c294174e3f72241}{%
           family={Bishop},
           familyi={B\bibinitperiod},
           given={Alan\bibnamedelima R.},
           giveni={A\bibinitperiod\bibinitdelim R\bibinitperiod}}}%
        {{hash=fe30c0e3043a9a37db7510debc32f9a2}{%
           family={Fehske},
           familyi={F\bibinitperiod},
           given={Holger},
           giveni={H\bibinitperiod}}}%
        {{hash=9e49d522461c2d5d9e44584ac6102f43}{%
           family={Hager},
           familyi={H\bibinitperiod},
           given={Georg},
           giveni={G\bibinitperiod}}}%
        {{hash=9f9c8f482908c659e21e689840507002}{%
           family={Schenk},
           familyi={S\bibinitperiod},
           given={Olaf},
           giveni={O\bibinitperiod}}}%
        {{hash=4f4a74d8304e90a4fb8b828611266096}{%
           family={Thies},
           familyi={T\bibinitperiod},
           given={Jonas},
           giveni={J\bibinitperiod}}}%
        {{hash=0623d76ccb0e0ac76b02be5a26c96d44}{%
           family={Wellein},
           familyi={W\bibinitperiod},
           given={Gerhard},
           giveni={G\bibinitperiod}}}%
      }
      \strng{namehash}{4325704b21807060d2bdce32e7558905}
      \strng{fullhash}{8647d206e3f56004958bc8a5d05eb07d}
      \strng{bibnamehash}{8647d206e3f56004958bc8a5d05eb07d}
      \strng{authorbibnamehash}{8647d206e3f56004958bc8a5d05eb07d}
      \strng{authornamehash}{4325704b21807060d2bdce32e7558905}
      \strng{authorfullhash}{8647d206e3f56004958bc8a5d05eb07d}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{The symmetric sparse matrix-vector multiplication (SymmSpMV) is an important building block for many numerical linear algebra kernel operations or graph traversal applications. Parallelizing SymmSpMV on today's multicore platforms with up to 100 cores is difficult due to the need to manage conflicting updates on the result vector. Coloring approaches can be used to solve this problem without data duplication, but existing coloring algorithms do not take load balancing and deep memory hierarchies into account, hampering scalability and full-chip performance. In this work, we propose the recursive algebraic coloring engine (RACE), a novel coloring algorithm and open-source library implementation that eliminates the shortcomings of previous coloring methods in terms of hardware efficiency and parallelization overhead. We describe the level construction, distance-k coloring, and load balancing steps in RACE, use it to parallelize SymmSpMV, and compare its performance on 31 sparse matrices with other state-of-the-art coloring techniques and Intel MKL on two modern multicore processors. RACE outperforms all other approaches substantially. By means of a parameterized roofline model, we analyze the SymmSpMV performance in detail and discuss outliers. While we focus on SymmSpMV in this article, our algorithm and software are applicable to any sparse matrix operation with data dependencies that can be resolved by distance-k coloring.}
      \field{issn}{2329-4949}
      \field{journaltitle}{ACM Transactions on Parallel Computing}
      \field{number}{3}
      \field{title}{A {Recursive} {Algebraic} {Coloring} {Technique} for {Hardware}-efficient {Symmetric} {Sparse} {Matrix}-vector {Multiplication}}
      \field{urlday}{17}
      \field{urlmonth}{1}
      \field{urlyear}{2023}
      \field{volume}{7}
      \field{year}{2020}
      \field{urldateera}{ce}
      \field{pages}{19:1\bibrangedash 19:37}
      \range{pages}{-1}
      \verb{doi}
      \verb 10.1145/3399732
      \endverb
      \keyw{graph algorithms,graph coloring,memory hierarchies,scheduling,Sparse matrix,sparse symmetric matrix-vector multiplication}
    \endentry
    \entry{enrico_stragiotti_truss_2023}{misc}{}
      \name{author}{4}{}{%
        {{hash=6c4965d3ad73fb11f44136afa897bb91}{%
           family={Stragiotti},
           familyi={S\bibinitperiod},
           given={Enrico},
           giveni={E\bibinitperiod}}}%
        {{hash=6ffe413a21f4954b0aac85ca037c7876}{%
           family={Irisarri},
           familyi={I\bibinitperiod},
           given={François-Xavier},
           giveni={F\bibinithyphendelim X\bibinitperiod}}}%
        {{hash=d9c42bf5ce7591763a45d8334a00d4e1}{%
           family={Julien},
           familyi={J\bibinitperiod},
           given={Cédric},
           giveni={C\bibinitperiod}}}%
        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
      }
      \list{publisher}{1}{%
        {Mendeley}%
      }
      \strng{namehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{fullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{bibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authorbibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authornamehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{authorfullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \field{extraname}{3}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This data set contains the starting point and the results of the article "3D Truss topology optimization with topological buckling constraints and reduced sensitivity to the initialization point" (Temporary name).}
      \field{month}{5}
      \field{title}{Truss {Topology} {Optimization} with {Topological} {Buckling} {Constraints} {Data} {Set}}
      \field{urlday}{3}
      \field{urlmonth}{5}
      \field{urlyear}{2023}
      \field{year}{2023}
      \field{urldateera}{ce}
      \verb{doi}
      \verb 10.17632/BW7XB2W6ST.1
      \endverb
      \keyw{own}
    \endentry
    \entry{rozvany_symmetry_2011}{article}{}
      \name{author}{1}{}{%
        {{hash=e5e9cc5d2d68294bd6c1b3a27caeaf7d}{%
           family={Rozvany},
           familyi={R\bibinitperiod},
           given={George\bibnamedelimb I.\bibnamedelimi N.},
           giveni={G\bibinitperiod\bibinitdelim I\bibinitperiod\bibinitdelim N\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{e5e9cc5d2d68294bd6c1b3a27caeaf7d}
      \strng{fullhash}{e5e9cc5d2d68294bd6c1b3a27caeaf7d}
      \strng{bibnamehash}{e5e9cc5d2d68294bd6c1b3a27caeaf7d}
      \strng{authorbibnamehash}{e5e9cc5d2d68294bd6c1b3a27caeaf7d}
      \strng{authornamehash}{e5e9cc5d2d68294bd6c1b3a27caeaf7d}
      \strng{authorfullhash}{e5e9cc5d2d68294bd6c1b3a27caeaf7d}
      \field{extraname}{4}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{The aim of this article is to initiate an exchange of ideas on symmetry and non-uniqueness in topology optimization. These concepts are discussed in the context of 2D trusses and grillages, but could be extended to other structures and design constraints, including 3D problems and numerical solutions. The treatment of the subject is pitched at the background of engineering researchers, and principles of mechanics are given preference to those of pure mathematics. The author hopes to provide some new insights into fundamental properties of exact optimal topologies. Combining elements of the optimal layout theory (of Prager and the author) with those of linear programming, it is concluded that for the considered problems the optimal topology is in general unique and symmetric if the loads, domain boundaries and supports are symmetric. However, in some special cases the number of optimal solutions may be infinite, and some of these may be non-symmetric. The deeper reasons for the above findings are explained in the light of the above layout theory.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{3}
      \field{number}{3}
      \field{title}{On symmetry and non-uniqueness in exact topology optimization}
      \field{urlday}{4}
      \field{urlmonth}{10}
      \field{urlyear}{2023}
      \field{volume}{43}
      \field{year}{2011}
      \field{urldateera}{ce}
      \field{pages}{297\bibrangedash 317}
      \range{pages}{21}
      \verb{doi}
      \verb 10.1007/s00158-010-0564-0
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\6WZJC9FY\\Rozvany - 2011 - On symmetry and non-uniqueness in exact topology o.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/s00158-010-0564-0
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s00158-010-0564-0
      \endverb
      \keyw{Grillages,Non-uniqueness,Optimal layout theory,Symmetry,Topology optimization,Trusses}
    \endentry
    \entry{guo_confirmation_2014}{article}{}
      \name{author}{3}{}{%
        {{hash=991f97b5b245ece2a1c7daba022fff1c}{%
           family={Guo},
           familyi={G\bibinitperiod},
           given={Xu},
           giveni={X\bibinitperiod}}}%
        {{hash=2bf269973a03f039e6f9151e065225a8}{%
           family={Du},
           familyi={D\bibinitperiod},
           given={Zongliang},
           giveni={Z\bibinitperiod}}}%
        {{hash=5fba7de724fe01e2541f05efe522b531}{%
           family={Cheng},
           familyi={C\bibinitperiod},
           given={Gengdong},
           giveni={G\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{cf3db1de93ec64959d24e9819c11dba7}
      \strng{fullhash}{cf3db1de93ec64959d24e9819c11dba7}
      \strng{bibnamehash}{cf3db1de93ec64959d24e9819c11dba7}
      \strng{authorbibnamehash}{cf3db1de93ec64959d24e9819c11dba7}
      \strng{authornamehash}{cf3db1de93ec64959d24e9819c11dba7}
      \strng{authorfullhash}{cf3db1de93ec64959d24e9819c11dba7}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{In this note, a conjecture on the existence of symmetric optimal solution under multiple loads made in Rozvany (Struct Multidisc Optim 43:297–317, 2011, Conjecture 4) has been confirmed.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{10}
      \field{number}{4}
      \field{title}{A confirmation of a conjecture on the existence of symmetric optimal solution under multiple loads}
      \field{urlday}{4}
      \field{urlmonth}{10}
      \field{urlyear}{2023}
      \field{volume}{50}
      \field{year}{2014}
      \field{urldateera}{ce}
      \field{pages}{659\bibrangedash 661}
      \range{pages}{3}
      \verb{doi}
      \verb 10.1007/s00158-014-1089-8
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\2R4ZQJJ2\\Guo et al. - 2014 - A confirmation of a conjecture on the existence of.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/s00158-014-1089-8
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s00158-014-1089-8
      \endverb
      \keyw{Multi-load case,Optimal solution,Symmetry}
    \endentry
    \entry{stragiotti_enhanced_2022}{inproceedings}{}
      \name{author}{4}{}{%
        {{hash=6c4965d3ad73fb11f44136afa897bb91}{%
           family={Stragiotti},
           familyi={S\bibinitperiod},
           given={Enrico},
           giveni={E\bibinitperiod}}}%
        {{hash=6ffe413a21f4954b0aac85ca037c7876}{%
           family={Irisarri},
           familyi={I\bibinitperiod},
           given={François-Xavier},
           giveni={F\bibinithyphendelim X\bibinitperiod}}}%
        {{hash=d9c42bf5ce7591763a45d8334a00d4e1}{%
           family={Julien},
           familyi={J\bibinitperiod},
           given={Cédric},
           giveni={C\bibinitperiod}}}%
        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
      }
      \list{location}{1}{%
        {Leeds, United Kingdom}%
      }
      \strng{namehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{fullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{bibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authorbibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authornamehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{authorfullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \field{extraname}{4}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Cellular architectured structures' most appealing characteristic is that they are able to create large structures assembling small repetitive components. Thanks to their modular nature, they bring interesting features among which reduced tooling, fast assembly, and short repair time. In the first part of the article, we formulate an optimizing method that minimizes the mass of a cellular architectured structure taking into account internal stresses, local buckling, and pattern repetition constraints. The proposed solving algorithm mitigates the appearance of local minima, a critical problem for discrete trusses. In the second part, the optimization method is applied to a real-size aeronautic application: the minimization of the mass of a cellular 3D wing box subject to lift and torsion loads. Compared to classic cell topologies, the proposed method found a cell 10-times lighter, at the cost of increased manufacturing difficulty.}
      \field{booktitle}{{ASMO}-{UK} 12 / {ASMO}-{Europe} 1 / {ISSMO} {Conference} on {Engineering} {Design} {Optimization} (2022)}
      \field{month}{7}
      \field{title}{Enhanced truss topology optimization ({TTO}) applied to a cellular wing box}
      \field{urlday}{14}
      \field{urlmonth}{11}
      \field{urlyear}{2023}
      \field{year}{2022}
      \field{urldateera}{ce}
      \verb{file}
      \verb HAL PDF Full Text:D\:\\estragio\\Zotero\\storage\\ZY7S5YZA\\Stragiotti et al. - 2022 - Enhanced truss topology optimization (TTO) applied.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://hal.science/hal-04283287
      \endverb
      \verb{url}
      \verb https://hal.science/hal-04283287
      \endverb
      \keyw{Optimisation,Optimisation Topologique,Structure Lattice,own}
    \endentry
    \entry{li_anisotropic_2020}{article}{}
      \name{author}{4}{}{%
        {{hash=5d347014590ab2d9450a92400b1f5f00}{%
           family={Li},
           familyi={L\bibinitperiod},
           given={Dawei},
           giveni={D\bibinitperiod}}}%
        {{hash=9e6a22a80aceb54ab0cdf5f2db5382dd}{%
           family={Liao},
           familyi={L\bibinitperiod},
           given={Wenhe},
           giveni={W\bibinitperiod}}}%
        {{hash=7cbe1c6cbd85cceaafcc34d0a22ec27a}{%
           family={Dai},
           familyi={D\bibinitperiod},
           given={Ning},
           giveni={N\bibinitperiod}}}%
        {{hash=8378d5b4061a021880b29f2f73452923}{%
           family={Xie},
           familyi={X\bibinitperiod},
           given={Yi\bibnamedelima Min},
           giveni={Y\bibinitperiod\bibinitdelim M\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{34744ed22b7e1b591e0dcfff89ba3714}
      \strng{fullhash}{6f858291a2f0be4e07a15294119275d5}
      \strng{bibnamehash}{6f858291a2f0be4e07a15294119275d5}
      \strng{authorbibnamehash}{6f858291a2f0be4e07a15294119275d5}
      \strng{authornamehash}{34744ed22b7e1b591e0dcfff89ba3714}
      \strng{authorfullhash}{6f858291a2f0be4e07a15294119275d5}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{In this work, we present a novel anisotropic lattice structure design and multi-scale optimization method that can generate conformal gradient lattice structures (CGLS). The goal of optimization is to achieve gradient density, adaptive orientation and variable scale (or periodic) lattice structures with the highest mechanical stiffness. The asymptotic homogenization method is employed for the calculation of the mechanical properties of various lattice structures. And an equation of elastic tensor and relative density of the unit cell is established. The established function above is then considered in the numerical optimization schemes. In the post-processing, we propose a numerical projecting method based on Fourier transform, which can synthesize conformal gradient lattice structure without changing the size and shape of the unit cells. Besides, the algorithm allows us to minimize distortion and prevent defects in the final lattice and keep the lattice structures smooth and continuous. Finally, in comparison with different parameters and methods are performed to demonstrate the superiority of our proposed method. The results show that the optimized anisotropic conformal gradient lattice structures are much stiffer and exhibit better structural robustness and buckling resistance than the uniform and the directly mapped designs.}
      \field{issn}{0010-4485}
      \field{journaltitle}{Computer-Aided Design}
      \field{month}{2}
      \field{title}{Anisotropic design and optimization of conformal gradient lattice structures}
      \field{urlday}{13}
      \field{urlmonth}{10}
      \field{urlyear}{2020}
      \field{volume}{119}
      \field{year}{2020}
      \field{urldateera}{ce}
      \field{pages}{102787}
      \range{pages}{1}
      \verb{doi}
      \verb 10.1016/j.cad.2019.102787
      \endverb
      \verb{file}
      \verb ScienceDirect Full Text PDF:D\:\\estragio\\Zotero\\storage\\92HYV5MH\\Li et al. - 2020 - Anisotropic design and optimization of conformal g.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb http://www.sciencedirect.com/science/article/pii/S0010448519302386
      \endverb
      \verb{url}
      \verb http://www.sciencedirect.com/science/article/pii/S0010448519302386
      \endverb
      \keyw{Anisotropic design,Conformal lattice,Lattice optimization,Multi-scale optimization,Synthesize algorithm}
    \endentry
    \entry{deshpande_effective_2001}{article}{}
      \name{author}{3}{}{%
        {{hash=5233a32272aa7ffdd5842786a86d44a7}{%
           family={Deshpande},
           familyi={D\bibinitperiod},
           given={V.\bibnamedelimi S.},
           giveni={V\bibinitperiod\bibinitdelim S\bibinitperiod}}}%
        {{hash=e2b30fe12c7d9bde635a5c2346741c56}{%
           family={Fleck},
           familyi={F\bibinitperiod},
           given={N.\bibnamedelimi A.},
           giveni={N\bibinitperiod\bibinitdelim A\bibinitperiod}}}%
        {{hash=4efbe37e741cfa6637ad06d22dcb5217}{%
           family={Ashby},
           familyi={A\bibinitperiod},
           given={M.\bibnamedelimi F.},
           giveni={M\bibinitperiod\bibinitdelim F\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{6938fda67f04d23e34e169a492c80b51}
      \strng{fullhash}{6938fda67f04d23e34e169a492c80b51}
      \strng{bibnamehash}{6938fda67f04d23e34e169a492c80b51}
      \strng{authorbibnamehash}{6938fda67f04d23e34e169a492c80b51}
      \strng{authornamehash}{6938fda67f04d23e34e169a492c80b51}
      \strng{authorfullhash}{6938fda67f04d23e34e169a492c80b51}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{issn}{0022-5096}
      \field{journaltitle}{Journal of the Mechanics and Physics of Solids}
      \field{month}{8}
      \field{number}{8}
      \field{title}{Effective properties of the octet-truss lattice material}
      \field{urlday}{2}
      \field{urlmonth}{10}
      \field{urlyear}{2020}
      \field{volume}{49}
      \field{year}{2001}
      \field{urldateera}{ce}
      \field{pages}{1747\bibrangedash 1769}
      \range{pages}{23}
      \verb{doi}
      \verb 10.1016/S0022-5096(01)00010-2
      \endverb
      \verb{urlraw}
      \verb http://www.sciencedirect.com/science/article/pii/S0022509601000102
      \endverb
      \verb{url}
      \verb http://www.sciencedirect.com/science/article/pii/S0022509601000102
      \endverb
      \keyw{A. Buckling,C. Finite elements,Collapse surfaces,Lattice materials,Porous solids}
    \endentry
    \entry{stegmann_discrete_2005}{article}{}
      \name{author}{2}{}{%
        {{hash=8d9585a790dc476e971271d1dfe7a347}{%
           family={Stegmann},
           familyi={S\bibinitperiod},
           given={J.},
           giveni={J\bibinitperiod}}}%
        {{hash=6c260b5ad86697f4fd9b0d5ea1dd1882}{%
           family={Lund},
           familyi={L\bibinitperiod},
           given={E.},
           giveni={E\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{4b7f41c1998f8ee163f45f26abc7dd21}
      \strng{fullhash}{4b7f41c1998f8ee163f45f26abc7dd21}
      \strng{bibnamehash}{4b7f41c1998f8ee163f45f26abc7dd21}
      \strng{authorbibnamehash}{4b7f41c1998f8ee163f45f26abc7dd21}
      \strng{authornamehash}{4b7f41c1998f8ee163f45f26abc7dd21}
      \strng{authorfullhash}{4b7f41c1998f8ee163f45f26abc7dd21}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{A novel method for doing material optimization of general composite laminate shell structures is presented and its capabilities are illustrated with three examples. The method is labelled Discrete Material Optimization (DMO) but uses gradient information combined with mathematical programming to solve a discrete optimization problem. The method can be used to solve the orientation problem of orthotropic materials and the material selection problem as well as problems involving both. The method relies on ideas from multiphase topology optimization to achieve a parametrization which is very general and reduces the risk of obtaining a local optimum solution for the tested conﬁgurations. The applicability of the DMO method is demonstrated for ﬁbre angle optimization of a cantilever beam and combined ﬁbre angle and material selection optimization of a four-point beam bending problem and a doubly curved laminated shell. Copyright ᭧ 2005 John Wiley \&amp; Sons, Ltd.}
      \field{issn}{0029-5981, 1097-0207}
      \field{journaltitle}{International Journal for Numerical Methods in Engineering}
      \field{month}{4}
      \field{number}{14}
      \field{title}{Discrete material optimization of general composite shell structures}
      \field{urlday}{19}
      \field{urlmonth}{9}
      \field{urlyear}{2019}
      \field{volume}{62}
      \field{year}{2005}
      \field{urldateera}{ce}
      \field{pages}{2009\bibrangedash 2027}
      \range{pages}{19}
      \verb{doi}
      \verb 10.1002/nme.1259
      \endverb
      \verb{file}
      \verb Stegmann and Lund - 2005 - Discrete material optimization of general composit.pdf:D\:\\estragio\\Zotero\\storage\\HRN74INW\\A_018.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb http://doi.wiley.com/10.1002/nme.1259
      \endverb
      \verb{url}
      \verb http://doi.wiley.com/10.1002/nme.1259
      \endverb
    \endentry
    \entry{hvejsel_material_2011}{article}{}
      \name{author}{2}{}{%
        {{hash=0d90c8ed5a026090b1c257eb157fedd3}{%
           family={Hvejsel},
           familyi={H\bibinitperiod},
           given={Christian\bibnamedelima Frier},
           giveni={C\bibinitperiod\bibinitdelim F\bibinitperiod}}}%
        {{hash=6916b89289aed683046be157b2981bbf}{%
           family={Lund},
           familyi={L\bibinitperiod},
           given={Erik},
           giveni={E\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{8e8bcbb7626a5186af97aef29c966aac}
      \strng{fullhash}{8e8bcbb7626a5186af97aef29c966aac}
      \strng{bibnamehash}{8e8bcbb7626a5186af97aef29c966aac}
      \strng{authorbibnamehash}{8e8bcbb7626a5186af97aef29c966aac}
      \strng{authornamehash}{8e8bcbb7626a5186af97aef29c966aac}
      \strng{authorfullhash}{8e8bcbb7626a5186af97aef29c966aac}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{This paper presents two multi-material interpolation schemes as direct generalizations of the well-known SIMP and RAMP material interpolation schemes originally developed for isotropic mixtures of two isotropic material phases. The new interpolation schemes provide generally applicable interpolation schemes between an arbitrary number of pre-defined materials with given (anisotropic) properties. The method relies on a large number of sparse linear constraints to enforce the selection of at most one material in each design subdomain. Topology and multi-material optimization is formulated within a unified parametrization.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{6}
      \field{number}{6}
      \field{title}{Material interpolation schemes for unified topology and multi-material optimization}
      \field{urlday}{27}
      \field{urlmonth}{4}
      \field{urlyear}{2023}
      \field{volume}{43}
      \field{year}{2011}
      \field{urldateera}{ce}
      \field{pages}{811\bibrangedash 825}
      \range{pages}{15}
      \verb{doi}
      \verb 10.1007/s00158-011-0625-z
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\3R73UJ2H\\Hvejsel and Lund - 2011 - Material interpolation schemes for unified topolog.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/s00158-011-0625-z
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s00158-011-0625-z
      \endverb
      \keyw{Topology optimization,Composite materials,Material interpolation,Multi-material parametrization}
    \endentry
    \entry{opgenoord_design_2019}{article}{}
      \name{author}{2}{}{%
        {{hash=8267983366f0bb66489b9a56c599787d}{%
           family={Opgenoord},
           familyi={O\bibinitperiod},
           given={Max\bibnamedelimb M.\bibnamedelimi J.},
           giveni={M\bibinitperiod\bibinitdelim M\bibinitperiod\bibinitdelim J\bibinitperiod}}}%
        {{hash=a51c06eb9ede4de9ef30715d223beb5c}{%
           family={Willcox},
           familyi={W\bibinitperiod},
           given={Karen\bibnamedelima E.},
           giveni={K\bibinitperiod\bibinitdelim E\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{dde3fcd637aca44c40b005701ced3151}
      \strng{fullhash}{dde3fcd637aca44c40b005701ced3151}
      \strng{bibnamehash}{dde3fcd637aca44c40b005701ced3151}
      \strng{authorbibnamehash}{dde3fcd637aca44c40b005701ced3151}
      \strng{authornamehash}{dde3fcd637aca44c40b005701ced3151}
      \strng{authorfullhash}{dde3fcd637aca44c40b005701ced3151}
      \field{extraname}{2}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{8}
      \field{number}{2}
      \field{title}{Design for additive manufacturing: cellular structures in early-stage aerospace design}
      \field{urlday}{5}
      \field{urlmonth}{10}
      \field{urlyear}{2020}
      \field{volume}{60}
      \field{year}{2019}
      \field{urldateera}{ce}
      \field{pages}{411\bibrangedash 428}
      \range{pages}{18}
      \verb{doi}
      \verb 10.1007/s00158-019-02305-8
      \endverb
    \endentry
    \entry{prokop_load-carrying_2022}{article}{}
      \name{author}{4}{}{%
        {{hash=393a98fa550a26ea2b4c979a7880edaa}{%
           family={Prokop},
           familyi={P\bibinitperiod},
           given={Jozef},
           giveni={J\bibinitperiod}}}%
        {{hash=28956ff38f8c4ec06499d91bd52589d7}{%
           family={Odrobiňák},
           familyi={O\bibinitperiod},
           given={Jaroslav},
           giveni={J\bibinitperiod}}}%
        {{hash=c8bd205055d7be34ba6abaef72c53aa5}{%
           family={Farbák},
           familyi={F\bibinitperiod},
           given={Matúš},
           giveni={M\bibinitperiod}}}%
        {{hash=8dc913d60c0c401bdd30c63d3440cd16}{%
           family={Novotný},
           familyi={N\bibinitperiod},
           given={Vladimír},
           giveni={V\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{e258ddd2003af260318df25c0e325479}
      \strng{fullhash}{e02dcd88c76c31d87b3ca27fdc05a822}
      \strng{bibnamehash}{e02dcd88c76c31d87b3ca27fdc05a822}
      \strng{authorbibnamehash}{e02dcd88c76c31d87b3ca27fdc05a822}
      \strng{authornamehash}{e258ddd2003af260318df25c0e325479}
      \strng{authorfullhash}{e02dcd88c76c31d87b3ca27fdc05a822}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{The paper presents an extensive study aimed to determine the applicability of the demountable Bailey bridge (BB) system on construction sites or in other temporary conditions while meeting the regulations for the design and assessment of steel bridges. The analysis is focused on whether and to what extent the BB system with spans between 12 and 36 m is usable for on-site freight transport with conventional lorries with a total weight of up to 22–28 tons. At the same time, the BB system within these spans should be utilized for construction vehicles with a total weight of up to 32–40 tons. To calculate the load-carrying capacity, spatial numerical models were analysed using FEM and procedures of actual design codes were utilized. In the case of the main girders, analysis is focused on the out-of-plane stability of their compressed chords. Recommendations for the use of this bridge system in different arrangements of the main girder and bridge deck are then summarized and discussed.}
      \field{issn}{2076-3417}
      \field{journaltitle}{Applied Sciences}
      \field{month}{1}
      \field{number}{8}
      \field{title}{Load-{Carrying} {Capacity} of {Bailey} {Bridge} in {Civil} {Applications}}
      \field{urlday}{13}
      \field{urlmonth}{12}
      \field{urlyear}{2023}
      \field{volume}{12}
      \field{year}{2022}
      \field{urldateera}{ce}
      \field{pages}{3788}
      \range{pages}{1}
      \verb{doi}
      \verb 10.3390/app12083788
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\WRQZ2FNA\\Prokop et al. - 2022 - Load-Carrying Capacity of Bailey Bridge in Civil A.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://www.mdpi.com/2076-3417/12/8/3788
      \endverb
      \verb{url}
      \verb https://www.mdpi.com/2076-3417/12/8/3788
      \endverb
      \keyw{Bailey bridge,load-carrying capacity,stability,steel bridge,temporary bridge}
    \endentry
    \entry{department_of_the_army_bailey_1986}{unpublished}{}
      \name{author}{1}{}{%
        {{hash=dbb3fba4ad28e4e23629e4149f8e6ca2}{%
           family={{Department of the Army}},
           familyi={D\bibinitperiod}}}%
      }
      \strng{namehash}{dbb3fba4ad28e4e23629e4149f8e6ca2}
      \strng{fullhash}{dbb3fba4ad28e4e23629e4149f8e6ca2}
      \strng{bibnamehash}{dbb3fba4ad28e4e23629e4149f8e6ca2}
      \strng{authorbibnamehash}{dbb3fba4ad28e4e23629e4149f8e6ca2}
      \strng{authornamehash}{dbb3fba4ad28e4e23629e4149f8e6ca2}
      \strng{authorfullhash}{dbb3fba4ad28e4e23629e4149f8e6ca2}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Department of the Army (1986) Bailey bridge. headquarters, Department of the Army, Washington DC. Field Manual No. 5–277}
      \field{title}{{Field} {Manual} {No}. 5–277, Panel Bridge, Bailey Type, {Washington} {DC}.}
      \field{urlday}{13}
      \field{urlmonth}{12}
      \field{urlyear}{2023}
      \field{year}{1986}
      \field{urldateera}{ce}
      \verb{file}
      \verb fm5-277(86).pdf:D\:\\estragio\\Zotero\\storage\\T5KHBXQC\\fm5-277(86).pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb http://www.bits.de/NRANEU/others/amd-us-archive/fm5-277%2886%29.pdf
      \endverb
      \verb{url}
      \verb http://www.bits.de/NRANEU/others/amd-us-archive/fm5-277%2886%29.pdf
      \endverb
    \endentry
    \entry{shahabsafa_novel_2018}{article}{}
      \name{author}{7}{}{%
        {{hash=aaa9ce3d7dc197da2f6cdfb7528a1cb0}{%
           family={Shahabsafa},
           familyi={S\bibinitperiod},
           given={Mohammad},
           giveni={M\bibinitperiod}}}%
        {{hash=e6a55d22efcca685f11ecdb919b4b46f}{%
           family={Mohammad-Nezhad},
           familyi={M\bibinithyphendelim N\bibinitperiod},
           given={Ali},
           giveni={A\bibinitperiod}}}%
        {{hash=a9e401c86ac01b246bcac3ee2468cce1}{%
           family={Terlaky},
           familyi={T\bibinitperiod},
           given={Tamás},
           giveni={T\bibinitperiod}}}%
        {{hash=52288ad88af8d2a82d791a180db2bc09}{%
           family={Zuluaga},
           familyi={Z\bibinitperiod},
           given={Luis},
           giveni={L\bibinitperiod}}}%
        {{hash=8a879f55d80ea2054dda018cde71a145}{%
           family={He},
           familyi={H\bibinitperiod},
           given={Sicheng},
           giveni={S\bibinitperiod}}}%
        {{hash=dbd845fd6b96bddc065ea1799f9b7512}{%
           family={Hwang},
           familyi={H\bibinitperiod},
           given={John\bibnamedelima T.},
           giveni={J\bibinitperiod\bibinitdelim T\bibinitperiod}}}%
        {{hash=f78019558101a841974c5f3b5a885657}{%
           family={Martins},
           familyi={M\bibinitperiod},
           given={Joaquim\bibnamedelimb R.\bibnamedelimi R.\bibnamedelimi A.},
           giveni={J\bibinitperiod\bibinitdelim R\bibinitperiod\bibinitdelim R\bibinitperiod\bibinitdelim A\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{d8f74ab1003f51c5ca60e6dc8d2c0b56}
      \strng{fullhash}{3ed1524cc70759aba8d1520dfbfe810f}
      \strng{bibnamehash}{3ed1524cc70759aba8d1520dfbfe810f}
      \strng{authorbibnamehash}{3ed1524cc70759aba8d1520dfbfe810f}
      \strng{authornamehash}{d8f74ab1003f51c5ca60e6dc8d2c0b56}
      \strng{authorfullhash}{3ed1524cc70759aba8d1520dfbfe810f}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Discrete truss sizing problems are very challenging to solve due to their combinatorial, nonlinear, non-convex nature. Consequently, truss sizing problems become unsolvable as the size of the truss grows. To address this issue, we consider various mathematical formulations for the truss design problem with the objective of minimizing weight, while the crosssectional areas of the bars take only discrete values. Euler buckling constraints, Hooke’s law, and bounds for stress and displacements are also considered. We propose mixed integer linear optimization (MILO) reformulations of the non-convex mixed integer models. The resulting MILO models are not solvable with existing MILO solvers as the size of the problem grows. Our novel methodology provides high-quality solutions for large-scale real truss sizing problems, as demonstrated through extensive numerical experiments.}
      \field{issn}{1615-147X, 1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{12}
      \field{number}{6}
      \field{title}{A novel approach to discrete truss design problems using mixed integer neighborhood search}
      \field{urlday}{23}
      \field{urlmonth}{6}
      \field{urlyear}{2022}
      \field{volume}{58}
      \field{year}{2018}
      \field{urldateera}{ce}
      \field{pages}{2411\bibrangedash 2429}
      \range{pages}{19}
      \verb{doi}
      \verb 10.1007/s00158-018-2099-8
      \endverb
    \endentry
    \entry{brooks_benchmark_2018}{article}{}
      \name{author}{3}{}{%
        {{hash=90b3c2058a3c750b7659a97d97e3b92d}{%
           family={Brooks},
           familyi={B\bibinitperiod},
           given={Timothy\bibnamedelima R.},
           giveni={T\bibinitperiod\bibinitdelim R\bibinitperiod}}}%
        {{hash=17c9d79f7c0b7c2e7eb2f3cd684cd508}{%
           family={Kenway},
           familyi={K\bibinitperiod},
           given={Gaetan\bibnamedelimb K.\bibnamedelimi W.},
           giveni={G\bibinitperiod\bibinitdelim K\bibinitperiod\bibinitdelim W\bibinitperiod}}}%
        {{hash=f78019558101a841974c5f3b5a885657}{%
           family={Martins},
           familyi={M\bibinitperiod},
           given={Joaquim\bibnamedelimb R.\bibnamedelimi R.\bibnamedelimi A.},
           giveni={J\bibinitperiod\bibinitdelim R\bibinitperiod\bibinitdelim R\bibinitperiod\bibinitdelim A\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{cffa287a9d3b4746720462e587e0f67e}
      \strng{fullhash}{cffa287a9d3b4746720462e587e0f67e}
      \strng{bibnamehash}{cffa287a9d3b4746720462e587e0f67e}
      \strng{authorbibnamehash}{cffa287a9d3b4746720462e587e0f67e}
      \strng{authornamehash}{cffa287a9d3b4746720462e587e0f67e}
      \strng{authorfullhash}{cffa287a9d3b4746720462e587e0f67e}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{issn}{0001-1452, 1533-385X}
      \field{journaltitle}{AIAA Journal}
      \field{month}{7}
      \field{number}{7}
      \field{title}{Benchmark {Aerostructural} {Models} for the {Study} of {Transonic} {Aircraft} {Wings}}
      \field{urlday}{12}
      \field{urlmonth}{9}
      \field{urlyear}{2022}
      \field{volume}{56}
      \field{year}{2018}
      \field{urldateera}{ce}
      \field{pages}{2840\bibrangedash 2855}
      \range{pages}{16}
      \verb{doi}
      \verb 10.2514/1.J056603
      \endverb
    \endentry
    \entry{fakhimi_discrete_2021}{article}{}
      \name{author}{7}{}{%
        {{hash=b717b4e1abf47b32aac90e145f515339}{%
           family={Fakhimi},
           familyi={F\bibinitperiod},
           given={Ramin},
           giveni={R\bibinitperiod}}}%
        {{hash=aaa9ce3d7dc197da2f6cdfb7528a1cb0}{%
           family={Shahabsafa},
           familyi={S\bibinitperiod},
           given={Mohammad},
           giveni={M\bibinitperiod}}}%
        {{hash=ff420034510e582a19f9526e9d6cf29d}{%
           family={Lei},
           familyi={L\bibinitperiod},
           given={Weiming},
           giveni={W\bibinitperiod}}}%
        {{hash=8a879f55d80ea2054dda018cde71a145}{%
           family={He},
           familyi={H\bibinitperiod},
           given={Sicheng},
           giveni={S\bibinitperiod}}}%
        {{hash=f78019558101a841974c5f3b5a885657}{%
           family={Martins},
           familyi={M\bibinitperiod},
           given={Joaquim\bibnamedelimb R.\bibnamedelimi R.\bibnamedelimi A.},
           giveni={J\bibinitperiod\bibinitdelim R\bibinitperiod\bibinitdelim R\bibinitperiod\bibinitdelim A\bibinitperiod}}}%
        {{hash=a9e401c86ac01b246bcac3ee2468cce1}{%
           family={Terlaky},
           familyi={T\bibinitperiod},
           given={Tamás},
           giveni={T\bibinitperiod}}}%
        {{hash=1ec5f170802538f9277ae2ac1e7e0208}{%
           family={Zuluaga},
           familyi={Z\bibinitperiod},
           given={Luis\bibnamedelima F.},
           giveni={L\bibinitperiod\bibinitdelim F\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{380c8aa31cab738c8c74b768ccb153dd}
      \strng{fullhash}{4ab2596912d228c66afb650f90fc5f9d}
      \strng{bibnamehash}{4ab2596912d228c66afb650f90fc5f9d}
      \strng{authorbibnamehash}{4ab2596912d228c66afb650f90fc5f9d}
      \strng{authornamehash}{380c8aa31cab738c8c74b768ccb153dd}
      \strng{authorfullhash}{4ab2596912d228c66afb650f90fc5f9d}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{shorttitle}
      \field{abstract}{Discrete multi-load truss sizing optimization (MTSO) problems are challenging to solve due to their combinatorial, nonlinear, and non-convex nature. This study highlights two important characteristics of the feasible set of MTSO problems considered here, in which force balance equations, Hooke’s law, yield stress, bound constraints on displacements, and local bucking are taken into account. Namely, we use the linear or bilinear nature of the problem to take advantage of re-scaling properties of both the problem’s design and auxiliary variables, as well as to extend the superposition principle to the case in which nonlinear stress constraints are considered. Taking advantage of these characteristics, we extend the neighborhood search mixed-integer linear optimization (NS-MILO) method (Shahabsafa et al. in SMO 63: 21–38, 2018), which provides an effective heuristic solution approach based on exact solution methods for MILO problems. Through extensive computational experiments, we demonstrate that the extended NS-MILO method provides highquality solutions for large-scale discrete MTSO problems in a reasonable time.}
      \field{issn}{1389-4420, 1573-2924}
      \field{journaltitle}{Optimization and Engineering}
      \field{month}{9}
      \field{shorttitle}{Discrete multi-load truss sizing optimization}
      \field{title}{Discrete multi-load truss sizing optimization: model analysis and computational experiments}
      \field{urlday}{23}
      \field{urlmonth}{6}
      \field{urlyear}{2022}
      \field{year}{2021}
      \field{urldateera}{ce}
      \verb{doi}
      \verb 10.1007/s11081-021-09672-6
      \endverb
    \endentry
    \entry{ashby_materials_1999}{book}{}
      \name{author}{1}{}{%
        {{hash=4efbe37e741cfa6637ad06d22dcb5217}{%
           family={Ashby},
           familyi={A\bibinitperiod},
           given={M.\bibnamedelimi F.},
           giveni={M\bibinitperiod\bibinitdelim F\bibinitperiod}}}%
      }
      \list{location}{1}{%
        {Oxford, OX ; Boston, MA}%
      }
      \list{publisher}{1}{%
        {Butterworth-Heinemann}%
      }
      \strng{namehash}{4efbe37e741cfa6637ad06d22dcb5217}
      \strng{fullhash}{4efbe37e741cfa6637ad06d22dcb5217}
      \strng{bibnamehash}{4efbe37e741cfa6637ad06d22dcb5217}
      \strng{authorbibnamehash}{4efbe37e741cfa6637ad06d22dcb5217}
      \strng{authornamehash}{4efbe37e741cfa6637ad06d22dcb5217}
      \strng{authorfullhash}{4efbe37e741cfa6637ad06d22dcb5217}
      \field{extraname}{2}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{edition}{2nd ed}
      \field{isbn}{978-0-7506-4357-3}
      \field{title}{Materials selection in mechanical design}
      \field{year}{1999}
      \keyw{Engineering design,Materials}
    \endentry
    \entry{watts_geometric_2017}{article}{}
      \name{author}{2}{}{%
        {{hash=71baf31625fa1536b2c32e1e2c07e97d}{%
           family={Watts},
           familyi={W\bibinitperiod},
           given={Seth},
           giveni={S\bibinitperiod}}}%
        {{hash=2dc94736fafc9292d9d5fe6bbacf2606}{%
           family={Tortorelli},
           familyi={T\bibinitperiod},
           given={Daniel\bibnamedelima A.},
           giveni={D\bibinitperiod\bibinitdelim A\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{b6a8bd4306522c6ca5bfc36bfc616306}
      \strng{fullhash}{b6a8bd4306522c6ca5bfc36bfc616306}
      \strng{bibnamehash}{b6a8bd4306522c6ca5bfc36bfc616306}
      \strng{authorbibnamehash}{b6a8bd4306522c6ca5bfc36bfc616306}
      \strng{authornamehash}{b6a8bd4306522c6ca5bfc36bfc616306}
      \strng{authorfullhash}{b6a8bd4306522c6ca5bfc36bfc616306}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Topology optimization is a methodology for assigning material or void to each point in a design domain in a way that extremizes some objective function, such as the compliance of a structure under given loads, subject to various imposed constraints, such as an upper bound on the mass of the structure. Geometry projection is a means to parameterize the topology optimization problem, by describing the design in a way that is independent of the mesh used for analysis of the design's performance; it results in many fewer design parameters, necessarily resolves the ill-posed nature of the topology optimization problem, and provides sharp descriptions of the material interfaces. We extend previous geometric projection work to 3 dimensions and design unit cells for lattice materials using inverse homogenization. We perform a sensitivity analysis of the geometric projection and show it has smooth derivatives, making it suitable for use with gradient-based optimization algorithms. The technique is demonstrated by designing unit cells comprised of a single constituent material plus void space to obtain light, stiff materials with cubic and isotropic material symmetry. We also design a single-constituent isotropic material with negative Poisson's ratio and a light, stiff material comprised of 2 constituent solids plus void space.}
      \field{issn}{1097-0207}
      \field{journaltitle}{International Journal for Numerical Methods in Engineering}
      \field{note}{\_eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.5569}
      \field{number}{11}
      \field{title}{A geometric projection method for designing three-dimensional open lattices with inverse homogenization}
      \field{urlday}{19}
      \field{urlmonth}{1}
      \field{urlyear}{2021}
      \field{volume}{112}
      \field{year}{2017}
      \field{urldateera}{ce}
      \field{pages}{1564\bibrangedash 1588}
      \range{pages}{25}
      \verb{doi}
      \verb https://doi.org/10.1002/nme.5569
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\5Q4LQ6RJ\\Watts and Tortorelli - 2017 - A geometric projection method for designing three-.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.5569
      \endverb
      \verb{url}
      \verb https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.5569
      \endverb
      \keyw{elasticity,finite element methods,topology design}
    \endentry
    \entry{kondoh_influence_1985}{article}{}
      \name{author}{2}{}{%
        {{hash=88d58ba25709c4eaa88a0fbf78f80bc4}{%
           family={Kondoh},
           familyi={K\bibinitperiod},
           given={K.},
           giveni={K\bibinitperiod}}}%
        {{hash=48d028fef60bd72c4da508cd230303e0}{%
           family={Atluri},
           familyi={A\bibinitperiod},
           given={S.\bibnamedelimi N.},
           giveni={S\bibinitperiod\bibinitdelim N\bibinitperiod}}}%
      }
      \strng{namehash}{c31bd804b4f35a53a62d5b9847e29bc6}
      \strng{fullhash}{c31bd804b4f35a53a62d5b9847e29bc6}
      \strng{bibnamehash}{c31bd804b4f35a53a62d5b9847e29bc6}
      \strng{authorbibnamehash}{c31bd804b4f35a53a62d5b9847e29bc6}
      \strng{authornamehash}{c31bd804b4f35a53a62d5b9847e29bc6}
      \strng{authorfullhash}{c31bd804b4f35a53a62d5b9847e29bc6}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{shorttitle}
      \field{abstract}{In this paper, the influences of local (individual member) buckling and minor variations in member properties on the global response of truss-type structures are studied. A simple and effective way of forming the tangent stiffness matrix of the structure and a modified arc length method are devised to trace the nonlinear response of the structure beyond limit points, etc. Several examples are presented to indicate: (i) the broad range of validity of the simple procedure for evaluating the tangent stiffness, (ii) the effect of buckling of individual members on global instability and post-buckling response and (iii) the interactive effects of member buckling and global imperfections.}
      \field{issn}{0045-7949}
      \field{journaltitle}{Computers \&amp; Structures}
      \field{month}{1}
      \field{number}{4}
      \field{shorttitle}{Influence of local buckling on global instability}
      \field{title}{Influence of local buckling on global instability: {Simplified}, large deformation, post-buckling analyses of plane trusses}
      \field{urlday}{8}
      \field{urlmonth}{2}
      \field{urlyear}{2024}
      \field{volume}{21}
      \field{year}{1985}
      \field{urldateera}{ce}
      \field{pages}{613\bibrangedash 627}
      \range{pages}{15}
      \verb{doi}
      \verb 10.1016/0045-7949(85)90140-3
      \endverb
      \verb{urlraw}
      \verb https://www.sciencedirect.com/science/article/pii/0045794985901403
      \endverb
      \verb{url}
      \verb https://www.sciencedirect.com/science/article/pii/0045794985901403
      \endverb
    \endentry
    \entry{tugilimana_including_2018}{article}{}
      \name{author}{3}{}{%
        {{hash=1aa69159af81958758aafc93b4a2a4d0}{%
           family={Tugilimana},
           familyi={T\bibinitperiod},
           given={Alexis},
           giveni={A\bibinitperiod}}}%
        {{hash=1462acafce6f777c7120022f3f81fcff}{%
           family={Filomeno\bibnamedelima Coelho},
           familyi={F\bibinitperiod\bibinitdelim C\bibinitperiod},
           given={Rajan},
           giveni={R\bibinitperiod}}}%
        {{hash=48da781e19224718578086f3f02cafad}{%
           family={Thrall},
           familyi={T\bibinitperiod},
           given={Ashley\bibnamedelima P.},
           giveni={A\bibinitperiod\bibinitdelim P\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{702d466b8b5a0b7cc2a70f3f5b990cb0}
      \strng{fullhash}{702d466b8b5a0b7cc2a70f3f5b990cb0}
      \strng{bibnamehash}{702d466b8b5a0b7cc2a70f3f5b990cb0}
      \strng{authorbibnamehash}{702d466b8b5a0b7cc2a70f3f5b990cb0}
      \strng{authornamehash}{702d466b8b5a0b7cc2a70f3f5b990cb0}
      \strng{authorfullhash}{702d466b8b5a0b7cc2a70f3f5b990cb0}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Including stability in truss topology optimization is critical to avoid unstable optimized designs in practical applications. While prior research addresses this challenge by implementing local buckling and linear prebuckling, numerical difficulties remain due to the global stability singularity phenomenon. Therefore, the goal of this paper is to develop an optimization formulation for truss topology optimization including global stability without numerical singularities, within the framework of the preliminary design of large-scale structures. This task is performed by considering an appropriate simultaneous analysis and design formulation, in which the use of a disaggregated form for the equilibrium equations alleviates the singularities inherent to global stability. By implementing a local buckling criterion for hollow truss elements, the resulting formulation is well-suited for the preliminary design of large-scale trusses in civil engineering applications. Three applications illustrate the efficiency of the proposed approach, including a benchmark truss structure and the preliminary design of a footbridge and a dome. The results demonstrate that including local buckling and global stability can considerably affect the optimized design, while offering a systematic means of avoiding unstable solutions. It is also shown that the proposed approach is in a good agreement with linear prebuckling assumptions.}
      \field{issn}{1615-1488}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{3}
      \field{number}{3}
      \field{title}{Including global stability in truss layout optimization for the conceptual design of large-scale applications}
      \field{urlday}{29}
      \field{urlmonth}{10}
      \field{urlyear}{2021}
      \field{volume}{57}
      \field{year}{2018}
      \field{urldateera}{ce}
      \field{pages}{1213\bibrangedash 1232}
      \range{pages}{20}
      \verb{doi}
      \verb 10.1007/s00158-017-1805-2
      \endverb
      \verb{file}
      \verb Springer Full Text PDF:D\:\\estragio\\Zotero\\storage\\4ZNYDC3A\\Tugilimana et al. - 2018 - Including global stability in truss layout optimiz.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/s00158-017-1805-2
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/s00158-017-1805-2
      \endverb
    \endentry
    \entry{duriez_properties_2022}{misc}{}
      \name{author}{4}{}{%
        {{hash=25797b3c896ef58bac4c5bf67740e61c}{%
           family={Duriez},
           familyi={D\bibinitperiod},
           given={Edouard},
           giveni={E\bibinitperiod}}}%
        {{hash=6562ac1f8239c50df0e604c9792fe4ef}{%
           family={Charlotte},
           familyi={C\bibinitperiod},
           given={Miguel},
           giveni={M\bibinitperiod}}}%
        {{hash=fed27bf5e0b1cedfe4dd9ff739ed0559}{%
           family={Azzaro-Pantel},
           familyi={A\bibinithyphendelim P\bibinitperiod},
           given={Catherine},
           giveni={C\bibinitperiod}}}%
        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
      }
      \list{publisher}{1}{%
        {arXiv}%
      }
      \strng{namehash}{58d2970fb8b7ccaeadabd03d1af1b724}
      \strng{fullhash}{bdf39542f7ee0b8cdbfbcacd789b5862}
      \strng{bibnamehash}{bdf39542f7ee0b8cdbfbcacd789b5862}
      \strng{authorbibnamehash}{bdf39542f7ee0b8cdbfbcacd789b5862}
      \strng{authornamehash}{58d2970fb8b7ccaeadabd03d1af1b724}
      \strng{authorfullhash}{bdf39542f7ee0b8cdbfbcacd789b5862}
      \field{extraname}{2}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Selecting the optimal material for a part designed through topology optimization is a complex problem. The shape and properties of the Pareto front plays an important role in this selection. In this paper we show that the compliance-volume fraction Pareto fronts of some topology optimization problems in linear elasticity share some useful properties. These properties provide an interesting point of view on the efficiency of topology optimization compared to other design approaches such as parametric structural optimization. We construct a simple meta-model which requires only one full topology optimization to fit the whole Pareto fronts. Precise Pareto fronts are obtained independently. The fast meta-model constructed has a maximum error of 6.4\% with respect to these precise Pareto fronts, on the different problems tested. The selection of the optimal material is then successfully tested on the mass minimization of an MBB beam with an illustrative choice of 4 materials.}
      \field{month}{11}
      \field{title}{On some properties of the compliance-volume fraction {Pareto} front in topology optimization useful for material selection}
      \field{urlday}{26}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{year}{2022}
      \field{urldateera}{ce}
      \verb{doi}
      \verb 10.48550/arXiv.2211.15358
      \endverb
      \verb{file}
      \verb arXiv Fulltext PDF:D\:\\estragio\\Zotero\\storage\\YLKFUZB9\\Duriez et al. - 2022 - On some properties of the compliance-volume fracti.pdf:application/pdf
      \endverb
      \keyw{Mathematics - Optimization and Control}
    \endentry
    \entry{coxeter_regular_1973}{book}{}
      \name{author}{1}{}{%
        {{hash=35d342023ede06d73f872619aaabc12c}{%
           family={Coxeter},
           familyi={C\bibinitperiod},
           given={Harold\bibnamedelimb Scott\bibnamedelima Macdonald},
           giveni={H\bibinitperiod\bibinitdelim S\bibinitperiod\bibinitdelim M\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \list{publisher}{1}{%
        {Courier Corporation}%
      }
      \strng{namehash}{35d342023ede06d73f872619aaabc12c}
      \strng{fullhash}{35d342023ede06d73f872619aaabc12c}
      \strng{bibnamehash}{35d342023ede06d73f872619aaabc12c}
      \strng{authorbibnamehash}{35d342023ede06d73f872619aaabc12c}
      \strng{authornamehash}{35d342023ede06d73f872619aaabc12c}
      \strng{authorfullhash}{35d342023ede06d73f872619aaabc12c}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Polytopes are geometrical figures bounded by portions of lines, planes, or hyperplanes. In plane (two dimensional) geometry, they are known as polygons and comprise such figures as triangles, squares, pentagons, etc. In solid (three dimensional) geometry they are known as polyhedra and include such figures as tetrahedra (a type of pyramid), cubes, icosahedra, and many more; the possibilities, in fact, are infinite! H. S. M. Coxeter's book is the foremost book available on regular polyhedra, incorporating not only the ancient Greek work on the subject, but also the vast amount of information that has been accumulated on them since, especially in the last hundred years. The author, professor of Mathematics, University of Toronto, has contributed much valuable work himself on polytopes and is a well-known authority on them. Professor Coxeter begins with the fundamental concepts of plane and solid geometry and then moves on to multi-dimensionality. Among the many subjects covered are Euler's formula, rotation groups, star-polyhedra, truncation, forms, vectors, coordinates, kaleidoscopes, Petrie polygons, sections and projections, and star-polytopes. Each chapter ends with a historical summary showing when and how the information contained therein was discovered. Numerous figures and examples and the author's lucid explanations also help to make the text readily comprehensible. Although the study of polytopes does have some practical applications to mineralogy, architecture, linear programming, and other areas, most people enjoy contemplating these figures simply because their symmetrical shapes have an aesthetic appeal. But whatever the reasons, anyone with an elementary knowledge of geometry and trigonometry will find this one of the best source books available on this fascinating study.}
      \field{isbn}{978-0-486-61480-9}
      \field{month}{1}
      \field{note}{Google-Books-ID: iWvXsVInpgMC}
      \field{title}{Regular {Polytopes}}
      \field{year}{1973}
      \keyw{Mathematics / Algebra / General,Mathematics / Geometry / General}
    \endentry
    \entry{loeb_space-filling_1991}{incollection}{}
      \name{author}{1}{}{%
        {{hash=6873fa6466849354f7f8d0178c0caa96}{%
           family={Loeb},
           familyi={L\bibinitperiod},
           given={Arthur\bibnamedelima L.},
           giveni={A\bibinitperiod\bibinitdelim L\bibinitperiod}}}%
      }
      \name{editor}{1}{}{%
        {{hash=6873fa6466849354f7f8d0178c0caa96}{%
           family={Loeb},
           familyi={L\bibinitperiod},
           given={Arthur\bibnamedelima L.},
           giveni={A\bibinitperiod\bibinitdelim L\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \list{location}{1}{%
        {Boston, MA}%
      }
      \list{publisher}{1}{%
        {Birkhäuser}%
      }
      \strng{namehash}{6873fa6466849354f7f8d0178c0caa96}
      \strng{fullhash}{6873fa6466849354f7f8d0178c0caa96}
      \strng{bibnamehash}{6873fa6466849354f7f8d0178c0caa96}
      \strng{authorbibnamehash}{6873fa6466849354f7f8d0178c0caa96}
      \strng{authornamehash}{6873fa6466849354f7f8d0178c0caa96}
      \strng{authorfullhash}{6873fa6466849354f7f8d0178c0caa96}
      \strng{editorbibnamehash}{6873fa6466849354f7f8d0178c0caa96}
      \strng{editornamehash}{6873fa6466849354f7f8d0178c0caa96}
      \strng{editorfullhash}{6873fa6466849354f7f8d0178c0caa96}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{In the previous chapter we defined a space filler as a cell whose replicas together can fill all of space without having any voids between them. We saw that all Dirichlet Domains are space fillers, but that not all space fillers are necessarily Dirichlet Domains.}
      \field{booktitle}{Space {Structures}}
      \field{isbn}{978-1-4612-0437-4}
      \field{series}{Design {Science} {Collection}}
      \field{title}{Space-filling {Polyhedra}}
      \field{urlday}{22}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{year}{1991}
      \field{urldateera}{ce}
      \field{pages}{127\bibrangedash 132}
      \range{pages}{6}
      \verb{doi}
      \verb 10.1007/978-1-4612-0437-4_16
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\57T8Y2VL\\Loeb - 1991 - Space-filling Polyhedra.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://doi.org/10.1007/978-1-4612-0437-4_16
      \endverb
      \verb{url}
      \verb https://doi.org/10.1007/978-1-4612-0437-4_16
      \endverb
      \keyw{Coordination Polyhedron,Lattice Complex,Short Vector,Space Filler,Space Structure}
    \endentry
    \entry{duriez_ecodesign_2022}{article}{}
      \name{author}{4}{}{%
        {{hash=25797b3c896ef58bac4c5bf67740e61c}{%
           family={Duriez},
           familyi={D\bibinitperiod},
           given={Edouard},
           giveni={E\bibinitperiod}}}%
        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
        {{hash=fed27bf5e0b1cedfe4dd9ff739ed0559}{%
           family={Azzaro-Pantel},
           familyi={A\bibinithyphendelim P\bibinitperiod},
           given={Catherine},
           giveni={C\bibinitperiod}}}%
        {{hash=6562ac1f8239c50df0e604c9792fe4ef}{%
           family={Charlotte},
           familyi={C\bibinitperiod},
           given={Miguel},
           giveni={M\bibinitperiod}}}%
      }
      \strng{namehash}{58d2970fb8b7ccaeadabd03d1af1b724}
      \strng{fullhash}{64e2ce6c0426584276f256227542124d}
      \strng{bibnamehash}{64e2ce6c0426584276f256227542124d}
      \strng{authorbibnamehash}{64e2ce6c0426584276f256227542124d}
      \strng{authornamehash}{58d2970fb8b7ccaeadabd03d1af1b724}
      \strng{authorfullhash}{64e2ce6c0426584276f256227542124d}
      \field{extraname}{3}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{In order to mitigate the impact of the transportation sector on climate change, light and ecological parts must be designed. A lifecycle oriented design methodology with C02 footprint minimization of parts used in various transports is presented in this work. Only material production and use phase are considered in this work, to have a better understanding of the different contributions. Simultaneous topological design and material choice are investigated for 2D examples. The results show that considering out-of-plane thickness as a variable, both problems can now be decoupled for simple load cases. It is shown that a very simple material index depending only on the type of transport can be used. An optimal volume fraction is obtained, specific only to each topology problem, but unrelated to the material chosen or the loads applied. The method is promising for fast ecodesign and its simple implementation enables easy future improvements.}
      \field{issn}{2212-8271}
      \field{journaltitle}{Procedia CIRP}
      \field{month}{1}
      \field{series}{32nd {CIRP} {Design} {Conference} ({CIRP} {Design} 2022) - {Design} in a changing world}
      \field{title}{Ecodesign with topology optimization}
      \field{urlday}{26}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{109}
      \field{year}{2022}
      \field{urldateera}{ce}
      \field{pages}{454\bibrangedash 459}
      \range{pages}{6}
      \verb{doi}
      \verb 10.1016/j.procir.2022.05.278
      \endverb
      \verb{file}
      \verb Full Text:D\:\\estragio\\Zotero\\storage\\T9QG7KIX\\Duriez et al. - 2022 - Ecodesign with topology optimization.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://www.sciencedirect.com/science/article/pii/S2212827122007272
      \endverb
      \verb{url}
      \verb https://www.sciencedirect.com/science/article/pii/S2212827122007272
      \endverb
      \keyw{Ashby index,Ecodesign,material choice,optimal volume fraction,topology optimization}
    \endentry
    \entry{duriez_co_2_2023}{article}{}
      \name{author}{3}{}{%
        {{hash=25797b3c896ef58bac4c5bf67740e61c}{%
           family={Duriez},
           familyi={D\bibinitperiod},
           given={Edouard},
           giveni={E\bibinitperiod}}}%
        {{hash=50b7cfca889df411d747b078ea7e7db7}{%
           family={Guadaño\bibnamedelima Martín},
           familyi={G\bibinitperiod\bibinitdelim M\bibinitperiod},
           given={Víctor\bibnamedelima Manuel},
           giveni={V\bibinitperiod\bibinitdelim M\bibinitperiod}}}%
        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{485988e421ed1fe21e7bfe74564b8fed}
      \strng{fullhash}{485988e421ed1fe21e7bfe74564b8fed}
      \strng{bibnamehash}{485988e421ed1fe21e7bfe74564b8fed}
      \strng{authorbibnamehash}{485988e421ed1fe21e7bfe74564b8fed}
      \strng{authornamehash}{485988e421ed1fe21e7bfe74564b8fed}
      \strng{authorfullhash}{485988e421ed1fe21e7bfe74564b8fed}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Multidisciplinary Design Optimization (MDO) enables one to reach a better solution than by optimizing each discipline independently. In particular, the optimal structure of a drone varies depending on the selected material. The \$\$CO\_2\$\$footprint of a solar-powered High Altitude Long Endurance (HALE) drone is optimized here, where the structural materials used is one of the design variables. Optimization is performed using a modified version of OpenAeroStruct, a framework based on OpenMDAO. Our EcoHale framework is validated on a classical HALE testcase in the MDO community (FBhale) constructed using high-fidelity codes compared to our low-fidelity approach. The originality of our work is to include two specific disciplines (energy and environment) to adapt to a new problem of \$\$CO\_2\$\$minimization. The choice of eco-materials is performed in the global MDO loop from a choice of discrete materials . This is achieved through a variable relaxation, enabling the use of continuous optimization algorithms inspired from multimaterial topology optimization. Our results show that, in our specific case of electric drone, the optimal material in terms of \$\$CO\_2\$\$footprint is also the optimal material in terms of weight. It opens the door to new researches on digital microarchitectured materials that will decrease the \$\$CO\_2\$\$footprint of the drone.}
      \field{issn}{2045-2322}
      \field{journaltitle}{Scientific Reports}
      \field{month}{7}
      \field{number}{1}
      \field{title}{CO$_2$ footprint minimization of solar-powered {HALE} using {MDO} and eco-material selection}
      \field{urlday}{26}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{13}
      \field{year}{2023}
      \field{urldateera}{ce}
      \field{pages}{11994}
      \range{pages}{1}
      \verb{doi}
      \verb 10.1038/s41598-023-39221-3
      \endverb
      \verb{file}
      \verb Full Text PDF:D\:\\estragio\\Zotero\\storage\\ATH8DQKT\\Duriez et al. - 2023 - \$\$CO_2\$\$ footprint minimization of solar-powered H.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://www.nature.com/articles/s41598-023-39221-3
      \endverb
      \verb{url}
      \verb https://www.nature.com/articles/s41598-023-39221-3
      \endverb
      \keyw{Aerospace engineering,Mechanical engineering}
    \endentry
    \entry{duriez_fast_2023}{article}{}
      \name{author}{4}{}{%
        {{hash=25797b3c896ef58bac4c5bf67740e61c}{%
           family={Duriez},
           familyi={D\bibinitperiod},
           given={Edouard},
           giveni={E\bibinitperiod}}}%
        {{hash=fed27bf5e0b1cedfe4dd9ff739ed0559}{%
           family={Azzaro-Pantel},
           familyi={A\bibinithyphendelim P\bibinitperiod},
           given={Catherine},
           giveni={C\bibinitperiod}}}%
        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
        {{hash=6562ac1f8239c50df0e604c9792fe4ef}{%
           family={Charlotte},
           familyi={C\bibinitperiod},
           given={Miguel},
           giveni={M\bibinitperiod}}}%
      }
      \strng{namehash}{58d2970fb8b7ccaeadabd03d1af1b724}
      \strng{fullhash}{9f550caf27069c0430f106140e161b47}
      \strng{bibnamehash}{9f550caf27069c0430f106140e161b47}
      \strng{authorbibnamehash}{9f550caf27069c0430f106140e161b47}
      \strng{authornamehash}{58d2970fb8b7ccaeadabd03d1af1b724}
      \strng{authorfullhash}{9f550caf27069c0430f106140e161b47}
      \field{extraname}{4}
      \field{sortinit}{1}
      \field{sortinithash}{4f6aaa89bab872aa0999fec09ff8e98a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{We propose an innovative approach to minimize the greenhouse gas impacts of additive manufactured structures over their entire life cycle. The novelty of our method lies in its simultaneous optimization of material selection, process selection, and design optimization. To fully leverage the potential benefits of additive manufacturing, we use topology optimization and compile a comprehensive database of printed materials and printing processes, which we share with the wider community. To account for the complex interdependence between materials and processes, our method employs a pairing system, which we efficiently reduce using topology optimization properties and a generalized form of Ashby indices. To enhance computational efficiency, we employ a meta-model. We validate our proposed method through successful testing on an aeronautical case and a pedestrian bridge, demonstrating its robustness even in the presence of environmental data uncertainty. The optimal material-process pair for the aeronautical structure is the cobalt-based super-alloy with the LENS process. Despite this pair having the highest material and processing emissions, the resulting lighter part lowers the use phase emissions. It appears that precise mechanical data is needed for the method to give accurate results: a 20\% drop of Young's modulus totally disrupts the material-process pair ranking.}
      \field{issn}{2666-7894}
      \field{journaltitle}{Cleaner Environmental Systems}
      \field{month}{6}
      \field{title}{A fast method of material, design and process eco-selection via topology optimization, for additive manufactured structures}
      \field{urlday}{26}
      \field{urlmonth}{1}
      \field{urlyear}{2024}
      \field{volume}{9}
      \field{year}{2023}
      \field{urldateera}{ce}
      \field{pages}{100114}
      \range{pages}{1}
      \verb{doi}
      \verb 10.1016/j.cesys.2023.100114
      \endverb
      \verb{urlraw}
      \verb https://www.sciencedirect.com/science/article/pii/S2666789423000089
      \endverb
      \verb{url}
      \verb https://www.sciencedirect.com/science/article/pii/S2666789423000089
      \endverb
      \keyw{Additive manufacturing,Ashby index,Ecodesign,Life cycle,Material selection,Process selection,Topology optimization}
    \endentry
  \enddatalist
\endrefsection

\refsection{1}
  \datalist[entry]{ynt/global/7FC56270E7A70FA81A5935B72EACBE29/global/global}
    \entry{stragiotti_towards_2021}{inproceedings}{}
      \name{author}{4}{}{%
        {{hash=6c4965d3ad73fb11f44136afa897bb91}{%
           family={Stragiotti},
           familyi={S\bibinitperiod},
           given={Enrico},
           giveni={E\bibinitperiod}}}%
        {{hash=6ffe413a21f4954b0aac85ca037c7876}{%
           family={Irisarri},
           familyi={I\bibinitperiod},
           given={François-Xavier},
           giveni={F\bibinithyphendelim X\bibinitperiod}}}%
        {{hash=d9c42bf5ce7591763a45d8334a00d4e1}{%
           family={Julien},
           familyi={J\bibinitperiod},
           given={Cédric},
           giveni={C\bibinitperiod}}}%
        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
      }
      \list{location}{1}{%
        {Lisbon, Portugal}%
      }
      \list{publisher}{1}{%
        {ECCOMAS}%
      }
      \strng{namehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{fullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{bibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authorbibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authornamehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{authorfullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \field{extraname}{1}
      \field{sortinit}{2}
      \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a}
      \field{labelprefix}{A}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{shorttitle}
      \field{booktitle}{{AeroBest} 2021 {International} {Conference} on {Multidisciplinary} {Design} {Optimization} of {Aerospace} {Systems}. {Book} of proceedings}
      \field{month}{7}
      \field{shorttitle}{Towards manufactured lattice structures}
      \field{title}{Towards manufactured lattice structures: a comparison between layout and topology optimization}
      \field{urlday}{22}
      \field{urlmonth}{10}
      \field{urlyear}{2021}
      \field{year}{2021}
      \field{urldateera}{ce}
      \true{nocite}
      \field{pages}{229\bibrangedash 244}
      \range{pages}{16}
      \verb{file}
      \verb HAL PDF Full Text:D\:\\estragio\\Zotero\\storage\\LTHX869B\\Stragiotti et al. - 2021 - Towards manufactured lattice structures a compari.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://hal.archives-ouvertes.fr/hal-03384893
      \endverb
      \verb{url}
      \verb https://hal.archives-ouvertes.fr/hal-03384893
      \endverb
      \keyw{Structural Optimization,Lattice Structures,Layout Optimization,Optimisation avec contraintes de stress,Optimisation des structures,Optimisation du Layout,Optimisation Topologique,Stress-Constrained Optimization,Structures Lattice,Topology Optimization,conf}
    \endentry
    \entry{stragiotti_enhanced_2022}{inproceedings}{}
      \name{author}{4}{}{%
        {{hash=6c4965d3ad73fb11f44136afa897bb91}{%
           family={Stragiotti},
           familyi={S\bibinitperiod},
           given={Enrico},
           giveni={E\bibinitperiod}}}%
        {{hash=6ffe413a21f4954b0aac85ca037c7876}{%
           family={Irisarri},
           familyi={I\bibinitperiod},
           given={François-Xavier},
           giveni={F\bibinithyphendelim X\bibinitperiod}}}%
        {{hash=d9c42bf5ce7591763a45d8334a00d4e1}{%
           family={Julien},
           familyi={J\bibinitperiod},
           given={Cédric},
           giveni={C\bibinitperiod}}}%
        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
      }
      \list{location}{1}{%
        {Leeds, United Kingdom}%
      }
      \strng{namehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{fullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{bibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authorbibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authornamehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{authorfullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \field{extraname}{2}
      \field{sortinit}{2}
      \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a}
      \field{labelprefix}{A}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Cellular architectured structures' most appealing characteristic is that they are able to create large structures assembling small repetitive components. Thanks to their modular nature, they bring interesting features among which reduced tooling, fast assembly, and short repair time. In the first part of the article, we formulate an optimizing method that minimizes the mass of a cellular architectured structure taking into account internal stresses, local buckling, and pattern repetition constraints. The proposed solving algorithm mitigates the appearance of local minima, a critical problem for discrete trusses. In the second part, the optimization method is applied to a real-size aeronautic application: the minimization of the mass of a cellular 3D wing box subject to lift and torsion loads. Compared to classic cell topologies, the proposed method found a cell 10-times lighter, at the cost of increased manufacturing difficulty.}
      \field{booktitle}{{ASMO}-{UK} 12 / {ASMO}-{Europe} 1 / {ISSMO} {Conference} on {Engineering} {Design} {Optimization} (2022)}
      \field{month}{7}
      \field{title}{Enhanced truss topology optimization ({TTO}) applied to a cellular wing box}
      \field{urlday}{14}
      \field{urlmonth}{11}
      \field{urlyear}{2023}
      \field{year}{2022}
      \field{urldateera}{ce}
      \true{nocite}
      \verb{file}
      \verb HAL PDF Full Text:D\:\\estragio\\Zotero\\storage\\ZY7S5YZA\\Stragiotti et al. - 2022 - Enhanced truss topology optimization (TTO) applied.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://hal.science/hal-04283287
      \endverb
      \verb{url}
      \verb https://hal.science/hal-04283287
      \endverb
      \keyw{Optimisation,Optimisation Topologique,Structure Lattice,conf}
    \endentry
    \entry{stragiotti_optimisation_2022}{inproceedings}{}
      \name{author}{4}{}{%
        {{hash=6c4965d3ad73fb11f44136afa897bb91}{%
           family={Stragiotti},
           familyi={S\bibinitperiod},
           given={Enrico},
           giveni={E\bibinitperiod}}}%
        {{hash=6ffe413a21f4954b0aac85ca037c7876}{%
           family={Irisarri},
           familyi={I\bibinitperiod},
           given={François-Xavier},
           giveni={F\bibinithyphendelim X\bibinitperiod}}}%
        {{hash=d9c42bf5ce7591763a45d8334a00d4e1}{%
           family={Julien},
           familyi={J\bibinitperiod},
           given={Cédric},
           giveni={C\bibinitperiod}}}%
        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
      }
      \list{location}{1}{%
        {Presqu'ile de Giens, France}%
      }
      \strng{namehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{fullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{bibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authorbibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authornamehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{authorfullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \field{extraname}{3}
      \field{sortinit}{2}
      \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a}
      \field{labelprefix}{A}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{shorttitle}
      \field{abstract}{Nous discutons et comparons deux méthodes d'optimisation structurale pertinentes pour les structures lattices : l'optimisation topologique et le layout optimization. Nous présentons une application originale de ces deux méthodes dans le cadre de la minimisation de la masse structures lattices cellules masse en tenant compte d'un critère de rupture en contrainte. Nous proposons ensuite une comparaison qualitative de ces deux méthodes et discutions de leur pertinence respective pour l'optimisation des structures lattices.}
      \field{booktitle}{{CSMA} 2022 15ème {Colloque} {National} en {Calcul} des {Structures}}
      \field{month}{5}
      \field{shorttitle}{Optimisation des structures lattices}
      \field{title}{Optimisation des structures lattices : une comparaison entre le layout optimization et l'optimisation topologique}
      \field{urlday}{24}
      \field{urlmonth}{11}
      \field{urlyear}{2022}
      \field{year}{2022}
      \field{urldateera}{ce}
      \true{nocite}
      \verb{file}
      \verb HAL PDF Full Text:D\:\\estragio\\Zotero\\storage\\YPT33TVR\\Stragiotti et al. - 2022 - Optimisation des structures lattices une compara.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://hal.archives-ouvertes.fr/hal-03687214
      \endverb
      \verb{url}
      \verb https://hal.archives-ouvertes.fr/hal-03687214
      \endverb
      \keyw{Layout optimisation,Optimisation topologique,Structures lattices,conf}
    \endentry
    \entry{stragiotti_truss_2023}{misc}{}
      \name{author}{4}{}{%
        {{hash=6c4965d3ad73fb11f44136afa897bb91}{%
           family={Stragiotti},
           familyi={S\bibinitperiod},
           given={Enrico},
           giveni={E\bibinitperiod}}}%
        {{hash=6ffe413a21f4954b0aac85ca037c7876}{%
           family={Irisarri},
           familyi={I\bibinitperiod},
           given={François-Xavier},
           giveni={F\bibinithyphendelim X\bibinitperiod}}}%
        {{hash=d9c42bf5ce7591763a45d8334a00d4e1}{%
           family={Julien},
           familyi={J\bibinitperiod},
           given={Cédric},
           giveni={C\bibinitperiod}}}%
        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
      }
      \list{publisher}{1}{%
        {Mendeley}%
      }
      \strng{namehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{fullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{bibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authorbibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authornamehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{authorfullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \field{extraname}{4}
      \field{sortinit}{2}
      \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a}
      \field{labelprefix}{A}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{month}{5}
      \field{title}{Truss {Topology} {Optimization} with {Topological} {Buckling} {Constraints} {Data} {Set}}
      \field{urlday}{3}
      \field{urlmonth}{5}
      \field{urlyear}{2023}
      \field{year}{2023}
      \field{urldateera}{ce}
      \true{nocite}
      \verb{doi}
      \verb 10.17632/BW7XB2W6ST.1
      \endverb
      \keyw{Structural Optimization,Lattice Structures,Layout Optimization,Optimisation avec contraintes de stress,Optimisation des structures,Optimisation du Layout,Optimisation Topologique,Stress-Constrained Optimization,Structures Lattice,Topology Optimization,misc}
    \endentry
    \entry{stragiotti_efficient_2024}{article}{}
      \name{author}{4}{}{%
        {{hash=6c4965d3ad73fb11f44136afa897bb91}{%
           family={Stragiotti},
           familyi={S\bibinitperiod},
           given={Enrico},
           giveni={E\bibinitperiod}}}%
        {{hash=6ffe413a21f4954b0aac85ca037c7876}{%
           family={Irisarri},
           familyi={I\bibinitperiod},
           given={François-Xavier},
           giveni={F\bibinithyphendelim X\bibinitperiod}}}%
        {{hash=d9c42bf5ce7591763a45d8334a00d4e1}{%
           family={Julien},
           familyi={J\bibinitperiod},
           given={Cédric},
           giveni={C\bibinitperiod}}}%
        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{fullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{bibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authorbibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authornamehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{authorfullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \field{extraname}{5}
      \field{sortinit}{2}
      \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a}
      \field{labelprefix}{A}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{1}
      \field{title}{Efficient 3D truss topology optimization for aeronautical structures (in press)}
      \field{year}{2024}
      \true{nocite}
      \verb{doi}
      \verb 10.1007/s00158-024-03739-5
      \endverb
      \keyw{art}
    \endentry
  \enddatalist
  \datalist[entry]{none/global//global/global}
    \entry{stragiotti_enhanced_2022}{inproceedings}{}
      \name{author}{4}{}{%
        {{hash=6c4965d3ad73fb11f44136afa897bb91}{%
           family={Stragiotti},
           familyi={S\bibinitperiod},
           given={Enrico},
           giveni={E\bibinitperiod}}}%
        {{hash=6ffe413a21f4954b0aac85ca037c7876}{%
           family={Irisarri},
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           given={François-Xavier},
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      \field{abstract}{Cellular architectured structures' most appealing characteristic is that they are able to create large structures assembling small repetitive components. Thanks to their modular nature, they bring interesting features among which reduced tooling, fast assembly, and short repair time. In the first part of the article, we formulate an optimizing method that minimizes the mass of a cellular architectured structure taking into account internal stresses, local buckling, and pattern repetition constraints. The proposed solving algorithm mitigates the appearance of local minima, a critical problem for discrete trusses. In the second part, the optimization method is applied to a real-size aeronautic application: the minimization of the mass of a cellular 3D wing box subject to lift and torsion loads. Compared to classic cell topologies, the proposed method found a cell 10-times lighter, at the cost of increased manufacturing difficulty.}
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      \field{abstract}{Nous discutons et comparons deux méthodes d'optimisation structurale pertinentes pour les structures lattices : l'optimisation topologique et le layout optimization. Nous présentons une application originale de ces deux méthodes dans le cadre de la minimisation de la masse structures lattices cellules masse en tenant compte d'un critère de rupture en contrainte. Nous proposons ensuite une comparaison qualitative de ces deux méthodes et discutions de leur pertinence respective pour l'optimisation des structures lattices.}
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      \field{title}{Truss {Topology} {Optimization} with {Topological} {Buckling} {Constraints} {Data} {Set}}
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\endrefsection

\refsection{2}
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        {{hash=6c4965d3ad73fb11f44136afa897bb91}{%
           family={Stragiotti},
           familyi={S\bibinitperiod},
           given={Enrico},
           giveni={E\bibinitperiod}}}%
        {{hash=6ffe413a21f4954b0aac85ca037c7876}{%
           family={Irisarri},
           familyi={I\bibinitperiod},
           given={François-Xavier},
           giveni={F\bibinithyphendelim X\bibinitperiod}}}%
        {{hash=d9c42bf5ce7591763a45d8334a00d4e1}{%
           family={Julien},
           familyi={J\bibinitperiod},
           given={Cédric},
           giveni={C\bibinitperiod}}}%
        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
      }
      \list{publisher}{1}{%
        {Mendeley}%
      }
      \strng{namehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{fullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{bibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authorbibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authornamehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{authorfullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \field{extraname}{4}
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      \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a}
      \field{labelprefix}{C}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{month}{5}
      \field{title}{Truss {Topology} {Optimization} with {Topological} {Buckling} {Constraints} {Data} {Set}}
      \field{urlday}{3}
      \field{urlmonth}{5}
      \field{urlyear}{2023}
      \field{year}{2023}
      \field{urldateera}{ce}
      \true{nocite}
      \verb{doi}
      \verb 10.17632/BW7XB2W6ST.1
      \endverb
      \keyw{Structural Optimization,Lattice Structures,Layout Optimization,Optimisation avec contraintes de stress,Optimisation des structures,Optimisation du Layout,Optimisation Topologique,Stress-Constrained Optimization,Structures Lattice,Topology Optimization,misc}
    \endentry
    \entry{stragiotti_efficient_2024}{article}{}
      \name{author}{4}{}{%
        {{hash=6c4965d3ad73fb11f44136afa897bb91}{%
           family={Stragiotti},
           familyi={S\bibinitperiod},
           given={Enrico},
           giveni={E\bibinitperiod}}}%
        {{hash=6ffe413a21f4954b0aac85ca037c7876}{%
           family={Irisarri},
           familyi={I\bibinitperiod},
           given={François-Xavier},
           giveni={F\bibinithyphendelim X\bibinitperiod}}}%
        {{hash=d9c42bf5ce7591763a45d8334a00d4e1}{%
           family={Julien},
           familyi={J\bibinitperiod},
           given={Cédric},
           giveni={C\bibinitperiod}}}%
        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{fullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{bibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authorbibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authornamehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{authorfullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
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      \field{labelprefix}{C}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{1}
      \field{title}{Efficient 3D truss topology optimization for aeronautical structures (in press)}
      \field{year}{2024}
      \true{nocite}
      \verb{doi}
      \verb 10.1007/s00158-024-03739-5
      \endverb
      \keyw{art}
    \endentry
  \enddatalist
  \datalist[entry]{none/global//global/global}
    \entry{stragiotti_enhanced_2022}{inproceedings}{}
      \name{author}{4}{}{%
        {{hash=6c4965d3ad73fb11f44136afa897bb91}{%
           family={Stragiotti},
           familyi={S\bibinitperiod},
           given={Enrico},
           giveni={E\bibinitperiod}}}%
        {{hash=6ffe413a21f4954b0aac85ca037c7876}{%
           family={Irisarri},
           familyi={I\bibinitperiod},
           given={François-Xavier},
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        {{hash=d9c42bf5ce7591763a45d8334a00d4e1}{%
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           familyi={J\bibinitperiod},
           given={Cédric},
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        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
      }
      \list{location}{1}{%
        {Leeds, United Kingdom}%
      }
      \strng{namehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{fullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{bibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authorbibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authornamehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{authorfullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
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      \field{sortinit}{2}
      \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{abstract}{Cellular architectured structures' most appealing characteristic is that they are able to create large structures assembling small repetitive components. Thanks to their modular nature, they bring interesting features among which reduced tooling, fast assembly, and short repair time. In the first part of the article, we formulate an optimizing method that minimizes the mass of a cellular architectured structure taking into account internal stresses, local buckling, and pattern repetition constraints. The proposed solving algorithm mitigates the appearance of local minima, a critical problem for discrete trusses. In the second part, the optimization method is applied to a real-size aeronautic application: the minimization of the mass of a cellular 3D wing box subject to lift and torsion loads. Compared to classic cell topologies, the proposed method found a cell 10-times lighter, at the cost of increased manufacturing difficulty.}
      \field{booktitle}{{ASMO}-{UK} 12 / {ASMO}-{Europe} 1 / {ISSMO} {Conference} on {Engineering} {Design} {Optimization} (2022)}
      \field{month}{7}
      \field{title}{Enhanced truss topology optimization ({TTO}) applied to a cellular wing box}
      \field{urlday}{14}
      \field{urlmonth}{11}
      \field{urlyear}{2023}
      \field{year}{2022}
      \field{urldateera}{ce}
      \true{nocite}
      \verb{file}
      \verb HAL PDF Full Text:D\:\\estragio\\Zotero\\storage\\ZY7S5YZA\\Stragiotti et al. - 2022 - Enhanced truss topology optimization (TTO) applied.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://hal.science/hal-04283287
      \endverb
      \verb{url}
      \verb https://hal.science/hal-04283287
      \endverb
      \keyw{Optimisation,Optimisation Topologique,Structure Lattice,conf}
    \endentry
    \entry{stragiotti_optimisation_2022}{inproceedings}{}
      \name{author}{4}{}{%
        {{hash=6c4965d3ad73fb11f44136afa897bb91}{%
           family={Stragiotti},
           familyi={S\bibinitperiod},
           given={Enrico},
           giveni={E\bibinitperiod}}}%
        {{hash=6ffe413a21f4954b0aac85ca037c7876}{%
           family={Irisarri},
           familyi={I\bibinitperiod},
           given={François-Xavier},
           giveni={F\bibinithyphendelim X\bibinitperiod}}}%
        {{hash=d9c42bf5ce7591763a45d8334a00d4e1}{%
           family={Julien},
           familyi={J\bibinitperiod},
           given={Cédric},
           giveni={C\bibinitperiod}}}%
        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
      }
      \list{location}{1}{%
        {Presqu'ile de Giens, France}%
      }
      \strng{namehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{fullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{bibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authorbibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authornamehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{authorfullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \field{extraname}{2}
      \field{sortinit}{3}
      \field{sortinithash}{ad6fe7482ffbd7b9f99c9e8b5dccd3d7}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{shorttitle}
      \field{abstract}{Nous discutons et comparons deux méthodes d'optimisation structurale pertinentes pour les structures lattices : l'optimisation topologique et le layout optimization. Nous présentons une application originale de ces deux méthodes dans le cadre de la minimisation de la masse structures lattices cellules masse en tenant compte d'un critère de rupture en contrainte. Nous proposons ensuite une comparaison qualitative de ces deux méthodes et discutions de leur pertinence respective pour l'optimisation des structures lattices.}
      \field{booktitle}{{CSMA} 2022 15ème {Colloque} {National} en {Calcul} des {Structures}}
      \field{month}{5}
      \field{shorttitle}{Optimisation des structures lattices}
      \field{title}{Optimisation des structures lattices : une comparaison entre le layout optimization et l'optimisation topologique}
      \field{urlday}{24}
      \field{urlmonth}{11}
      \field{urlyear}{2022}
      \field{year}{2022}
      \field{urldateera}{ce}
      \true{nocite}
      \verb{file}
      \verb HAL PDF Full Text:D\:\\estragio\\Zotero\\storage\\YPT33TVR\\Stragiotti et al. - 2022 - Optimisation des structures lattices une compara.pdf:application/pdf
      \endverb
      \verb{urlraw}
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      \endverb
      \verb{url}
      \verb https://hal.archives-ouvertes.fr/hal-03687214
      \endverb
      \keyw{Layout optimisation,Optimisation topologique,Structures lattices,conf}
    \endentry
    \entry{stragiotti_towards_2021}{inproceedings}{}
      \name{author}{4}{}{%
        {{hash=6c4965d3ad73fb11f44136afa897bb91}{%
           family={Stragiotti},
           familyi={S\bibinitperiod},
           given={Enrico},
           giveni={E\bibinitperiod}}}%
        {{hash=6ffe413a21f4954b0aac85ca037c7876}{%
           family={Irisarri},
           familyi={I\bibinitperiod},
           given={François-Xavier},
           giveni={F\bibinithyphendelim X\bibinitperiod}}}%
        {{hash=d9c42bf5ce7591763a45d8334a00d4e1}{%
           family={Julien},
           familyi={J\bibinitperiod},
           given={Cédric},
           giveni={C\bibinitperiod}}}%
        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
      }
      \list{location}{1}{%
        {Lisbon, Portugal}%
      }
      \list{publisher}{1}{%
        {ECCOMAS}%
      }
      \strng{namehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{fullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{bibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authorbibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authornamehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{authorfullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \field{extraname}{3}
      \field{sortinit}{4}
      \field{sortinithash}{9381316451d1b9788675a07e972a12a7}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{shorttitle}
      \field{booktitle}{{AeroBest} 2021 {International} {Conference} on {Multidisciplinary} {Design} {Optimization} of {Aerospace} {Systems}. {Book} of proceedings}
      \field{month}{7}
      \field{shorttitle}{Towards manufactured lattice structures}
      \field{title}{Towards manufactured lattice structures: a comparison between layout and topology optimization}
      \field{urlday}{22}
      \field{urlmonth}{10}
      \field{urlyear}{2021}
      \field{year}{2021}
      \field{urldateera}{ce}
      \true{nocite}
      \field{pages}{229\bibrangedash 244}
      \range{pages}{16}
      \verb{file}
      \verb HAL PDF Full Text:D\:\\estragio\\Zotero\\storage\\LTHX869B\\Stragiotti et al. - 2021 - Towards manufactured lattice structures a compari.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://hal.archives-ouvertes.fr/hal-03384893
      \endverb
      \verb{url}
      \verb https://hal.archives-ouvertes.fr/hal-03384893
      \endverb
      \keyw{Structural Optimization,Lattice Structures,Layout Optimization,Optimisation avec contraintes de stress,Optimisation des structures,Optimisation du Layout,Optimisation Topologique,Stress-Constrained Optimization,Structures Lattice,Topology Optimization,conf}
    \endentry
    \entry{stragiotti_truss_2023}{misc}{}
      \name{author}{4}{}{%
        {{hash=6c4965d3ad73fb11f44136afa897bb91}{%
           family={Stragiotti},
           familyi={S\bibinitperiod},
           given={Enrico},
           giveni={E\bibinitperiod}}}%
        {{hash=6ffe413a21f4954b0aac85ca037c7876}{%
           family={Irisarri},
           familyi={I\bibinitperiod},
           given={François-Xavier},
           giveni={F\bibinithyphendelim X\bibinitperiod}}}%
        {{hash=d9c42bf5ce7591763a45d8334a00d4e1}{%
           family={Julien},
           familyi={J\bibinitperiod},
           given={Cédric},
           giveni={C\bibinitperiod}}}%
        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
      }
      \list{publisher}{1}{%
        {Mendeley}%
      }
      \strng{namehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{fullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{bibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authorbibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authornamehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{authorfullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \field{extraname}{4}
      \field{sortinit}{5}
      \field{sortinithash}{20e9b4b0b173788c5dace24730f47d8c}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{month}{5}
      \field{title}{Truss {Topology} {Optimization} with {Topological} {Buckling} {Constraints} {Data} {Set}}
      \field{urlday}{3}
      \field{urlmonth}{5}
      \field{urlyear}{2023}
      \field{year}{2023}
      \field{urldateera}{ce}
      \true{nocite}
      \verb{doi}
      \verb 10.17632/BW7XB2W6ST.1
      \endverb
      \keyw{Structural Optimization,Lattice Structures,Layout Optimization,Optimisation avec contraintes de stress,Optimisation des structures,Optimisation du Layout,Optimisation Topologique,Stress-Constrained Optimization,Structures Lattice,Topology Optimization,misc}
    \endentry
    \entry{stragiotti_efficient_2024}{article}{}
      \name{author}{4}{}{%
        {{hash=6c4965d3ad73fb11f44136afa897bb91}{%
           family={Stragiotti},
           familyi={S\bibinitperiod},
           given={Enrico},
           giveni={E\bibinitperiod}}}%
        {{hash=6ffe413a21f4954b0aac85ca037c7876}{%
           family={Irisarri},
           familyi={I\bibinitperiod},
           given={François-Xavier},
           giveni={F\bibinithyphendelim X\bibinitperiod}}}%
        {{hash=d9c42bf5ce7591763a45d8334a00d4e1}{%
           family={Julien},
           familyi={J\bibinitperiod},
           given={Cédric},
           giveni={C\bibinitperiod}}}%
        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{fullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{bibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authorbibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authornamehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{authorfullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \field{extraname}{5}
      \field{sortinit}{6}
      \field{sortinithash}{b33bc299efb3c36abec520a4c896a66d}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{1}
      \field{title}{Efficient 3D truss topology optimization for aeronautical structures (in press)}
      \field{year}{2024}
      \true{nocite}
      \verb{doi}
      \verb 10.1007/s00158-024-03739-5
      \endverb
      \keyw{art}
    \endentry
  \enddatalist
\endrefsection

\refsection{3}
  \datalist[entry]{ynt/global/69691C7BDCC3CE6D5D8A1361F22D04AC/global/global}
    \entry{stragiotti_towards_2021}{inproceedings}{}
      \name{author}{4}{}{%
        {{hash=6c4965d3ad73fb11f44136afa897bb91}{%
           family={Stragiotti},
           familyi={S\bibinitperiod},
           given={Enrico},
           giveni={E\bibinitperiod}}}%
        {{hash=6ffe413a21f4954b0aac85ca037c7876}{%
           family={Irisarri},
           familyi={I\bibinitperiod},
           given={François-Xavier},
           giveni={F\bibinithyphendelim X\bibinitperiod}}}%
        {{hash=d9c42bf5ce7591763a45d8334a00d4e1}{%
           family={Julien},
           familyi={J\bibinitperiod},
           given={Cédric},
           giveni={C\bibinitperiod}}}%
        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
      }
      \list{location}{1}{%
        {Lisbon, Portugal}%
      }
      \list{publisher}{1}{%
        {ECCOMAS}%
      }
      \strng{namehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{fullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{bibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
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      \field{booktitle}{{AeroBest} 2021 {International} {Conference} on {Multidisciplinary} {Design} {Optimization} of {Aerospace} {Systems}. {Book} of proceedings}
      \field{month}{7}
      \field{shorttitle}{Towards manufactured lattice structures}
      \field{title}{Towards manufactured lattice structures: a comparison between layout and topology optimization}
      \field{urlday}{22}
      \field{urlmonth}{10}
      \field{urlyear}{2021}
      \field{year}{2021}
      \field{urldateera}{ce}
      \true{nocite}
      \field{pages}{229\bibrangedash 244}
      \range{pages}{16}
      \verb{file}
      \verb HAL PDF Full Text:D\:\\estragio\\Zotero\\storage\\LTHX869B\\Stragiotti et al. - 2021 - Towards manufactured lattice structures a compari.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://hal.archives-ouvertes.fr/hal-03384893
      \endverb
      \verb{url}
      \verb https://hal.archives-ouvertes.fr/hal-03384893
      \endverb
      \keyw{Structural Optimization,Lattice Structures,Layout Optimization,Optimisation avec contraintes de stress,Optimisation des structures,Optimisation du Layout,Optimisation Topologique,Stress-Constrained Optimization,Structures Lattice,Topology Optimization,conf}
    \endentry
    \entry{stragiotti_enhanced_2022}{inproceedings}{}
      \name{author}{4}{}{%
        {{hash=6c4965d3ad73fb11f44136afa897bb91}{%
           family={Stragiotti},
           familyi={S\bibinitperiod},
           given={Enrico},
           giveni={E\bibinitperiod}}}%
        {{hash=6ffe413a21f4954b0aac85ca037c7876}{%
           family={Irisarri},
           familyi={I\bibinitperiod},
           given={François-Xavier},
           giveni={F\bibinithyphendelim X\bibinitperiod}}}%
        {{hash=d9c42bf5ce7591763a45d8334a00d4e1}{%
           family={Julien},
           familyi={J\bibinitperiod},
           given={Cédric},
           giveni={C\bibinitperiod}}}%
        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
      }
      \list{location}{1}{%
        {Leeds, United Kingdom}%
      }
      \strng{namehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{fullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
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      \strng{authorbibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authornamehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{authorfullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
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      \field{abstract}{Cellular architectured structures' most appealing characteristic is that they are able to create large structures assembling small repetitive components. Thanks to their modular nature, they bring interesting features among which reduced tooling, fast assembly, and short repair time. In the first part of the article, we formulate an optimizing method that minimizes the mass of a cellular architectured structure taking into account internal stresses, local buckling, and pattern repetition constraints. The proposed solving algorithm mitigates the appearance of local minima, a critical problem for discrete trusses. In the second part, the optimization method is applied to a real-size aeronautic application: the minimization of the mass of a cellular 3D wing box subject to lift and torsion loads. Compared to classic cell topologies, the proposed method found a cell 10-times lighter, at the cost of increased manufacturing difficulty.}
      \field{booktitle}{{ASMO}-{UK} 12 / {ASMO}-{Europe} 1 / {ISSMO} {Conference} on {Engineering} {Design} {Optimization} (2022)}
      \field{month}{7}
      \field{title}{Enhanced truss topology optimization ({TTO}) applied to a cellular wing box}
      \field{urlday}{14}
      \field{urlmonth}{11}
      \field{urlyear}{2023}
      \field{year}{2022}
      \field{urldateera}{ce}
      \true{nocite}
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    \entry{stragiotti_optimisation_2022}{inproceedings}{}
      \name{author}{4}{}{%
        {{hash=6c4965d3ad73fb11f44136afa897bb91}{%
           family={Stragiotti},
           familyi={S\bibinitperiod},
           given={Enrico},
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        {{hash=6ffe413a21f4954b0aac85ca037c7876}{%
           family={Irisarri},
           familyi={I\bibinitperiod},
           given={François-Xavier},
           giveni={F\bibinithyphendelim X\bibinitperiod}}}%
        {{hash=d9c42bf5ce7591763a45d8334a00d4e1}{%
           family={Julien},
           familyi={J\bibinitperiod},
           given={Cédric},
           giveni={C\bibinitperiod}}}%
        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
      }
      \list{location}{1}{%
        {Presqu'ile de Giens, France}%
      }
      \strng{namehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{fullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{bibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authorbibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
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      \field{labeltitlesource}{shorttitle}
      \field{abstract}{Nous discutons et comparons deux méthodes d'optimisation structurale pertinentes pour les structures lattices : l'optimisation topologique et le layout optimization. Nous présentons une application originale de ces deux méthodes dans le cadre de la minimisation de la masse structures lattices cellules masse en tenant compte d'un critère de rupture en contrainte. Nous proposons ensuite une comparaison qualitative de ces deux méthodes et discutions de leur pertinence respective pour l'optimisation des structures lattices.}
      \field{booktitle}{{CSMA} 2022 15ème {Colloque} {National} en {Calcul} des {Structures}}
      \field{month}{5}
      \field{shorttitle}{Optimisation des structures lattices}
      \field{title}{Optimisation des structures lattices : une comparaison entre le layout optimization et l'optimisation topologique}
      \field{urlday}{24}
      \field{urlmonth}{11}
      \field{urlyear}{2022}
      \field{year}{2022}
      \field{urldateera}{ce}
      \true{nocite}
      \verb{file}
      \verb HAL PDF Full Text:D\:\\estragio\\Zotero\\storage\\YPT33TVR\\Stragiotti et al. - 2022 - Optimisation des structures lattices une compara.pdf:application/pdf
      \endverb
      \verb{urlraw}
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      \verb{url}
      \verb https://hal.archives-ouvertes.fr/hal-03687214
      \endverb
      \keyw{Layout optimisation,Optimisation topologique,Structures lattices,conf}
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        {{hash=6c4965d3ad73fb11f44136afa897bb91}{%
           family={Stragiotti},
           familyi={S\bibinitperiod},
           given={Enrico},
           giveni={E\bibinitperiod}}}%
        {{hash=6ffe413a21f4954b0aac85ca037c7876}{%
           family={Irisarri},
           familyi={I\bibinitperiod},
           given={François-Xavier},
           giveni={F\bibinithyphendelim X\bibinitperiod}}}%
        {{hash=d9c42bf5ce7591763a45d8334a00d4e1}{%
           family={Julien},
           familyi={J\bibinitperiod},
           given={Cédric},
           giveni={C\bibinitperiod}}}%
        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
      }
      \list{publisher}{1}{%
        {Mendeley}%
      }
      \strng{namehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{fullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{bibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authorbibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authornamehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{authorfullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
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      \field{sortinit}{2}
      \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a}
      \field{labelprefix}{M}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{month}{5}
      \field{title}{Truss {Topology} {Optimization} with {Topological} {Buckling} {Constraints} {Data} {Set}}
      \field{urlday}{3}
      \field{urlmonth}{5}
      \field{urlyear}{2023}
      \field{year}{2023}
      \field{urldateera}{ce}
      \true{nocite}
      \verb{doi}
      \verb 10.17632/BW7XB2W6ST.1
      \endverb
      \keyw{Structural Optimization,Lattice Structures,Layout Optimization,Optimisation avec contraintes de stress,Optimisation des structures,Optimisation du Layout,Optimisation Topologique,Stress-Constrained Optimization,Structures Lattice,Topology Optimization,misc}
    \endentry
    \entry{stragiotti_efficient_2024}{article}{}
      \name{author}{4}{}{%
        {{hash=6c4965d3ad73fb11f44136afa897bb91}{%
           family={Stragiotti},
           familyi={S\bibinitperiod},
           given={Enrico},
           giveni={E\bibinitperiod}}}%
        {{hash=6ffe413a21f4954b0aac85ca037c7876}{%
           family={Irisarri},
           familyi={I\bibinitperiod},
           given={François-Xavier},
           giveni={F\bibinithyphendelim X\bibinitperiod}}}%
        {{hash=d9c42bf5ce7591763a45d8334a00d4e1}{%
           family={Julien},
           familyi={J\bibinitperiod},
           given={Cédric},
           giveni={C\bibinitperiod}}}%
        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
      }
      \list{language}{1}{%
        {en}%
      }
      \strng{namehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{fullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{bibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authorbibnamehash}{c6a32d38ed1b00a934977cd0a4f8c680}
      \strng{authornamehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{authorfullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
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      \field{sortinit}{2}
      \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a}
      \field{labelprefix}{M}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{1}
      \field{title}{Efficient 3D truss topology optimization for aeronautical structures (in press)}
      \field{year}{2024}
      \true{nocite}
      \verb{doi}
      \verb 10.1007/s00158-024-03739-5
      \endverb
      \keyw{art}
    \endentry
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      \name{author}{4}{}{%
        {{hash=6c4965d3ad73fb11f44136afa897bb91}{%
           family={Stragiotti},
           familyi={S\bibinitperiod},
           given={Enrico},
           giveni={E\bibinitperiod}}}%
        {{hash=6ffe413a21f4954b0aac85ca037c7876}{%
           family={Irisarri},
           familyi={I\bibinitperiod},
           given={François-Xavier},
           giveni={F\bibinithyphendelim X\bibinitperiod}}}%
        {{hash=d9c42bf5ce7591763a45d8334a00d4e1}{%
           family={Julien},
           familyi={J\bibinitperiod},
           given={Cédric},
           giveni={C\bibinitperiod}}}%
        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
      }
      \list{location}{1}{%
        {Leeds, United Kingdom}%
      }
      \strng{namehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{fullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
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      \field{sortinithash}{8b555b3791beccb63322c22f3320aa9a}
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      \field{abstract}{Cellular architectured structures' most appealing characteristic is that they are able to create large structures assembling small repetitive components. Thanks to their modular nature, they bring interesting features among which reduced tooling, fast assembly, and short repair time. In the first part of the article, we formulate an optimizing method that minimizes the mass of a cellular architectured structure taking into account internal stresses, local buckling, and pattern repetition constraints. The proposed solving algorithm mitigates the appearance of local minima, a critical problem for discrete trusses. In the second part, the optimization method is applied to a real-size aeronautic application: the minimization of the mass of a cellular 3D wing box subject to lift and torsion loads. Compared to classic cell topologies, the proposed method found a cell 10-times lighter, at the cost of increased manufacturing difficulty.}
      \field{booktitle}{{ASMO}-{UK} 12 / {ASMO}-{Europe} 1 / {ISSMO} {Conference} on {Engineering} {Design} {Optimization} (2022)}
      \field{month}{7}
      \field{title}{Enhanced truss topology optimization ({TTO}) applied to a cellular wing box}
      \field{urlday}{14}
      \field{urlmonth}{11}
      \field{urlyear}{2023}
      \field{year}{2022}
      \field{urldateera}{ce}
      \true{nocite}
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      \verb HAL PDF Full Text:D\:\\estragio\\Zotero\\storage\\ZY7S5YZA\\Stragiotti et al. - 2022 - Enhanced truss topology optimization (TTO) applied.pdf:application/pdf
      \endverb
      \verb{urlraw}
      \verb https://hal.science/hal-04283287
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      \verb{url}
      \verb https://hal.science/hal-04283287
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      \keyw{Optimisation,Optimisation Topologique,Structure Lattice,conf}
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        {{hash=6c4965d3ad73fb11f44136afa897bb91}{%
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        {{hash=6ffe413a21f4954b0aac85ca037c7876}{%
           family={Irisarri},
           familyi={I\bibinitperiod},
           given={François-Xavier},
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        {{hash=d9c42bf5ce7591763a45d8334a00d4e1}{%
           family={Julien},
           familyi={J\bibinitperiod},
           given={Cédric},
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        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
      }
      \list{location}{1}{%
        {Presqu'ile de Giens, France}%
      }
      \strng{namehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{fullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
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      \field{abstract}{Nous discutons et comparons deux méthodes d'optimisation structurale pertinentes pour les structures lattices : l'optimisation topologique et le layout optimization. Nous présentons une application originale de ces deux méthodes dans le cadre de la minimisation de la masse structures lattices cellules masse en tenant compte d'un critère de rupture en contrainte. Nous proposons ensuite une comparaison qualitative de ces deux méthodes et discutions de leur pertinence respective pour l'optimisation des structures lattices.}
      \field{booktitle}{{CSMA} 2022 15ème {Colloque} {National} en {Calcul} des {Structures}}
      \field{month}{5}
      \field{shorttitle}{Optimisation des structures lattices}
      \field{title}{Optimisation des structures lattices : une comparaison entre le layout optimization et l'optimisation topologique}
      \field{urlday}{24}
      \field{urlmonth}{11}
      \field{urlyear}{2022}
      \field{year}{2022}
      \field{urldateera}{ce}
      \true{nocite}
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      \endverb
      \verb{urlraw}
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      \verb{url}
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        {{hash=6c4965d3ad73fb11f44136afa897bb91}{%
           family={Stragiotti},
           familyi={S\bibinitperiod},
           given={Enrico},
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        {{hash=6ffe413a21f4954b0aac85ca037c7876}{%
           family={Irisarri},
           familyi={I\bibinitperiod},
           given={François-Xavier},
           giveni={F\bibinithyphendelim X\bibinitperiod}}}%
        {{hash=d9c42bf5ce7591763a45d8334a00d4e1}{%
           family={Julien},
           familyi={J\bibinitperiod},
           given={Cédric},
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        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
      }
      \list{location}{1}{%
        {Lisbon, Portugal}%
      }
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        {ECCOMAS}%
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      \field{sortinithash}{9381316451d1b9788675a07e972a12a7}
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      \field{booktitle}{{AeroBest} 2021 {International} {Conference} on {Multidisciplinary} {Design} {Optimization} of {Aerospace} {Systems}. {Book} of proceedings}
      \field{month}{7}
      \field{shorttitle}{Towards manufactured lattice structures}
      \field{title}{Towards manufactured lattice structures: a comparison between layout and topology optimization}
      \field{urlday}{22}
      \field{urlmonth}{10}
      \field{urlyear}{2021}
      \field{year}{2021}
      \field{urldateera}{ce}
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      \endverb
      \verb{urlraw}
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      \endverb
      \verb{url}
      \verb https://hal.archives-ouvertes.fr/hal-03384893
      \endverb
      \keyw{Structural Optimization,Lattice Structures,Layout Optimization,Optimisation avec contraintes de stress,Optimisation des structures,Optimisation du Layout,Optimisation Topologique,Stress-Constrained Optimization,Structures Lattice,Topology Optimization,conf}
    \endentry
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        {{hash=6c4965d3ad73fb11f44136afa897bb91}{%
           family={Stragiotti},
           familyi={S\bibinitperiod},
           given={Enrico},
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        {{hash=6ffe413a21f4954b0aac85ca037c7876}{%
           family={Irisarri},
           familyi={I\bibinitperiod},
           given={François-Xavier},
           giveni={F\bibinithyphendelim X\bibinitperiod}}}%
        {{hash=d9c42bf5ce7591763a45d8334a00d4e1}{%
           family={Julien},
           familyi={J\bibinitperiod},
           given={Cédric},
           giveni={C\bibinitperiod}}}%
        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
           familyi={M\bibinitperiod},
           given={Joseph},
           giveni={J\bibinitperiod}}}%
      }
      \list{publisher}{1}{%
        {Mendeley}%
      }
      \strng{namehash}{299f30aa7c3f4b47ec8bbbc9ba700864}
      \strng{fullhash}{c6a32d38ed1b00a934977cd0a4f8c680}
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      \field{month}{5}
      \field{title}{Truss {Topology} {Optimization} with {Topological} {Buckling} {Constraints} {Data} {Set}}
      \field{urlday}{3}
      \field{urlmonth}{5}
      \field{urlyear}{2023}
      \field{year}{2023}
      \field{urldateera}{ce}
      \true{nocite}
      \verb{doi}
      \verb 10.17632/BW7XB2W6ST.1
      \endverb
      \keyw{Structural Optimization,Lattice Structures,Layout Optimization,Optimisation avec contraintes de stress,Optimisation des structures,Optimisation du Layout,Optimisation Topologique,Stress-Constrained Optimization,Structures Lattice,Topology Optimization,misc}
    \endentry
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           family={Stragiotti},
           familyi={S\bibinitperiod},
           given={Enrico},
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        {{hash=6ffe413a21f4954b0aac85ca037c7876}{%
           family={Irisarri},
           familyi={I\bibinitperiod},
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        {{hash=d9c42bf5ce7591763a45d8334a00d4e1}{%
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        {{hash=632aec531cee24c2c49fc7f0958698d4}{%
           family={Morlier},
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      \field{extraname}{5}
      \field{sortinit}{6}
      \field{sortinithash}{b33bc299efb3c36abec520a4c896a66d}
      \field{labelnamesource}{author}
      \field{labeltitlesource}{title}
      \field{journaltitle}{Structural and Multidisciplinary Optimization}
      \field{month}{1}
      \field{title}{Efficient 3D truss topology optimization for aeronautical structures (in press)}
      \field{year}{2024}
      \true{nocite}
      \verb{doi}
      \verb 10.1007/s00158-024-03739-5
      \endverb
      \keyw{art}
    \endentry
  \enddatalist
\endrefsection
\endinput

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