From 3f25cb789b26c5df8dad451ee88b0de84713be7d Mon Sep 17 00:00:00 2001 From: Suneth Warnakulasuriya Date: Tue, 22 Oct 2024 07:14:34 +0200 Subject: [PATCH 1/2] updated the bushing doc --- .../Elements/Bushing.md | 460 ++++++++++++++++++ 1 file changed, 460 insertions(+) create mode 100644 docs/pages/Applications/Structural_Mechanics_Application/Elements/Bushing.md diff --git a/docs/pages/Applications/Structural_Mechanics_Application/Elements/Bushing.md b/docs/pages/Applications/Structural_Mechanics_Application/Elements/Bushing.md new file mode 100644 index 000000000000..15f80a878f0d --- /dev/null +++ b/docs/pages/Applications/Structural_Mechanics_Application/Elements/Bushing.md @@ -0,0 +1,460 @@ +--- +title: Bushing +keywords: [bushing element structural] +tags: [bushing.md] +sidebar: structural_mechanics_application +summary: +--- +## Brief + +`BushingElement` is a superelement modeling complex behavior between two nodes. It is frequently used for example in automotive applications to simplify modeling rubber bushings at the suspension. `BushingElement` assumes fairly simple kinematics but can model complex behavior by defining force-displacement relationships in different (combinations of) directions. + +## Usage + +Force(moment) - displacement(rotation) relationships at the two nodes can be generated by carrying out an analysis on a full model of the bushing's geometry under different load cases and recording the displacements(rotations) at the attachment points (nodes) in a table. Alternatively, a linear behavior can also be specified. In any case, `NODAL_DISPLACEMENT_STIFFNESS` (representing $$K^\square$$) and `NODAL_ROTATIONAL_STIFFNESS` (suneth representing $$K^\square_\theta$$) must be defined in the material JSON. + +### Example anisotropic linear behavior: +```json +{ + "properties" : [ + { + "model_part_name" : "root.bushing", + "properties_id" : 1, + "Material" : { + "name" : "BushingMaterial", + "Variables" : { + "NODAL_DISPLACEMENT_STIFFNESS" : [/*K^x=*/1e9, /*K^y=*/1e8, /*K^z=*/2e8], + "NODAL_ROTATIONAL_STIFFNESS" : [/*K^x_\theta=*/1e7, /*K^y_\theta=*/1e6, /*K^z_\theta=*/1e5] + } + } + } + ] +} +``` + +### Example anisotropic nonlinear behavior: +```json +{ + "properties" : [ + { + "model_part_name" : "root.bushing", + "properties_id" : 1, + "Material" : { + "name" : "BushingMaterial", + "Tables" : { + "ux_vs_fx" : { + "input_variable" : "DISPLACEMENT_X", + "output_variable" : "NODAL_DISPLACEMENT_STIFFNESS_X", + "data" : [ + [-1e-5, 1e8], + [ 0e0, 1e9], + [ 1e-5, 5e8] + ] + }, + + ... + + "thetaz_vs_mz" : { + "input_variable" : "ROTATION_Z", + "output_variable" : "NODAL_ROTATIONAL_STIFFNESS_Z", + "data" : [ + [-1e-2, 1e7], + [ 0e0, 1e8], + [ 1e-2, 5e7] + ] // "data" + } // "thetaz_vs_mz" + } // "Tables" + } // "Material" + } + ] // "properties" +} +``` + +### Example usage using Force(moment) and Displacement(rotation) data: + +The bushing element can use linear / non-linear data from force-displacement and/or moment-rotation graphs (refer "Defining nonlinear spring behavior" in [abaqus](https://classes.engineering.wustl.edu/2009/spring/mase5513/abaqus/docs/v6.6/books/usb/pt06ch26s01alm35.html#espring-nonlinear)). Following is an example: +```json +{ + "properties" : [ + { + "model_part_name" : "root.bushing", + "properties_id" : 1, + "Material" : { + "name" : "BushingMaterial", + "Tables" : { + "ux_vs_fx" : { + "input_variable" : "DISPLACEMENT_X", + "output_variable" : "FORCE_X", + "data" : [ + [-1e-5, 1e8], + [ 0e0, 1e9], + [ 1e-5, 5e8] + ] + }, + + ... + + "thetaz_vs_mz" : { + "input_variable" : "ROTATION_Z", + "output_variable" : "MOMENT_Z", + "data" : [ + [-1e-2, 1e7], + [ 0e0, 1e8], + [ 1e-2, 5e7] + ] // "data" + } // "thetaz_vs_mz" + } // "Tables" + } // "Material" + } + ] // "properties" +} +``` + +## Kinematics + +This section details the `BushingElement`'s kinematics in the $$xy$$ plane. Similar derivations apply in the other planes. + +

+ +

+ +The kinematics of `BushingElement` is heavily simplified and restricted to small displacements as well as small distances between the two nodes. The line connecting the two nodes is assumed to deform along the arc of a circle, meaning that the deformed configuration has a constant radius of curvature $$\rho^z$$. + +The length of the line between the two nodes $$s$$ is initially $$l$$ but changes as a function of $$\theta^z$$ during deformation: +$$ + ds = \rho^z d\theta^z \stackrel{\text{small } \theta^z}{\approx} dx +$$ +$$ + \tan \theta^z = \frac{dy}{dx} \stackrel{\text{small } \theta^z}{\approx} \theta +$$ + +An ODE defining the deformed shape follows. +$$ +\begin{align*} + \frac{d^2 y}{d x^2} = \frac{1}{\rho^z} + \quad \rightarrow \quad + & \theta^z(x) = \frac{x}{\rho^z} + c_0 \\ + & y(x) = \frac{x^2}{2 \rho^z} + c_0 x + c_1 +\end{align*} +$$ + +Applying the boundary conditions $$\theta^z(0) = \theta^z_0$$ and $$y(0) = u^y_0$$: +$$ +\begin{align*} + & \theta^z(x) = \frac{\theta^z_1 - \theta^z_0}{l}x + \theta^z_0 \\ + & y(x) = \frac{\theta^z_1 - \theta^z_0}{l}x^2 + \theta^z_0 x + u^y_0 +\end{align*} +$$ + +## Stiffnesses + +### XY Plane + +This section details the `BushingElement`'s stiffnesses in the $xy$ plane. Similar derivations apply in other planes as well. Stiffnesses are defined in terms of the provided force(moment)-displacement(rotation) curves, which are internally reduced to tangent stiffnesses. + +

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

+ +$$ +\begin{align*} + F^y_{int} &= K^y (u^y_1 - y(l)) = K^y (u^y_1 - u^y_0 - \frac{\theta^z_0 + \theta^z_1}{2} l) \\ + M^z_{int} &= K^z_\theta (\theta^z_0 - \theta^z_1) +\end{align*} +$$ + +Forces in terms of DoFs: + +$$ +\begin{align*} + F^y_0 &= -F_{int} = -K^y (u^y_1 - u^y_0 - \frac{\theta^z_0 + \theta^z_1}{2} l) \\ + M^z_0 &= M^z_{int} - F^y_{int} \frac{l}{2} = K^z_\theta (\theta^z_0 - \theta^z_1) - K^y (u^y_1 - u^y_0 - \frac{\theta^z_0 + \theta^z_1}{2} l) \frac{l}{2} \\ + F^y_1 &= F_{int} = K_y (u^y_1 - u^y_0 - \frac{\theta^z_0 + \theta^z_1}{2}l) \\ + M^z_1 &= -M^z_{int} - F^y_{int} \frac{l}{2} = -K^z_\theta (\theta^z_0 - \theta^z_1) - K^y (u^y_1 - u^y_0 - \frac{\theta^z_0 + \theta^z_1}{2}l) \frac{l}{2} +\end{align*} +$$ + +The stiffness matrix $$K$$ in the $$xy$$ plane follows. +$$ +\overset{K}{ + \begin{bmatrix} + K^y & K^y \frac{l}{2} & -K^y & K^y \frac{l}{2} \\ + K^y \frac{l}{2} & K^z_\theta + K^y (\frac{l}{2})^2 & -K^y \frac{l}{2} & -K^z_\theta + K^y (\frac{l}{2})^2 \\ + -K^y & -K^y \frac{l}{2} & K^y & -K^y \frac{l}{2} \\ + K^y \frac{l}{2} & -K^z_\theta + K^y (\frac{l}{2})^2 & -K^y \frac{l}{2} & K^z_\theta + K^y (\frac{l}{2})^2 + \end{bmatrix} +} +\overset{u}{ + \begin{bmatrix} + u^y_0 \\ + \theta^z_0 \\ + u^y_1 \\ + \theta^z_1 + \end{bmatrix} +} += +\overset{f}{ + \begin{bmatrix} + F^y_0 \\ + M^z_0 \\ + F^y_1 \\ + M^z_0 + \end{bmatrix} +} +$$ + +### 3D + +The remaining components of the stiffness matrix can be derived similarly in other planes. + +$$u$$: + +| row # | DoF | +| :---: | :---: | +| 0 | $$u^x_0$$ | +| 1 | $$u^y_0$$ | +| 2 | $$u^z_0$$ | +| 3 | $$\theta^x_0$$ | +| 4 | $$\theta^y_0$$ | +| 5 | $$\theta^z_0$$ | +| 6 | $$u^x_1$$ | +| 7 | $$u^y_1$$ | +| 8 | $$u^z_1$$ | +| 9 | $$\theta^x_1$$ | +| 11 | $$\theta^y_1$$ | +| 12 | $$\theta^z_1$$ | + +$$K$$: + +| row # | column # | Value | +| :---: | :---: | :---: | +| 0 | 0 | $$K^x$$ | +| 0 | 6 | $$-K^x$$ | +| 1 | 1 | $$K^y$$ | +| 1 | 5 | $$K^y \frac{l}{2}$$ | +| 1 | 7 | $$-K^y$$ | +| 1 | 11 | $$K^y \frac{l}{2}$$ | +| 2 | 2 | $$K^z$$ | +| 2 | 4 | $$-K^z \frac{l}{2}$$ | +| 2 | 8 | $$-K^z$$ | +| 2 | 10 | $$-K^z \frac{l}{2}$$ | +| 3 | 3 | $$K^x_\theta$$ | +| 3 | 9 | $$-K^x_\theta$$ | +| 4 | 2 | $$-K^z \frac{l}{2}$$ | +| 4 | 4 | $$K^y_\theta + K^z (\frac{l}{2})^2$$ | +| 4 | 8 | $$K^z \frac{l}{2}$$ | +| 4 | 10 | $$-K^y_\theta + K^z (\frac{l}{2})^2$$ | +| 5 | 1 | $$K^y \frac{l}{2}$$ | +| 5 | 5 | $$K^z_\theta + K^y (\frac{l}{2})^2$$ | +| 5 | 7 | $$-K^y \frac{l}{2}$$ | +| 5 | 11 | $$-K^z_\theta + K^y (\frac{l}{2})^2$$ | +| 6 | 0 | $$-K^x$$ | +| 6 | 6 | $$K^x$$ | +| 7 | 1 | $$-K^y$$ | +| 7 | 5 | $$-K^y \frac{l}{2}$$ | +| 7 | 7 | $$K^y$$ | +| 7 | 11 | $$-K^y \frac{l}{2}$$ | +| 8 | 2 | $$-K^z$$ | +| 8 | 4 | $$K^z \frac{l}{2}$$ | +| 8 | 8 | $$K^z$$ | +| 8 | 10 | $$K^z \frac{l}{2}$$ | +| 9 | 3 | $$-K^x_\theta$$ | +| 9 | 9 | $$K^x_\theta$$ | +| 10 | 2 | $$-K^z \frac{l}{2}$$ | +| 10 | 4 | $$-K^y_\theta + K^z (\frac{l}{2})^2$$ | +| 10 | 8 | $$K^z \frac{l}{2}$$ | +| 10 | 10 | $$K^y_\theta + K^z (\frac{l}{2})^2$$ | +| 11 | 1 | $$K^y \frac{l}{2}$$ | +| 11 | 5 | $$-K^z_\theta + K^y (\frac{l}{2})^2$$ | +| 11 | 7 | $$-K^y \frac{l}{2}$$ | +| 11 | 11 | $$K^z_\theta + K^y (\frac{l}{2})^2$$ | From 9c0118c8dd33124226fa62a2dea1ec107572ef64 Mon Sep 17 00:00:00 2001 From: Suneth Warnakulasuriya Date: Tue, 22 Oct 2024 07:16:13 +0200 Subject: [PATCH 2/2] restructure struct app docs --- .../Composite-clamped-cylinder.md | 0 ...ite-hinged-cylindrical-roof-snapthrough.md | 0 .../Formfinding-and-Membrane-Analysis.md | 0 .../Hinged-cylindrical-roof-snapthrough.md | 0 .../Non-linear-cantilever-beam.md | 0 .../Open-cylinder-pull-out.md} | 0 .../Roll-up-beam-cantilever.md} | 0 .../Shallow-angle-beam.md | 0 .../Shell-obstacle-course-Pinched-cylinder.md | 0 ...hell-obstacle-course-Pinched-hemisphere.md | 0 ...Shell-obstacle-course-Scordelis-Lo-roof.md | 0 .../Two-bar-truss---snap-through.md | 0 ...aws-in-Structural-Mechanics-Application.md | 69 +++++++++++-------- .../General/Overview.md | 7 ++ 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a16f98a90343..1138a369c8f1 100644 --- a/docs/pages/Applications/Structural_Mechanics_Application/General/KratosStructuralMechanicsAPI-Constitutive-laws-in-Structural-Mechanics-Application.md +++ b/docs/pages/Applications/Structural_Mechanics_Application/General/KratosStructuralMechanicsAPI-Constitutive-laws-in-Structural-Mechanics-Application.md @@ -1,6 +1,6 @@ --- -title: KratosStructuralMechanicsAPI Constitutive laws in Structural Mechanics Application -keywords: +title: Constitutive laws +keywords: [structural constitutive laws api] tags: [KratosStructuralMechanicsAPI-Constitutive-laws-in-Structural-Mechanics-Application.md] sidebar: structural_mechanics_application summary: @@ -14,26 +14,41 @@ Since this is a work-in-progress, we are going to describe the present state of At this point, there are some Constitutive Laws (CL from now on) that are available and ready to use: -1. [Isotropic Elasticity (2D, 3D, Axisymmetric, truss, beam)](#isotropic-elasticity) -2. [HyperElasticity (2D, 3D)](#hyperelasticity) - 1. [Kirchhoff Material](#kirchhoff-material) - 2. [Neo-Hookean Material](#neo-hookean-material) -3. [Isotropic Plasticity (3D)](#isotropic-plasticity) - 1. [Brief summary of the modualr design](#brief-summary-of-the-modular-design) - 1. [Introduction](#introduction) - 2. [Yield Surface](#yield-surface) - 3. [Plastic Potential](#plastic-potential) - 1. [Flow Rules](#flow-rules) - 2. [Small Strain Plasticity](#small-strain-plasticity) - 1. [General description](#general-description) - 2. [Constitutive Law Integrator](#constitutive-law-integrator) - 3. [Finite Strain Plasticity](#finite-strain-plasticity) - 1. [General description](#general-description) -4. [Kinematic Plasticity (3D)] -4. [Isotropic Damage (3D)](#isotropic-damage) -5. [ViscoElasticity (3D)](#) -6. [ViscoPlasticity (3D)](#) -7. [d+d- Damage Model](#d+d-damage-model) +- [Overview](#overview) +- [Isotropic Elasticity](#isotropic-elasticity) +- [HyperElasticity](#hyperelasticity) + - [Common properties](#common-properties) + - [Kirchhoff Material](#kirchhoff-material) + - [Neo-Hookean Material](#neo-hookean-material) +- [Isotropic Plasticity](#isotropic-plasticity) + - [Brief summary of the modular design](#brief-summary-of-the-modular-design) + - [Introduction](#introduction) + - [Yield Surface](#yield-surface) + - [Plastic Potential](#plastic-potential) + - [Flow Rules](#flow-rules) + - [Small Strain Plasticity](#small-strain-plasticity) + - [General Description](#general-description) + - [Constitutive Law Integrator](#constitutive-law-integrator) + - [Finite Strain Plasticity](#finite-strain-plasticity) + - [General Description](#general-description-1) + - [How to use it?](#how-to-use-it) +- [Small Strain Isotropic Damage](#small-strain-isotropic-damage) + - [General Description](#general-description-2) + - [How to use it?](#how-to-use-it-1) +- [Small Strain d+d- Damage](#small-strain-dd--damage) + - [General Description](#general-description-3) + - [How to use it?](#how-to-use-it-2) +- [ViscoElasticity](#viscoelasticity) + - [General Description](#general-description-4) + - [Generalized Maxwell model](#generalized-maxwell-model) + - [How to use it?](#how-to-use-it-3) + - [Generalized Kelvin model](#generalized-kelvin-model) + - [How to use it?](#how-to-use-it-4) +- [ViscoPlasticity](#viscoplasticity) +- [Appendix](#appendix) + - [The Mohr-Coulomb modified yield surface](#the-mohr-coulomb-modified-yield-surface) +- [References](#references) +- [Contact us!](#contact-us) A description of the previous models will be done in the following paragraphs. @@ -238,7 +253,7 @@ The parameters needed for the plasticity (neglecting the young modulus and poiss * `FRICTION_ANGLE`: Defines the friction angle value in degrees * `DILATANCY_ANGLE`: Defines the dilatancy angle value in degrees (usually 0.5*friction_angle) -# Small Strain Isotropic Damage +# Small Strain Isotropic Damage ## General Description @@ -283,7 +298,7 @@ The parameters are the following (use International System): * `FRICTION_ANGLE`: Defines the friction angle value in degrees * `SOFTENING_TYPE`: Defines the softening type (linear softening=0, exponential softening=1) -# Small Strain d+d- Damage +# Small Strain d+d- Damage ## General Description @@ -296,7 +311,7 @@ Once we have Decomposed the stress tensor we proceed to the calculation of the d ![plasti.](https://raw.githubusercontent.com/KratosMultiphysics/Documentation/master/Wiki_files/CL%20StructuralMech/integrated.png) -In order to guarantee flexibility, we have designed an structure capable of combining different yield surfaces in tension and in compression. This has been achieved by _templating_ two integrators named **TConstLawIntegratorTensionType** and +In order to guarantee flexibility, we have designed an structure capable of combining different yield surfaces in tension and in compression. This has been achieved by _templating_ two integrators named **TConstLawIntegratorTensionType** and **TConstLawIntegratorCompressionType** which define the tension/compression yield surfaces and flow rules. The implementation is described below (`generic_small_strain_d_plus_d_minus_damage.cpp`): @@ -342,7 +357,7 @@ The parameters required for this model have been explained previously and the wa 1. Rankine 2. Tresca 3. VonMises -4. ModifiedMohrCoulomb +4. ModifiedMohrCoulomb 5. DruckerPrager 6. SimoJu 7. Classical Mohr-Coulomb @@ -455,7 +470,7 @@ where the stress function "_f_" is expressed as[1] (being θ the Lode's angle, I Through this new Mohr-Coulomb modified function any strength relation required by the different materials can be established by only modifying **K**i , without increasing -dilatancy. +dilatancy. The values of the **K**i and the parameters required can be seen in the figures below[1]. diff --git a/docs/pages/Applications/Structural_Mechanics_Application/General/Overview.md b/docs/pages/Applications/Structural_Mechanics_Application/General/Overview.md new file mode 100644 index 000000000000..17eeaf23a486 --- /dev/null +++ b/docs/pages/Applications/Structural_Mechanics_Application/General/Overview.md @@ -0,0 +1,7 @@ +--- +title: Overview +keywords: +tags: [Overview.md] +sidebar: structural_mechanics_application +summary: +--- diff --git a/docs/pages/Applications/Structural_Mechanics_Application/General/menu_info.json b/docs/pages/Applications/Structural_Mechanics_Application/General/menu_info.json new file mode 100644 index 000000000000..0cc207564821 --- /dev/null +++ b/docs/pages/Applications/Structural_Mechanics_Application/General/menu_info.json @@ -0,0 +1,5 @@ +{ + "custom_entries": [ + "Overview.md" + ] +} \ No newline at end of file diff --git a/docs/pages/Applications/Structural_Mechanics_Application/menu_info.json b/docs/pages/Applications/Structural_Mechanics_Application/menu_info.json index 07d0fc02e11d..4f9b2457c490 100644 --- a/docs/pages/Applications/Structural_Mechanics_Application/menu_info.json +++ b/docs/pages/Applications/Structural_Mechanics_Application/menu_info.json @@ -1,8 +1,13 @@ { "side_bar_name": "structural_mechanics_application", - "landing_page": "General/0_Roll-up-beam-cantilever.md", + "landing_page": "General/Overview.md", "additional_menu_options": { "product": "Structural Mechanics Application", "title": "sidebar" - } + }, + "custom_entries": [ + "General", + "Elements", + "Examples" + ] } \ No newline at end of file