Questions tagged [solidmechanics]
The solidmechanics tag has no usage guidance.
42
questions
1
vote
1
answer
116
views
Animating a double spring spherical pendulum
I want to make an animation of a double spring spherical pendulum. The first mass is connected to the ceiling with a spring, and the second mass is attached to the first one with a spring too. The ...
3
votes
4
answers
167
views
NDSolve over derivatives of Heaviside function
I am trying to numerically solve for the strain of a Maxwell material in response to a step stress. The governing equations are $$\dot{\sigma} + \sigma = \dot{\varepsilon}$$ and I want to find $\...
- 335
6
votes
2
answers
355
views
Simulating buckling
We are trying to implement buckling using a newly implemented FEM solver. However, if we try to reproduce the buckling phenomena using a thin rod, it is just compressed, and we cannot observe the ...
- 321
1
vote
1
answer
266
views
How to find the analytical or numerical solution of a system of partial differential equations?
I am trying to use mathematica to solve a system of second-order partial differential equations, but I have been unable to solve it. The code of mathematica is as follows:
...
3
votes
0
answers
150
views
FEM stress analysis by considering bending moment
I found an example of using FEM for stress analysis in the forum, the code provided by @user21, which is very friendly for beginners.
...
- 583
4
votes
3
answers
279
views
Solid Mechanics FEM Simulation with Different Material Properties
How would I assign different material properties to the "bar" and "support"? Meaning, for example, the bar would be assigned the properties of single-crystal Copper and the support ...
- 7,485
1
vote
1
answer
144
views
Displaying NDEigensystem Results
I want to display a collection of deformed meshes in a GraphicsGrid where the surface colors are proportional to the displacement.
...
- 7,485
2
votes
1
answer
121
views
Where to find SolidMechanicsExtendedStrain and SolidMechanicsExtendedStress?
The introduction to solid mechanics from Wolfram:
https://reference.wolfram.com/language/PDEModels/tutorial/StructuralMechanics/SolidMechanics.html#775646651
mentions two functions:
PDEModels`...
- 47.3k
8
votes
2
answers
299
views
Alternative Material Models for Finite Element
The Solid Mechanics capabilities of Mathematica make it an interesting alternative to using other software especially when considering multi-physics problems. I would like to collect here (for the ...
- 3,923
1
vote
0
answers
68
views
Is there any documentation for vibration and solid mechanics research via Mathematica? [closed]
I am interested in the solid mechanics (elastic mechanics and structural mechanics, etc.), and vibration, is there any material or documentation in this aspect via FEM in Mathematica?
- 129
2
votes
1
answer
110
views
How to access implementations of MaterialModel?
In the documentation for Hyperelasticity there is an example of the MaterialModel for NeoHookean and the St Venant Kirchoff models. These are very useful in helping develop ones own materials models. ...
- 3,923
4
votes
2
answers
288
views
Symbolic integration in a region obtained using a boolean combination
Inertia tensors for non-typical rigid bodies
Calculate inertia tensors
Integrate over a region
I'm trying to calculate the moment of inertia for a complex figure depending on the $r$ parameter.
...
- 2,374
8
votes
2
answers
1k
views
Inertia tensors for non-typical rigid bodies
Calculate inertia tensors
This topic inspired me to experiment with calculating tensors of more complex shapes of rigid bodies (I did not find them in the Mathematica database).
For simple shapes of ...
- 2,374
2
votes
1
answer
92
views
How to use ElementMeshInterpolation to interpolate to deformed mesh?
I'm solving a problem in solid mechanics, but I ran into problems when I tried to plot some stuff over the deformed mesh, because the plots are cut off. They end when the undeformed mesh ends.
...
- 402
6
votes
2
answers
276
views
SolidMechanicsStress returns, that the stress is equal to zero
Bug introduced in 13.1 and fixed in 13.2.0
I am trying to compute a deformation and a stress of a material with a custom material law. I have successfully computed the deformation using ...
- 402
1
vote
1
answer
134
views
It is possible to use a different stress tensor than Cauchy stress tensor when creating a custom material law?
I would like to use Mathematica to solve some solid mechanics problems, which will include an implementation of a different model than the ones that Mathematica offers. The way how to write custom ...
- 402
6
votes
1
answer
231
views
Solving system of nonlinear PDEs
My aim is to solve a system of nonlinear PDEs arising in nonlinear elasticity. I am new to Mathematica so I started by modifying this example. I tried to change it to neo-Hookean solid. The resulting ...
- 402
2
votes
1
answer
134
views
Why does SolidMechanicsStrain calculated inside a module give strange results?
Bug introduced in 13.0 and fixed in 13.1.0
I am exploring the FE capabilities of Mathematica and trying a few solid mechanics problems with the aim of bringing them into my teaching. The problem is a ...
- 3,923
20
votes
2
answers
954
views
Large deformation of solids
Link to notebook with this question and code
I'd like to understand how large deformations of solid mechanics work and how they are implemented. For this am looking at the following reference problem: ...
- 39.1k
8
votes
1
answer
461
views
FEM: elastic cylinder under circumferential pressure
Suppose you have an elastic cylinder of radius $R$ and height $H$ and you want to solve the mechanical 3D equilibrium with Mathematica's FEM.
How do you impose a pressure $p$ only on the cylinder ...
- 5,433
1
vote
0
answers
130
views
DSolve for deflection of an elastic beam
I have to write a notebook about comparing the results of the deflection of an elastic beam, calculated with discrete methods and FE methods. The code has to be generalized for any kind of beam ...
- 11
2
votes
0
answers
65
views
How to use GreenFunction for multifield PDE on finite cuboid?
Is it possible to use GreenFunction for a multifield PDE?
Explicit problem
I want to compute Green's function with Mathematica on the finite 3D-cube $\Omega = [0,1]^...
- 5,433
5
votes
1
answer
264
views
How to solve the wave velocity in steel
In the simulation of stress wave propagation, I have the following two problems.
First question:
This question comes from page 69 of this book.
The Lame equation for a linear elastic body without ...
8
votes
1
answer
794
views
How to explain the meaning of `NeumannValue` function in detail
I saw here that NeumannValue is used to represent the stress boundary condition when solving the plane stress problem.
In the help information of the ...
7
votes
3
answers
455
views
FEM stress analysis by considering thermal strain
Following the question in this post, I am trying to do a stress analysis by including thermal strain. @user21 already showed how to do a pre-stressed analysis. Analogically, I modified the code and ...
- 131
2
votes
0
answers
160
views
Formulating equations for 3D stress in the finite element method
I would like to know how you formulate equations for the finite element method for stress calculations. We know the answer because user21 has put it here. It involves usage of ...
- 16.1k
11
votes
4
answers
817
views
Stress analysis in axisymmetric bodies
I would like to do some finite element calculations in axisymmetric cylindrical coordinates. I wish to calculate stress in terms of {r,z} coordinates. The radial ...
- 16.1k
5
votes
4
answers
262
views
Plotting displacement values over defined region
I have a deformed 2D region of triangular Elements specified by their Nodes in $x$ and $y$ coordinate system. In addition, I ...
- 163
1
vote
2
answers
2k
views
How to find the parametric equation of the von Mises yield function?
The von Mises yield function is given by:
$
\Phi(\sigma_1,\sigma_2)=\sqrt{\sigma_{1}^{2} +\sigma_{2}^{2}-\sigma_{1} \sigma_{2}} - \sigma_y
$
were $\sigma_1$ and $\sigma_2$ are the principal ...
- 2,882
10
votes
0
answers
784
views
Stress Operators for Finite Element Analysis
For stress analysis in the finite element method you need a stress operator. For two dimensional plane stress it can be found here. For two dimensional plain strain it can be found here. I need the ...
- 16.1k
4
votes
1
answer
193
views
How to improve quality of NeumannValue boundary conditions for stress calculations
When doing stress calculations forces are applied to a boundary of a region. Here I am applying the forces over an interval but the stress resolution is poor near the edge of the interval. Can this be ...
- 16.1k
4
votes
1
answer
246
views
A Trial Boundary Element Approach to Solving Integral Equation
I am trying to numerically solve an integral equation in Starfield and Crouch textbook (Boundary Element Methods in Solid Mechanics: With Applications in Rock Mechanics and Geological Engineering), ...
- 423
8
votes
1
answer
528
views
Neumann conditions on circle in 2D elastic deformation
I have the following problem: I am currently doing calculations with some physical background in research and need a short and sweet finite element simulation of a 2D deformation problem. Usually I ...
- 81
8
votes
1
answer
1k
views
Stress calculations in three dimensions (finite element method)
Calculation of stress in two dimensions is covered in this post by the helpful user21. I am now trying to work in three dimensions. For this we need a stress operator which I have taken from Help.
<...
- 16.1k
23
votes
1
answer
1k
views
Numerical inverse Laplace-Hankel transform
When trying to reproduce the result of this paper about numerical solution of Lamb's problem, I encountered the following double integral (to be more precise, the 0-order inverse Hankel-Laplace ...
- 63.9k
3
votes
1
answer
460
views
Errors Solving Elliptic PDES with FEM
I am trying to solve the equation below governing transversely isotropic plane strain in cartesian coordinates with the given boundary conditions based on code found here using Mathematica 10.1 on OSX ...
- 167
29
votes
1
answer
5k
views
Stress calculations using finite elements
A standard engineering problem is to calculate stresses in a structure due to applied forces. With the inclusion of the finite element method in version 10 this question attempts to investigate how ...
- 16.1k
14
votes
3
answers
1k
views
Time evolution/dynamics of circular plate with hole (Biharmonic equation and stiffness)
On this Mathematica.SE form, there exists information on how to use Mathematica to demonstrate the vibration of a circular membrane and the deflection of an orifice plate (the latter I had raised ...
- 5,321
2
votes
1
answer
275
views
Swinging Beam example from Help. Not Understanding/Not Working
To help me understand finite element analysis with Mathematica I have been reading the Finite Element Method User Guide in Help and am stuck on the example in Coupled PDEs. Here there is a static beam ...
- 16.1k
9
votes
3
answers
1k
views
FEM Solution desired for "Plate with orifice" deflection: Application of Boundary Conditions and use of Regions
I found the deflection of an orifice plate (circular plate with a hole) subject to uniform pressure using Mathematica's NDSolve functionality. The plate is fixed at its outer circumference and is ...
- 5,321
13
votes
1
answer
3k
views
FEM: user material subroutines (UMAT in ABAQUS), mechanics
Just a quick question (mainly for those who are also familiar with ABAQUS or other comparable FEM programs and non-linear modelling of mechanical behavior, e.g., plasticity). Is there any module in ...
- 5,433
7
votes
1
answer
3k
views
SymmetrizedArray of stiffness/compliance tensor
The stiffness and compliance tensors of a material are 3x3x3x3 tensors relating stress and strain.
...
- 3,793