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Stabilise equations for motion of Inextensible string subject to spatially non-uniform forces

I would like to simulate the motion of an inextensible membrane in 1D as an inextensible string subject to spatially-dependent body forces. For now, I would like it to be constrained at both ends. I ...
Ariana Fenris's user avatar
2 votes
2 answers
132 views

How to interpolate and visualize a finite element integration point solution

I can intepolate the nodal solution using the function ufun = ElementMeshInterpolation[{mesh}, nodalsol] and visualize the nodal solution with the function ...
Stratus's user avatar
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0 answers
48 views

Minimizing stress and deflection (separately) using higher-order theory for static analyses of functionally graded cantilever beams

I wanted to generate an FGM beam's optimized volume fraction, minimizing stress and deflection separately. I wanted to use the following article as a reference for the related equations. DOI 10.1007/...
nuj_hossain's user avatar
1 vote
1 answer
156 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 ...
Denis D. Bavrin's user avatar
3 votes
4 answers
188 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 $\...
JamesVR's user avatar
  • 407
6 votes
2 answers
389 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 ...
Takashi Miura's user avatar
1 vote
1 answer
313 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: ...
RuiQiang Kang's user avatar
3 votes
0 answers
217 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. ...
lumw's user avatar
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4 votes
3 answers
301 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 ...
Young's user avatar
  • 7,495
1 vote
1 answer
148 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. ...
Young's user avatar
  • 7,495
2 votes
1 answer
127 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`...
Daniel Huber's user avatar
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8 votes
2 answers
374 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 ...
Dunlop's user avatar
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1 vote
0 answers
75 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?
fhrl's user avatar
  • 129
2 votes
1 answer
121 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. ...
Dunlop's user avatar
  • 4,023
4 votes
2 answers
296 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. ...
dtn's user avatar
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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 ...
dtn's user avatar
  • 2,404
2 votes
1 answer
104 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. ...
lemurman's user avatar
  • 412
6 votes
2 answers
291 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 ...
lemurman's user avatar
  • 412
1 vote
1 answer
160 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 ...
lemurman's user avatar
  • 412
6 votes
1 answer
255 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 ...
lemurman's user avatar
  • 412
2 votes
1 answer
137 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 ...
Dunlop's user avatar
  • 4,023
20 votes
2 answers
1k 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: ...
user21's user avatar
  • 39.9k
8 votes
1 answer
478 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 ...
Mauricio Fernández's user avatar
1 vote
0 answers
135 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 ...
andris0110's user avatar
2 votes
0 answers
67 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]^...
Mauricio Fernández's user avatar
5 votes
1 answer
275 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 ...
A little mouse on the pampas's user avatar
9 votes
1 answer
911 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 ...
A little mouse on the pampas's user avatar
7 votes
3 answers
503 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 ...
XIJUN SHI's user avatar
  • 131
3 votes
3 answers
3k views

First to fifth order natural frequencies of a cantilever beam with known material constants

We assume that the homogeneous Euler-Bernoulli cantilever with constant cross-section length is 1, the material constant EI is 1 and ρS is 1. According to the constraints, we can establish the ...
A little mouse on the pampas's user avatar
2 votes
0 answers
170 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 ...
Hugh's user avatar
  • 16.5k
11 votes
4 answers
876 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 ...
Hugh's user avatar
  • 16.5k
5 votes
4 answers
283 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 ...
KeVal's user avatar
  • 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 ...
Stratus's user avatar
  • 2,954
10 votes
1 answer
846 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 ...
Hugh's user avatar
  • 16.5k
4 votes
1 answer
198 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 ...
Hugh's user avatar
  • 16.5k
4 votes
1 answer
251 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), ...
D. Andrew's user avatar
  • 423
8 votes
1 answer
534 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 ...
u53r's user avatar
  • 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. <...
Hugh's user avatar
  • 16.5k
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 ...
xzczd's user avatar
  • 66.8k
3 votes
1 answer
467 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 ...
seyisulu's user avatar
  • 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 ...
Hugh's user avatar
  • 16.5k
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 ...
dearN's user avatar
  • 5,351
2 votes
1 answer
276 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 ...
Hugh's user avatar
  • 16.5k
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 ...
dearN's user avatar
  • 5,351
13 votes
1 answer
4k 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 ...
Mauricio Fernández's user avatar
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. ...
Timothy Wofford's user avatar