Questions tagged [solidmechanics]

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Solid mechanics - traction boundary condition in the reference configuration

Both SolidBoundaryLoadValue or NeumannValue can be used to specify the traction boundary condition, because ...
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6 votes
2 answers
177 views

SolidMechanicsStress returns, that the stress is equal to zero

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 ...
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1 vote
1 answer
75 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 ...
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5 votes
1 answer
149 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 ...
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2 votes
1 answer
114 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 ...
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19 votes
2 answers
712 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: ...
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8 votes
1 answer
381 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 ...
1 vote
0 answers
106 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 ...
2 votes
0 answers
59 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 votes
1 answer
225 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 ...
7 votes
1 answer
512 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
294 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 ...
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2 votes
0 answers
131 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 ...
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11 votes
3 answers
639 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 ...
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5 votes
4 answers
205 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 ...
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1 vote
2 answers
1k 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 ...
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10 votes
0 answers
714 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 ...
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4 votes
1 answer
168 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 ...
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4 votes
1 answer
240 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), ...
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7 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. <...
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28 votes
1 answer
4k 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 ...
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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 ...
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2 votes
1 answer
267 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 ...
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11 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 ...
7 votes
1 answer
2k views

SymmetrizedArray of stiffness/compliance tensor

The stiffness and compliance tensors of a material are 3x3x3x3 tensors relating stress and strain. ...