# Questions tagged [solidmechanics]

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### Finite element method for 3D built-up structures using two materials

I wish to do finite element calculations of a steel structure supported on rubber blocks. As a warm up problem I make an all steel structure as follows. ...
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45 views

### How to manage tensor in mathematica

I open this topic because I would like to ask the community how to handle this tensor sum regarding solid mechanics. I apologize if what comes next will generate some confusion, but I am new to using ...
179 views

### Finite Element beam model with three supports

I have defined a 3 support beam, with a uniform load over part of the span. The end BC are simple to define - deflection and moment = 0. The midspan BC for deflection =0 but but the moment can not ...
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54 views

### 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 ...
137 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 ...
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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/...
1 vote
164 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 ...
197 views

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280 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 ...
953 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 ...
520 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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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 ...
172 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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897 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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290 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
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 ...
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863 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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200 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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252 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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540 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 ...
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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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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 ...
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472 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 ...
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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 ...
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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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278 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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### 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 ...
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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 ...
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