Thermoelasticity problem with FEM in MATLAB

In summary, the thermoelasticity problem involves analyzing the interaction between thermal and mechanical stresses in materials. The Finite Element Method (FEM) is used in MATLAB to numerically solve these complex problems by discretizing the material into finite elements. The process typically includes formulating the governing equations, applying boundary and initial conditions, and implementing the FEM algorithm to simulate the thermal and mechanical behavior of the material under various conditions. The results provide insights into the stress distribution and deformation, essential for engineering applications.
  • #1
Chakad
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TL;DR Summary
I want to find distribution of temperature, and stress in cylinder with inner and outer temperature and pressure.
Hello I want to find distribution of temperature, and stress in cylinder with inner and outer temperature and pressure , I used linear elements with 3 nodes and wrote matlab code, moreover I want to solve that coupled but I have problem in first and last point because those have something like shock. please help me.

My Matlab code
 
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  • #2
Your description is very very short and your code hardly has any comments. This means we would need to do a lot of work to understand your problem. If you want help you need to explain a lot more about what you are actually trying to do. Please:

- Provide a drawing with the problem you are trying to solve with a cylinder and all boundary conditions, initial conditions, material assumptions etc etc, all there is to know about your problem
- Please provide a description of the finite element model you are trying to solve, where you apply what boundary conditions (yes, again!) etc.
- Please clean up your code and add in comments where you do what.
- Please describe exactly what you see in your results that doesn't seem to be right and why you think that. What do you expect? 'something like a shock' is not nearly good enough...

In other words, please make it as easy as possible for us to help you.
 
  • #3
I ran your code and the results were a couple of plots without definition of the axis and no legend. Please don't make me guess and fix that as well.
 

FAQ: Thermoelasticity problem with FEM in MATLAB

What is the thermoelasticity problem?

The thermoelasticity problem involves the study of the interaction between thermal and mechanical fields in materials. It addresses how temperature changes affect the stress and strain in materials, taking into account both thermal expansion and mechanical loading. This is crucial in applications where materials are subjected to varying temperatures and mechanical forces.

How can I set up a thermoelasticity problem in MATLAB using FEM?

To set up a thermoelasticity problem in MATLAB using the Finite Element Method (FEM), you need to define the geometry of the domain, the material properties (such as thermal conductivity, Young's modulus, and Poisson's ratio), boundary conditions, and the governing equations for heat transfer and elasticity. You can use built-in functions in MATLAB or external toolboxes like PDE Toolbox to facilitate the modeling process.

What are the key equations involved in the thermoelasticity FEM analysis?

The key equations involved in thermoelasticity FEM analysis include the heat conduction equation for thermal analysis and the elasticity equations for mechanical analysis. The heat conduction equation is typically given by Fourier's law, while the elasticity equations are derived from Hooke's law. Coupling these equations allows for the simulation of thermal effects on mechanical behavior.

What are common challenges when solving thermoelasticity problems with FEM in MATLAB?

Common challenges include ensuring numerical stability, handling complex geometries, accurately defining boundary conditions, and managing the coupling between thermal and mechanical fields. Additionally, selecting appropriate mesh sizes and ensuring convergence of the solution can also pose difficulties in the analysis.

How can I visualize the results of a thermoelasticity analysis in MATLAB?

You can visualize the results of a thermoelasticity analysis in MATLAB using various plotting functions. Common methods include using 'surf' or 'mesh' for 3D surface plots of temperature distribution or stress fields, and 'contour' for 2D representations. Additionally, MATLAB allows for the creation of animations to illustrate changes over time or under varying conditions.

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