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[Solution]

This example is taken from Cornell University’s ANSYS AIM Learning Modules

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Contents

1. Problem Specification
2. Pre-Analysis
3. Geometry
4. Mesh
5. Physics Setup
6. Results Evaluation
7. Validation

Problem Specification

A steel bar (E=2.0E11 Pa,=0.3,α=1.2E-5) with the dimensions shown below is placed between two walls. On one side, the bar is rigidly fixed to the wall and on the other, there is a 2 mm gap between the wall and the bar. What is the maximum stress in the bar after the temperature increases 100 degrees Celsius?

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Pre-Analysis

First, we need to know if the expansion of the bar is greater than the free space between the bar and the wall, x = 0.002 meters. Below are the equation and the calculated result used for the expansion of the bar.

Now that we know that the deformation due to the change in temperature will be greater than the space between the bar and the wall, we know that there will be a stress on the bar. If the wall was not there, the bar would fully deform to the calculated value above. Since the wall does stop the deformation process, the following equation can be used.

Where T is the strain contribution from the change in temperature and is the strain contribution from the force imparted by the wall on the bar. This equation can be combined with the first one to make the following.

Substituting  , we get the solvable equation

Solving for , we find that

After substituting, we find

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Geometry

In this video, you will learn how to create a square shaped bar and then split it to retain a symmetrical section of the model.

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Mesh

In this video, you will learn how to generate fine mesh on the geometry.

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Physics Setup

In this video, you will learn how to define structural and thermal conditions required for this analysis.

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Results Evaluation

In this video, you will learn how to evaluate thermal and structural results.

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Validation

In the pre-analysis, the maximum stress was calculated. In order to verify that our simulation was accurate, a comparison must be made. This maximum stress value is calculated as shown in Results video.  This maximum value can also be seen in the panel on the left when the Equivalent Stress 1 contour is displayed.

It can be seen that the maximum stress value from simulation (160 MPa) and the calculated value (160 MPa) are matching.