Calculation of Stress due to temperature increase using the Abaqus software and the Analytical Solution

Calculation of Stress due to temperature increase using the Abaqus software and the Analytical Solution

In this example, we intend to calculate the Stress due to temperature increase using the Abaqus software and the Analytical Solution and then compare the results obtained from the Abaqus software with those of the Analytical Solution

As you observe in this picture, the Model includes rod AC, cylinder BD and, Rigid bar CDE. The length of rod AC is equal to 0.9 m, cylinder BD is 0.3 m and that of bar CDE is 0.75 m. The cylinder BD is made of brass, and the rod AC is made of steel

 This problem has been selected from Mechanics of Materials book

The statement is that the temperature of the entire model is 20 degrees Celsius, then the temperature of the brass cylinder increases to 50 degrees Celsius, while the temperature of the steel rod remains constant at the same temperature of 20 degrees Celsius

The purpose is to calculate the Stress in the cylinder BD. Actually, we will solve the problem using the Abaqus software and then compare the results obtained from the Abaqus software with Analytical Solution

The Stress in the cylinder BD obtained from the Abaqus software is equal to 44.75 MPa and the Stress in the cylinder BD obtained from the Analytical Solution is equal to 44.8 MPa. As you observe, the results obtained from the Abaqus software are so close to those gained from the Analytical Solution

As you observe, the direction of the force applied to cylinder BD is upwards and the direction of the force applied to the rod AC is also downward

In the next step , we want to calculate the force applied to the cylinder BD

The force having been applied to cylinder BD has been obtained from the Abaqus software is equal to 31633 Newton and The force having been applied to cylinder BD has been obtained from the Analytical Solution is equal to 31700 Newton