Project Overview
In this Abaqus project, the stress caused by a temperature increase is calculated using both Abaqus and an analytical solution. The results obtained from the Abaqus simulation are then compared with the analytical results.
This problem is selected from a Mechanics of Materials book and provides a useful example for understanding the effect of thermal expansion on a constrained mechanical system.
Model Geometry and Materials
The model consists of Rod AC, Cylinder BD, and a Rigid Bar CDE.
The length of Rod AC is 0.9 m, the length of Cylinder BD is 0.3 m, and the length of Bar CDE is 0.75 m.
Cylinder BD is made of brass, while Rod AC is made of steel.
Geometry and material configuration of the model.
Temperature Increase
Initially, the temperature of the entire model is 20°C. During the analysis, the temperature of the brass cylinder BD is increased to 50°C, while the temperature of the steel rod AC remains constant at 20°C.
The temperature increase in the brass cylinder causes thermal expansion, which is constrained by the surrounding mechanical system. As a result, thermal stress develops in the cylinder.
Stress in Cylinder BD
The main objective of the analysis is to calculate the stress generated in Cylinder BD as a result of the temperature increase.
The stress obtained from the Abaqus simulation is 44.75 MPa, while the analytical solution gives a stress of 44.8 MPa.
Stress obtained in Cylinder BD from the Abaqus analysis.
Analytical Solution
The thermal stress in Cylinder BD is also calculated using an analytical solution.
First, the temperature increase in the brass cylinder is determined. The cylinder temperature increases from 20°C to 50°C, resulting in a temperature change of 30°C.
The free thermal expansion of Cylinder BD is then determined based on its length and the thermal expansion properties of brass. Because the cylinder is part of a constrained mechanical system, its free thermal expansion cannot occur without resistance from the surrounding components.
The resulting force in Cylinder BD is determined by considering the equilibrium of the system and the deformation compatibility between Rod AC, Cylinder BD, and the rigid Bar CDE.
Finally, the thermal stress in the brass cylinder is calculated from the resulting force and the cross-sectional area of Cylinder BD.
The analytical solution gives a stress of 44.8 MPa in Cylinder BD. The corresponding force in the cylinder is 31,700 N.
These analytical results are used as reference values for comparison with the results obtained from the Abaqus simulation.
Analytical calculation of the thermal stress in Cylinder BD.
Comparison with Analytical Solution
The stress obtained from Abaqus is very close to the value calculated using the analytical solution. The Abaqus result is 44.75 MPa, compared with 44.8 MPa from the analytical solution.
This close agreement demonstrates that the Abaqus model can accurately reproduce the expected thermal stress in the system.
Force in Cylinder BD
In addition to the stress, the force acting on Cylinder BD is calculated using Abaqus and compared with the analytical solution.
The force obtained from the Abaqus simulation is 31,633 N, while the analytical solution gives a force of 31,700 N.
Force acting on Cylinder BD during the thermal analysis.
Direction of the Forces
The force acting on Cylinder BD is directed upward, while the force acting on Rod AC is directed downward.
Direction of the forces acting on Cylinder BD and Rod AC.
What You Will Learn
- How to model a thermally loaded mechanical system in Abaqus.
- How to define steel and brass materials.
- How to model a rigid bar in Abaqus.
- How to apply a temperature increase to a component.
- How to calculate thermal stress in a constrained component.
- How to obtain stress results from Abaqus.
- How to calculate the force generated by thermal expansion.
- How to solve the problem using an analytical solution.
- How to compare Abaqus results with analytical results.
Key Features
- Thermal stress analysis using Abaqus.
- Analytical solution for comparison.
- Steel Rod AC.
- Brass Cylinder BD.
- Rigid Bar CDE.
- Temperature increase from 20°C to 50°C in the brass cylinder.
- Stress calculation in Cylinder BD.
- Force calculation in Cylinder BD.
- Comparison between Abaqus and analytical results.
- Abaqus CAE file.
- Abaqus INP file.
- Step-by-step training video.
Project Information
Important information about this project
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Abhinav T
Thank you for sharing information and hands-on exercises on Abaqus software concepts.
Admin
Thank you