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Theoretical solution of a spherically isotropic hollow sphere for dynamic thermoelastic problems
Hui-ming Wang1, Hao-jiang Ding, Wei-qiu Chen
1Department of Mechanics, Zhejiang University, Hangzhou 310027, China. wanghuiming@cmee.zju.edu.cn
Journal of Zhejiang University. Science
|March 27, 2003
Summary
A novel separation of variables method efficiently solves dynamic thermoelastic problems for hollow spheres, avoiding complex integral transforms. This approach accurately predicts stress responses under various thermal and mechanical conditions.
Area of Science:
- Solid Mechanics
- Continuum Mechanics
- Thermoelasticity
Background:
- Dynamic thermoelastic problems involve coupled thermal and mechanical stresses.
- Analyzing hollow spheres requires specialized methods due to geometry and boundary conditions.
- Existing methods may involve complex integral transforms, limiting applicability.
Purpose of the Study:
- To develop an efficient analytical method for spherically symmetric dynamic thermoelastic problems.
- To resolve the problem for hollow spheres of arbitrary thickness.
- To analyze responses under arbitrary thermal and mechanical loads.
Main Methods:
- Separation of variables method applied to the governing thermoelastic equations.
- Avoidance of integral transform techniques.
- Analytical solution for spherically isotropic elastic hollow spheres.
Main Results:
- The separation of variables method successfully resolved the dynamic thermoelastic problem.
- The method is applicable to hollow spheres of arbitrary thickness.
- Numerical results demonstrate dynamic stress responses in uniformly heated hollow spheres.
Conclusions:
- The separation of variables method provides an effective alternative to integral transform methods.
- This technique offers a robust approach for analyzing complex thermoelastic behaviors in hollow spheres.
- The findings are valuable for engineering applications involving hollow spherical structures.