用热场模拟应力函数场进行扭杆拓扑优化

基于稳态热传导问题和等直截面杆扭转问题控制方程形式上的相似性，利用现有的有限元分析软件，通过求解热场解决了扭转问题，并以此为基础，建立扭转问题的优化模型，采用罚函数法，对扭杆的横截面进行拓扑优化。最后，给出实例说明了该方法的可行性、可靠性和高效性。

Topology optimization of bars in torsion by means of simulation of stress field with thermal field

Based on the phenomenon that the problem of steadystate thermal conduction is mathematically similar to that of torsion of a straight bar with uniform cross-section, the torsion problem of the bars is solved with the help of the solution of thermal field and the software of finite element analysis. Taking this as a basis,an optimization model of bar torsion is set up and topology optimization of cross-section of bars in torsion is conducted with penalty function. Finally, an illustration is given to show the feasibility, reliability, and high-effectiveness.