模拟求解任意截面杆扭转的化复为单有限元方法

根据柱体扭转问题的应力函数理论,采用空心材料刚度弱化思想,提出“化复为单”的有限元近似离散与计算新方法,建立了求解具有任意横截面形状的扭杆扭转问题的二维通用有限元方法.并根据稳态热传导问题和扭转问题的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分析热场,模拟求解了扭转问题.数值计算结果表明,该方法概念简单、通用性强、适用于任意截面扭杆,是一种分析任意直杆扭转问题的应力和抗扭刚度的有效方法.

A special simulation solution for torsional bars with arbitrary cross-section using finite element method

According to stress function theory of torsion bars,a general 2-dimensional finite element method has been developed for the analysis of torsional bars with arbitrary cross-section,where a new idea of "multiplicity-to-simplicity transformation" was proposed.And based on the analogy between controlling equation of steady thermal conduction and that of torsional bars,the latter was simulatively solved by analyzing the corresponding thermal conduction together with the existing FEA software.Numerical results showed that the proposed method has an advantage of simplicity and generality in stress analysis and torsional rigidity computation.It is an efficient method suitable for dealing with torsional bars with arbitrary cross-section.