任意多连通截面扭转应力函数的有限元解法  

Finite Element Solution for Torsion Stress Function With Arbitrary Multi-Connected Section

作　　者：王家林[1] 何琳[1] 张德立[1] 

机构地区：[1]重庆交通大学土木建筑学院,重庆400074

出　　处：《应用数学和力学》2013年第5期488-495,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(钢箱-砼组合拱结构性能与分析方法研究)(51078373)

摘　　要：杆件扭转问题的求解,主要有基于扭转理论翘曲函数的边界元法和有限元法、基于薄壁杆件理论的数值解法和基于扭转理论应力函数的有限元法.根据任意多连通截面直杆扭转问题的应力函数理论,讨论并改进了与微分方程及定解条件等效的泛函,在此基础上推导了求解多连通截面扭转应力函数的有限元列式,将扭转问题的翘曲位移单值条件转化为边界节点上的集中荷载.采用主从节点法满足孔洞边界上应力函数的同值条件,实现了任意多连通复杂截面扭转应力函数的有限元直接求解,通过应力函数积分获得截面的扭转常数.算例验证了方法的可行性和有效性.The major three methods can be used to solute the torsion bars＇ torsion problem. One is the boundary element method and the finite element method that is based on the warping function of torsion theory, the others are numerical solution based on the thin-wall theory and the finite element method based on the torsion stress function of torsion theory. According to stress function theory of torsion bars with arbitrary cross section, a functional equivalent to the torsion＇ s differential equation and definite condition was discussed and improved, finite ele-ment formulas were deduced to solute the torsion stress function for multi-connected section, the boundary condition of single warping-displacement value was changed to concentrated force loaded on boundary nodes. The condition that the stress function might be constant value on each hole boundary was satisfied by using master-slave node method, so the torsion stress function with arbitrary multi-connected complex section could be obtained directly by finite ele- ment method, and the torsion constant was solved by integrating from the torsion stress func- tion. Examples verified the feasibility and validity of this method.

关 键 词：多连通截面 扭转 应力函数 有限元 

分 类 号：O242.21[理学—计算数学] O343[理学—数学]