一种基于H-R变分的杂交广义元方法  

A Hybrid Generalized Element Method Based on H-R Variational Principle

作　　者：杨森森[1] 马永其[1,2] 冯伟[1] 

机构地区：[1]上海大学上海市应用数学和力学研究所,上海200072 [2]上海大学理学院力学系,上海200444

出　　处：《应用数学和力学》2013年第3期272-281,共10页Applied Mathematics and Mechanics

基　　金：上海市科委基金资助项目(11231202700)

摘　　要：基于Hellinger-Reissner变分原理,通过构造合适的应力场函数使其能更方便和更准确地得到节点上的应力值,同时结合广义有限元构造广义位移插值的方法,在不提高单元节点数目的前提下提高位移场函数的阶次,从而提高其求解精度.这种方法能同时灵活地构造应力场和位移场,在同等精度条件下能占用较少内存和求解更少的方程数目,计算结果也显示了这种方法的有效性和很高的计算精度.Combining HeUinger-Reissner variational principle and the way of constructing displacement interpolation function of generalized finite element method to construct stress field and displacement field independently, through the suitable stress field could get a more precise stress value of node conveniently, and in the same time to increase the order of displacement function without increasing the number of element＇ s nodes, in this way a more accurate result was got. This method combines the above two methods of flexibility of constructing the stress field and displacement field, meanwhile, using less memory and equations on the same condition compared with some other methods, and the results also show that of efficiency and higher presicion.

关 键 词：杂交元 Hellinger-Reissner变分原理 广义有限元法 节点位移插值函数 应力函数 

分 类 号：O34[理学—固体力学]