正交各向异性轴对称位势问题的Trefftz有限元分析  

Trefftz Finite Element Analysis of Axisymmetric Potential Problems in Orthotropic Media

作　　者：王克用[1,2] 黄争鸣[2] 李培超[1] 刘博[1] 

机构地区：[1]上海工程技术大学机械工程学院,上海201620 [2]同济大学航空航天与力学学院,上海200092

出　　处：《应用数学和力学》2013年第5期462-469,共8页Applied Mathematics and Mechanics

基　　金：上海高校青年骨干教师国内访问学者计划基金资助项目

摘　　要：Trefftz有限元法(Trefftz finite element method,TFEM)因其独特的优良品质而备受关注.针对正交各向异性轴对称位势问题,提出了一种4节点四边形环状单元.在该单元模型中,首先假设两套独立的位势插值模式:即单元域内场和网线场,然后代入修正变分泛函并利用Gauss散度定理消除区域积分,最后根据驻值原理导得只含边界积分的单元刚度方程.数值算例表明了该单元的准确性、稳定性以及对网格畸变的不敏感性.Trefftz finite element method （TFEM） has received considerable attention due to its excellent feasures. A four-node quadrilateral annular element was proposed for analyzing axi-symmetric potential problems in orthotropic media. In the element model, two independent po-tential interpolation modes, namely intra-element field and frame field, were firstly assumed. Then, they were both substituted into the modified variational functional and the domain inte-gral involved was eliminated using the Gaussian divergence theorem. Finally, the element stiff-ness equation including boundary integrals only was derived based on the stationary principle. Numerical examples demonstrate that the developed element is accurate, stable and insensitive to mesh distortion.

关 键 词：Trefftz有限元法 修正变分泛函 位势问题 轴对称 正交各向异性介质 

分 类 号：O343.1[理学—固体力学]