摘要
利用基面力概念,给出一种任意形状网格都可以使用的柔度矩阵表达式的具体形式,运用拉格朗日乘子法得到以基面力为基本未知量的余能原理有限元支配方程,提出计算节点位移的表达式,编制出相应的任意网格有限元计算程序。该文对不同形状的单元网格以及畸变网格进行了计算分析,并与理论解和传统的有限元进行了对比和讨论。结果表明:该方法可以适用于任意形状的有限元网格,对网格的畸变不敏感。
An explicit expression of element compliance matrix of the finite element method for arbitrary meshes is derived using the base forces. The governing equations expressed by the base forces are obtained using Lagrangian multiplier method, and the displacements formulation of nodes is given. A program of the finite element method is developed. The method is used to solve several problems of arbitrary polygonal meshes and aberrant meshes, and the numerical results are compared with those of the theoretical solutions and traditional finite element method solutions. The results show that the method proposed is efficient to employ the arbitrary meshes and is free from mesh aberrant.
出处
《工程力学》
EI
CSCD
北大核心
2007年第10期41-45,56,共6页
Engineering Mechanics
基金
国家自然科学基金资助项目(19572001)
教育部高等学校博士学科点专项科研基金资助项目(20030004003)
北京市教委科技发展计划面上项目(KM200510005016)
北京市属市管高校人才强教计划资助项目(05004999200602)
关键词
有限元
余能
柔度矩阵
基面力
任意网格
finite element
complementary energy
compliance matrix
base forces
arbitrary meshes
