摘要
传统的位移有限元法采用多项式形式的位移试函数,对于边数大于4的多边形单元,构造满足单元间协调性要求的多项式形式位移插值函数是一件困难的工作。本文利用逆距离权插值的思想并考虑到单元节点的分布,建立了边数大于4多边形单元上的有理函数形式的形函数。利用有理试函数,采用Galerkin法推导出求解平面弹性力学问题的有理单元法。采用有理单元法求解弹性力学问题,求解区域根据需要可以划分为任意多边形单元,极大地提高了网格划分的灵活性。有理单元法不依赖等参变换,不同单元的形函数表达形式统一,方便计算程序的编写。
In this paper by combining the ideas of inverse distance weighted interpolation and considering element nodes distribution, the shape functions of rational function forms are constructed on a polygonal element. The rational trial functions are automatically to ensure interelement compatibility. Adopting Galerkin method and rational trial function, the rational element method for solving elastic problems is derived. The computing domain could be divided into arbitrary polygonal elements. So it is very flexible in grid generation. The rational element method is independent of isoparametric transformation. Rational shape function expressions of different edge-number elements are similar in forms, so it is easy to deal with the program.
出处
《计算力学学报》
EI
CAS
CSCD
北大核心
2006年第5期611-616,共6页
Chinese Journal of Computational Mechanics
基金
山东建筑大学科研基金资助项目
关键词
弹性力学
多边形单元
有理函数形函数
有理函数插值
有理单元法
数值方法
elasticity problem
polygonal element
ratioanl shape functions
rational functioninterpolation
rational element method
