二维任意多边形有限单元

ARBITRARILY POLYGONAL 2-D FINITE ELEMENTS

目前常用于单晶体材料的计算细观力学分析方法是将晶体细分成许多三角形或四边形有限元，对于多晶体材料，这方法的计算量之大将难于承受，实验观测表明，多晶体材料中除角点附近局部区域外每个晶体内部的变形、滑移基本上是绶慢变化的，因此可以将每个晶体简化为一个多边形有限单元，晶界简化为界面单元，使计算量大大减少，本文导出一类任意多边形等参有限元格式，并证明这类多边形单元中的任意两个都是相互协调的，无论其边数是否相等，算例表明任意多边形单元是有效可行的．

At present, the computational analysis of micromechanics used to single crystalis to divide a crystai into many triangular or quadrilateral finite elements. If we use thismethod to analyze polycrystalline materials, the computation work will be too massive。Experimental observations show that the deformation and slide state vary slowly inside everycrystal of the polycrystalline material. Therefore each crystal may be idealized to a polygonalelement and each crystal interface to an interface eleinent, in so doing the computation workwill considerably reduce, In this paper we deduce flnite element formulations for a set ofarbitrarily polygonal isoparametric elements and show that such elements are compatibleone another, regardless of the difference of number of sides betweJen adjacent elements。Numerical examples are presented to check the validity of proposed polygonal elements。