多尺度四边形单元网格连接方法研究  

Research on the Connection of Multi-scale Quadrilateral Finite Element Meshes

作　　者：方锡武[1] 林晓华[1] 刘振宇[2] FANG Xiwu;LIN Xiaohua;LIU Zhenyu(School of Mechanical Engineering,Nanjing Institute of Technology,Nanjing 211167;State Key Laboratory of CAD& CG,Zhejiang University,Hangzhou 310027)

机构地区：[1]南京工程学院机械工程学院,南京211167 [2]浙江大学CAD&CG国家重点实验室,杭州310027

出　　处：《机械工程学报》2019年第9期100-106,共7页Journal of Mechanical Engineering

基　　金：国家自然科学基金(51475418,U1608256);南京工程学院引进人才科研启动基金(YKJ201402)资助项目

摘　　要：针对多尺度问题分析时在两个异构的有限元网格接触界面存在单元结点不匹配而导致结点属性不能连续传递的问题,提出了多结点四边形单元结点形函数构建方法。首先将不规则四边形单元及其多结点通过等参逆变换转成规则正方形单元及其多结点,然后在规则单元中,以每个结点为基点,沿相互正交的两个方向在本单元内寻找近邻结点,以基点与近邻结点之间的距离和它们的属性变化值来建立该结点形函数的两个乘积因子,从而构建多结点形函数和修正原结点形函数,形函数将结点属性值的影响域限制在由基点和近邻结点所确定的四边形可控区域之内,实现了两接触网格结点属性在接触界面的无缝连接,从而保证了分析区域的场量变化的连续性、一致性和各向同性。A nodal shape function construction method of a multi-node quadrilateral element is put forward in this paper for the discontinuous transmission of nodal property on the interface of two nonmatching finite element meshes in analyzing multi-scale problems. First, each irregular quadrilateral element and its nodes including additional nodes are transferred into regular quadrilateral element and nodes by interpolating with numerical inverse isoparametric mapping, then, each node on the regular quadrilateral element is treated as a base point, its neighboring nodes can be searched in two orthogonal directions, and two product factors of this nodal shape function are established by the distance from the base point to its neighboring nodes and the changing value of their nodal properties, thus all the nodal shape functions can be built. Each of the shape function makes the influence range of a nodal property in a controlled quadrilateral area determined by the base point and its neighboring nodes. It makes the property of the nodes on the interface of two contact meshes seamless connect, and it ensures the change of the field in the region for analysis be continuous,conforming and isotropic.

关 键 词：虚结点 异构网格:形函数 有限元 等参变换 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]