四节点四边形数值流形方法及其改进  

Four Nodal Quadrilateral Numerical Manifold Method and Its Improvement

作　　者：魏高峰[1] 冯伟[1] 

机构地区：[1]上海大学上海市应用数学和力学研究所

出　　处：《力学季刊》2006年第1期112-117,共6页Chinese Quarterly of Mechanics

摘　　要：本文对四节点四边形流形元提出了改进措施,将覆盖位移函数用自然坐标表示,使得在一般非规则有限数学覆盖网格下,数值积分变得比较容易,克服了现有四节点四边形流形单元数值积分困难的缺点。数值算例将其应用于复合材料数值模拟,计算结果表明,当覆盖位移函数采用完全一阶等参多项式时,计算精度较传统有限元法有很大改进。在力应集中或应力突变的区域,无需网格加密,只需提高覆盖位移函数的阶次即可。The four nodal quadrilateral numerical manifold method was improved for the covered displacement function expressed by natural coordinate. It makes much easy for the integration of four nodal quadrilateral numerical manifold element in irregular covered mathematical mesh form. An example for a type of composites was presented by numerical calulation. The results show that the improved method is more accurate than the traditional finite element method when first order isoparametric polynomial is adopted in the covered displacement function. In order to get efficient simulation results in the stress concentration or sudden stress change area, the higher order of covered displacement function can be implemented rather than locally adding mesh density.

关 键 词：流形方法 有限覆盖技术 数值模拟 等参变换 覆盖位移函数 

分 类 号：O343.2[理学—固体力学]