平面应变问题广义有限元法

结合广义有限元和理性有限元,针对平面应变问题提出一种广义四边形单元.该单元考虑泊松效应,以节点位移自由度约束弹性力学平面应变方程的半解析解,构造单元位移模式的附加项,较准确地反映真实位移场,提高了单元的计算精度.首先推导广义单元及其等参单元的形函数,之后设计分片试验和数值算例来验证单元的精度,数值算例表明,在规则和非规则网格下新单元计算精度均优于传统有限元和广义有限元.新单元精度高且易于程序实现,可应用于实际工程的结构分析.

A Generalized Finite Element for Plane-Strain Problem

Considering advantages of generalized finite element and rational finite element a kind of quadrilateral elements (generalized element) is developed for plane-strain problem. The element includes Poisson's effect. Additional terms of displacement mode inside element are constructed according to semianalytical solution of node displacement degrees of freedom constraint elastic plane strain equation. The element reflects real displacement field accurately and elemental calculation accuracy was improved. Shape functions of generalized elements and generalized isoparametric elements are constructed and patch test and numerical tests are designed to verify calculation accuracy. Numerical tests indicate that whether in regular or irregular grid new element has higher accuracy than conventional element and generalized element. The element is convenient for implementation, which is suitable for practical engineering.