拉压不同模量材料的参变量变分原理和有限元方法  

THE PARAMETRIC VARIATIONAL PRINCIPLE AND FINITE ELEMENT METHOD FOR MATERIAL WITH DIFFERENT MODULUS IN TENSION AND COMPRESSION

作　　者：张洪武[1] 张亮[1] 高强[1] 

机构地区：[1]大连理工大学工程力学系工业装备结构分析国家重点实验室,大连116024

出　　处：《工程力学》2012年第8期22-27,38,共7页Engineering Mechanics

基　　金：国家自然科学基金项目(90715037;11072051;10721062);73项目(2010CB832704)

摘　　要：对具有拉伸和压缩不同模量的材料,建立了平面静力问题的参变量变分原理。基于参变量变分原理,并结合有限元方法,将拉压不同模量平面问题转化为互补问题求解。经典的Lemke算法被用于求解此互补问题。该方法避免了应力状态的假设和刚度矩阵的更新,算法稳定,且收敛速度快。The parametric variational principle is established for the static problem with different modulus in tension and compression. Based on the parametric variational principle and finite element method, the 2-D bimodular static problem is transformed into a linear complementarity problem that can be solved by using Lemke＇s algorithm. The method doesn＇t need the pre-assumption of the stress state and the update of the stiffness matrix. Numerical examples show that the proposed method is stable and significantly accelerates the convergence of solution.

关 键 词：拉压不同 非线性 参变量变分原理 互补问题 有限元 

分 类 号：O343[理学—固体力学]