一个二阶收敛的平面弹性问题Locking-free三角形元  

A Locking-free Triangular Element with Second-order Convergence for the Planar Elasticity Problem

作　　者：陈绍春[1] 任国彪[1] 

机构地区：[1]郑州大学数学系,郑州450052

出　　处：《工程数学学报》2009年第3期509-518,共10页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10771198;10590353)

摘　　要：对于纯位移平面弹性问题,以往构造的单元的能量模误差多是一阶收敛的,本文在不完全三次多项式空间中,基于divv∈P1的限制构造了一个14自由度的非协调三角形单元,该单元是Locking-free的,且能量模和L2―模误差分别达到了二阶和三阶收敛,并且通过数值实验验证了该单元的理论结果。Most of the existing finite elements for the pure displacement planar elasticity problem are one order convergent. In this paper, a 14 degrees of freedom nonconforming triangular element is constructed whose shape function space is a subspace of P3^2 with div∈P1. The element is locking-free, its error rates of energy norm and L2 norm are order 2 and 3, respectively. Some numerical experiments are carried out to show the validity of our theoretical analysis.

关 键 词：平面弹性 LOCKING-FREE 有限元 

分 类 号：O242.21[理学—计算数学]