纯位移线弹性方程Locking-Free非协调三棱柱单元的构造分析  

A Nonconforming Locking-Free Triangular Prism Element Analysis for Linear Elasticity Problem

作　　者：孙艳萍 陈绍春 Yanping Sun;Shaochun Chen(College of Science, Henan Institute of Engineering, Zhenzhou 451191;School of Mathematics and Statistics, Zhengzhou University, Zhenzhou 450001)

机构地区：[1]河南工程学院理学院 [2]郑州大学数学与统计学院

出　　处：《数学物理学报（A辑）》2019年第2期329-338,共10页Acta Mathematica Scientia

基　　金：国家自然科学基金(11701522);河南省教育厅科学技术研究重点项目(17A110017)~~

摘　　要：主要构造了三维空间中线弹性问题纯位移变分形式下无闭锁三棱柱单元.此单元是具有18个自由度的非协调元.单元的形函数满足位移的散度属于零次多项式空间,通过分析得到有限元解和真解误差的能量模具有一阶收敛性,L^2模具有二阶收敛性.This paper discuss the linear elasticity problem and constructs a nonconforming triangular prism element with 18 degrees of freedom. The shape functions of this element satisfy that the divergence of displacement is zeroth polynomial. We can deduce that the energy norm has the first order convergence rate and the L^2 norm has the second order convergence rate.

关 键 词：平面弹性问题 非协调单元 三棱柱单元 Strong引理 Lamé常数 

分 类 号：O242.21[理学—计算数学]