线弹性问题的locking-free双参数元(英文)  

Locking-free DSP Element for Linear Elasticity Problem

作　　者：孙会霞[1] 肖留超[1] 

机构地区：[1]河南工业大学理学院,郑州450001

出　　处：《工程数学学报》2011年第1期118-128,共11页Chinese Journal of Engineering Mathematics

基　　金：The Natural Science Foundation of the Education Department of Henan Province (2009A110003;2010A110005);the International Science and Technology Cooperation Project of Henan Province;the Foundation of Henan University of Technology

摘　　要：文中运用双参数法提出了一个4参数的四边形非协调有限元,讨论了该单元对纯位移边界条件下的均匀介质线弹性方程的逼近问题.证明了在材料几乎不可压时单元对弹性问题的一致最优收敛性,数值试验验证了理论分析结果.并通过构造后处理算子,得到了超收敛结果.所有的分析结果都可以推广到三维情形.A four-parameter quadrilateral nonconforming finite element with DSP（double set parameters） is proposed to approximate the pure displacement linear elasticity problem for homogeneous isotropic material.It is shown that the performance of the scheme does not deteriorate as the material becomes nearly incompressible.Numerical results are also given to verify the theoretical analysis.Furthermore,the superconvergence result is obtained through a postprocessing operator.All the results can be extended to three dimensional case.

关 键 词：四边形非协调元 双参数 无闭锁 线弹性 插值后处理 

分 类 号：O242.21[理学—计算数学]