纯位移线弹性方程Locking-Free非协调三棱柱单元的构造分析

数学物理学报 ›› 2019, Vol. 39 ›› Issue (2): 329-338.

纯位移线弹性方程Locking-Free非协调三棱柱单元的构造分析

孙艳萍^1,*(),陈绍春²

¹ 河南工程学院理学院郑州 451191
² 郑州大学数学与统计学院郑州 450001

收稿日期:2017-10-12 出版日期:2019-04-26 发布日期:2019-05-05
通讯作者: 孙艳萍 E-mail:yanpingsun2007@126.com
基金资助:
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)

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

Yanping Sun^1,*(),Shaochun Chen²

¹ College of Science, Henan Institute of Engineering, Zhenzhou 451191
² School of Mathematics and Statistics, Zhengzhou University, Zhenzhou 450001

Received:2017-10-12 Online:2019-04-26 Published:2019-05-05
Contact: Yanping Sun E-mail:yanpingsun2007@126.com
Supported by:
the NSFC(11701522);the Science and Technology Research Program of Education Department of Henan Province(17A110017)

摘要/Abstract

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，L²模具有二阶收敛性.

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

Abstract:

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 L² norm has the second order convergence rate.

Key words: Planar elasticity problem, Nonconforming element, Triangular prism element, Strong lemma, Lamé constant

中图分类号:

O242.21

孙艳萍,陈绍春. 纯位移线弹性方程Locking-Free非协调三棱柱单元的构造分析[J]. 数学物理学报, 2019, 39(2): 329-338.

Yanping Sun,Shaochun Chen. A Nonconforming Locking-Free Triangular Prism Element Analysis for Linear Elasticity Problem[J]. Acta mathematica scientia,Series A, 2019, 39(2): 329-338.

图/表 1

参考文献 18

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