A locking-free weak Galerkin finite element method for elasticity problems in the primal formulation
A locking-free weak Galerkin finite element method for elasticity problems in the primal formulation
复制标题
解决原始公式弹性问题的无锁弱伽辽金有限元方法
DOI：
10.1016/j.cam.2015.12.015
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发表时间：
2016-12-01
影响因子：
2.4
通讯作者：
Zhang, Ran
中科院分区：
文献类型：
--
作者：
Wang, Chunmei;Wang, Junping;Zhang, Ran
本文利用弱伽辽金（WG）有限元方法，给出了一般多边形/多面体分区上线弹性问题的任意阶无锁定数值格式。与其他WG方法一样，线弹性力学的关键思想是引入离散的弱应变和应力张量，这些张量通过求解每个单元上的廉价局部问题来定义和计算。这样的局部问题是从相应的微分算子的弱公式，通过积分的部分。当精确解是光滑的时，在离散的H-1模和通常的L-2模下，得到了最优阶的无锁定误差估计。数值结果表明，弱伽辽金有限元方法的效率，精度和锁定自由的财产。由爱思唯尔公司出版
This paper presents an arbitrary order locking-free numerical scheme for linear elasticity on general polygonal/polyhedral partitions by using weak Galerkin (WG) finite element methods. Like other WG methods, the key idea for the linear elasticity is to introduce discrete weak strain and stress tensors which are defined and computed by solving inexpensive local problems on each element. Such local problems are derived from weak formulations of the corresponding differential operators through integration by parts. Locking-free error estimates of optimal order are derived in a discrete H-1-norm and the usual L-2-norm for the approximate displacement when the exact solution is smooth. Numerical results are presented to demonstrate the efficiency, accuracy, and the locking free property of the weak Galerkin finite element method. Published by Elsevier B.V.