虚拟元方法求解混合边界条件下的线弹性问题  

Solving the linear elasticity problem with mixed boundary conditions on virtual element method

作　　者：马俊驰 程新博 梁晓坤 MA Junchi;CHENG Xinbo;LIANG Xiaokun(School of Mathematics,Liaoning Normal University,Dalian 116081,China)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116081

出　　处：《辽宁师范大学学报（自然科学版）》2023年第4期451-458,共8页Journal of Liaoning Normal University:Natural Science Edition

基　　金：国家自然科学基金资助青年项目(12001256);辽宁省教育厅高校基本科研项目(JYTMS20231045)。

摘　　要：研究虚拟元方法求解具有混合边界条件的线弹性问题.首先给定具有Dirichlet和Neumann混合边界条件的二维线弹性问题,通过变分原理得到其弱对称形式的变分格式,其次通过构造虚拟元空间和自由度得到相应的离散格式,然后根据投影算子与插值算子得到原问题的误差估计,最后通过带孔板的数值算例验证理论分析的可行性.This paper research the virtual element method is applied to linear elasticity problems with mixed boundary conditions.Firstly,the two dimensional linear elastic problem with mixed boundary conditions is given.The variational scheme of the weakly symmetric form is obtained by the variational principle.Secondly,the discrete scheme is obtained by constructing the virtual element space and degree of freedom.Then the error estimation of this problem is obtained according to the projection operator and interpolation operator.Finally,a numerical example of a plate with holes is given to verify the feasibility of the theoretical analysis.

关 键 词：虚拟元方法 线弹性问题 弱对称形式 混合边界条件 

分 类 号：O241.82[理学—计算数学]