Existence and numerical approximation of a solution to frictional contact problem for electro-elastic materials

作     者：Othman Baiz EL-Hassan Benkhira Rachid Fakhar Othman Baiz;EL-Hassan Benkhira;Rachid Fakhar

作者机构：University Ibn ZohrLab.ESERFP of OuarzazateMorocco University Moulay IsmailFaculty of SciencesLaboratory MACSESTMBP 3103Toulal-MeknesMorocco University Sultan Moulay SlimaneLaboratory LS2MEPolydisciplary Faculty of Khouribga25000 KhouribgaMorocco 

出 版 物：《Applied Mathematics(A Journal of Chinese Universities)》 (高校应用数学学报（英文版）（B辑）)

年 卷 期：2024年第39卷第2期

页      面：201-219页

核心收录：

学科分类：08[工学] 080101[工学-一般力学与力学基础] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

主　　题：piezoelectric material frictional contact variational Inequality fixed point process finite element method error estimation iteration method 

摘      要：In this paper,a frictional contact problem between an electro-elastic body and an electrically conductive foundation is studied.The contact is modeled by normal compliance with finite penetration and a version of Coulomb’s law of dry friction in which the coefficient of friction depends on the slip.In addition,the effects of the electrical conductivity of the foundation are taken into account.This model leads to a coupled system of the quasi-variational inequality of the elliptic type for the displacement and the nonlinear variational equation for the electric potential.The existence of a weak solution is proved by using an abstract result for elliptic variational inequalities and a fixed point argument.Then,a finite element approximation of the problem is presented.Under some regularity conditions,an optimal order error estimate of the approximate solution is derived.Finally,a successive iteration technique is used to solve the problem numerically and a convergence result is established.