The goal of this paper is to study a mathematical model of a nonlinear static frictional contact problem in elasticity with the mixed boundary conditions described by a combination of the Signorini unilateral friction...The goal of this paper is to study a mathematical model of a nonlinear static frictional contact problem in elasticity with the mixed boundary conditions described by a combination of the Signorini unilateral frictionless contact condition,and nonmonotone multivalued contact,and friction laws of subdifferential form.First,under suitable assumptions,we deliver the weak formulation of the contact model,which is an elliptic system with Lagrange multipliers,and which consists of a hemivariational inequality and a variational inequality.Then,we prove the solvability of the contact problem.Finally,employing the notion of H-convergence of nonlinear elasticity tensors,we provide a result on the convergence of solutions under perturbations which appear in the elasticity operator,body forces,and surface tractions.展开更多
基金The project supported by the NNSF of China Grants Nos.12001478,12026255,12026256 and 11961074,H2020-MSCA-RISE-2018 ResearchInnovation Staff Exchange Scheme Fellowship within the Project No.823731 CONMECH+3 种基金National Science Center of Poland under Preludium Project No.2017/25/N/ST1/00611It is also supported by the Startup Project of Doctor Scientific Research of Yulin Normal University No.G2020ZK07Natural Science Foundation of Guangxi Province Grants Nos.2018GXNSFDA281028 and 2020GXNSFBA297137the High Level Innovation Team Program from Guangxi Higher Education Institutions of China(Document no.[2018]35).
文摘The goal of this paper is to study a mathematical model of a nonlinear static frictional contact problem in elasticity with the mixed boundary conditions described by a combination of the Signorini unilateral frictionless contact condition,and nonmonotone multivalued contact,and friction laws of subdifferential form.First,under suitable assumptions,we deliver the weak formulation of the contact model,which is an elliptic system with Lagrange multipliers,and which consists of a hemivariational inequality and a variational inequality.Then,we prove the solvability of the contact problem.Finally,employing the notion of H-convergence of nonlinear elasticity tensors,we provide a result on the convergence of solutions under perturbations which appear in the elasticity operator,body forces,and surface tractions.
