Variational Inequalities For The Plane Elastic Contact Problems And Its Numerical Solution

The contact problem is often encountered in the engineering and other practice fields.It is highly linear because the contact surface between the related bodies is indefinite,and the constraint equation for a contact state is taken as the essential non- linear behavior which usually controls the entire process of the deformation.Therefo- re,the contact problem is very complex from the view points of theoretical research and engineering design.The recently developed parallel method for solving variation- al inequality problems, provides a united frame and a powerful facility for the study of contact problem.It formulates all the boundary conditions and contact conditions to one variational inequality so that the related theoretical analysis becomes relatively easy.In this thesis,We describe the variational principles for the boundary problem, along with the related concepts and theory,and point out the generalized Schwarz algorithms for variational inequalities of contact problem firstly.Compared with the classical Schwarz algorithm,the generalized Schwarz algorithms replace transmission conditions on the interface between subdomains by the Robin conditions with parame- ters.It is intent to speeding up the convergence rate by choosing Robin parameters.S- econdly,we describe the contact problem based on the fundamental relational expres- sion of elastic mechanics,and give the variational inequality of the plane elasticity contact problem with frictionless based on the Green's formula and smallest potential energy theory,and then proved the existence and uniqueness of solution.Furthermo- re, it is given of the generalized Schwarz algorithms with two nonoverlapping subdo- mains and extended the two subdomains into multi-domains based on plane elasticity contact problem.We establish the convergence theorems.Finally,we present some numerical results.These numerical tests show that the algorithms are efficient and si- gnificant.