Thermomechanical Contact of Elastic Bodies with Nonlinear Winkler Surface Layers

Abstract

We consider a thermoelastic contact problem for several bodies under the conditions of unilateral mechanical contact through nonlinear Winkler surface layers and the conditions of imperfect thermal contact. We obtain a weak formulation of this problem in the form of a system formed by a variational equation and variational inequality and also an alternative weak formulation in the form of a system of linear and nonlinear variational equations. To solve the system of variational equations of the thermomechanical contact problem, we develop parallel iterative Robin-type domain decomposition algorithms in each step of which it is necessary to solve two linear variational equations for each body one of which corresponds to the problem of heat conduction with Newton conditions in the zones of possible contact and the other corresponds to a problem of the theory of elasticity with Robin conditions in these zones and additional volume forces. We perform the analysis of the numerical efficiency of the proposed algorithms for the plane thermomechanical problem of contact between two elastic bodies by using finiteelement approximations.