Investigation of Contact between Elastic Bodies One of Which has a Thin Coating Connected with the Body through a Nonlinear Winkler Layer by the Domain Decomposition Methods

We consider the problem of contact interaction between two elastic bodies one of which has a coating in the form of a thin Timoshenko-type shell connected with the body through a nonlinear Winkler layer. We present a weak formulation of this problem in the form of a nonlinear variational equation. We propose a class of iterative domain decomposition methods that reduce the solution of this equation to the solution, in each iteration, of independent linear variational equations corresponding to problems of elasticity for massive bodies and a problem of the Timoshenko theory of shells for the coating with Robin boundary conditions imposed on the contact boundaries. The conditions of weak convergence of these methods are established. We analyze the numerical efficiency of the obtained algorithms with the use of finite-element approximations.