Abstract
We present equivalent variational formulations of the problem of unilateral contact of elastic bodies with nonlinear Winkler surface layers in the form of a nonquadratic variational inequality and a nonlinear variational equation. The existence and uniqueness of solutions of these variational problems are studied. To solve the nonlinear variational equation corresponding to the original contact problem, we propose a class of parallel iterative domain decomposition methods. In each step of these methods, it is necessary to simultaneously solve the linear variational equations for separate bodies equivalent (in a weak sense) to the problems of elasticity with the Robin boundary conditions in possible contact zones. The numerical investigation of the efficiency of proposed methods is carried out with the use of finite-element approximations.
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