Domain decomposition methods for problem of static equilibrium of system of elastic bodies connected through thin nonlinear interlayers

Abstract

We have proposed variational formulations of a problem of static equilibrium of a system
of elastic bodies connected through intermediate layers, the normal and tangential stiffness of
which is described by the nonlinear Winkler model. The conditions of existence and uniqueness of
a solution of the variational problems have been established. For solving the nonlinear variational
equation, that corresponds to the original contact problem, on the continuous level we have
developed a set of parallel nonstationary iterative domain decomposition methods of Robin type.
The numerical investigations of these methods for the problem of plane deformation of the threelayered
rectangular body using the finite element approximations have been performed.