Fictitious domain method in the equilibrium problem for a Timoshenko-type plate contacting with a rigid obstacle

In this paper we study the nonlinear equilibrium problem for the plate with the Signorini condition on the part of the boundary. We construct a family of auxiliary problems defined in an extended domain so that their solutions converge properly to a solution of the Signorini problem. Each problem of this family describes the equilibrium of the plate with a crack. On the curve defining the crack we impose a boundary condition of an inequality type describing the non-penetration of opposite crack edges. Equivalent differential formulation of the problems is found.