An equilibrium problem for the Timoshenko-type plate containing a crack on the boundary of a rigid inclusion

An equilibrium problem for an elastic Timoshenko type plate containing a rigid inclusion is considered. On the interface between the elastic plate and the rigid inclusion, there is a vertical crack. It is assumed that at both crack faces, boundary conditions of inequality type are considered describing a mutual non-penetration of the faces. A solvability of the problem is proved, and a complete system of boundary conditions is found. It is also shown that the problem is the limit one for a family of other problems posed for a wider domain and describing an equilibrium of elastic plates with a vertical crack as the rigidity parameter goes to infinity.