Kirchhoff — Love plate with a flat rigid inclusion

An equilibrium problem for a plate under the action of external forces is studied. It is assumed that the plate has a flat rigid inclusion. We suppose that there is a throng crack along a fixed part of the inclusions boundary. To exclude a mutual penetration between crack faces, inequality type of boundary conditions are imposed. The problem is formulated as a variational inequality. The differential formulation of the problem is obtained provided that the solution is smooth. An equivalence of two settings is established: variational and differential. The contact problem for an elastic plate with a flat rigid inclusion is also considered. The differential and variational formulations of the problem are given. The unique solvability of the problem is substantiated.