A contact problem for an elastic plate with a thin rigid inclusion

Under study is an equilibrium problem for a plate under the influence of external forces. The plate is assumed to have a thin rigid inclusion that reaches the boundary at the zero angle and partially contacts a rigid body. On the inclusion face, there is a delamination. We consider the complete Kirchhoff–Love model, where the unknown functions are the vertical and horizontal displacements of the middle surface points of the plate. We present differential and variational formulations of the problem and prove the existence and uniqueness of a solution.