An equilibrium problem for an elastic plate with an inclined crack on the boundary of a rigid inclusion

We consider an equilibrium problem for a Kirchhoff–Love elastic plate with an inclined crack on the boundary of a rigid inclusion. The nonpenetration conditions are considered at the crack faces in the form of equalities and inequalities. On the boundary of the rigid inclusion, some identity holds describing the action of the external forces on the rigid part of the plate. The variational statement of the problem is studied, and an equivalent boundary value problem is formulated. For a family of problems about a plate with inclined crack on the boundary, we analyze the passage to the limit as the rigidity parameter of the inclusion tends to infinity.