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

Abstract

The problem of equilibrium of a Kirchhoff–Love elastic plate with an inclined crack on the boundary of a rigid inclusion is considered. On the crack faces, the nonpenetration conditions are set in the form of equations and inequalities. On the boundary of the rigid inclusion, an identity holds that describes the impact of external forces on the rigid part of the plate. Some variational formulation of the problem is studied, and also an equivalent boundary value problem is formulated. The passage to the limit is considered for a family of problems about a plate with an inclined crack on the boundary of an elastic inclusion as the parameter of inclusion rigidity tends to infinity.