Problem of equilibrium of the Timoshenko plate containing a crack on the boundary of an elastic inclusion with an infinite shear rigidity

A problem of equilibrium of a composite plate consisting of a matrix and an elastic inclusion with a through crack along the boundary of this inclusion is studied. The matrix deformation is described by the Timoshenko model, and the elastic inclusion deformation is described by the Kirchhoff–Love model. Conditions of mutual non-penetration of the crack edges are imposed on the curve that describes the crack. Unique solvability of the variational problem is proved. A system of boundary conditions on the curve bounding (in the mid-plane) the elastic inclusion is obtained. A differential formulation of the problem equivalent to the initial variational formulation is given.