Invariant integrals in equilibrium problem for a Timoshenko type plate with the Signorini type condition on the crack

The equilibrium problem for the elastic Timoshenko type plate with a crack is considered. On the crack faces, the non-penetration conditions of inequality type (Signorini type conditions) are given. It is proved that there exist invariant integrals that are equal to the derivative of the energy functional with respect to perturbation parameter.