Shape sensitivity analysis of the energy integrals for the Timoshenko-type plate containing a crack on the boundary of a rigid inclusion.

An equilibrium problem for an elastic Timoshenko-type plate containing a rigid inclusion is considered. On the interface between the elastic plate and the rigid inclusion, there is a vertical crack. Inequality-type boundary conditions are imposed at the crack faces to guarantee mutual nonpenetration. By using a sufficiently smooth perturbation determined in the middle plate plane, the variation of plate geometry is specified. The formula of the derivative of the plate energy functional with respect to the perturbation parameter is deduced. [ABSTRACT FROM AUTHOR]