Shape sensitivity analysis of Timoshenko's plate with a crack under the nonpenetration condition

An equilibrium problem for an elastic transversely isotropic Timoshenko's plate with a curvilinear crack is considered. On the crack faces, the nonpenetration conditions, which have the form of inequalities (conditions of the Signorini type), are given. 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. An equilibrium problem for an elastic transversely isotropic Timoshenko's plate with a curvilinear crack is considered. On the crack faces, the nonpenetration conditions, which have the form of inequalities (conditions of the Signorini type), are given. 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.