Energy functional derivative of the length of a curvilinear oblique cut in the problem of equilibrium of a Timoshenko plate

This paper describes the dependence of the solution of the problem of equilibrium of a Timoshenko plate and the total energy functional of the plate on the surface perturbation, which is an oblique crack. The nonlinearity of the problem is caused by the boundary conditions in the form of inequalities (conditions such as the Signorini conditions), which simulate mutual nonpenetration of the opposite crack faces. The continuous dependence of the solution of the problem on the perturbation of the crack length is established. A formula for the energy functional derivative of the perturbation of the crack length is obtained.