Differentiation of the energy functionals for equilibrium problems of the Kirchhoff–Love plates with nonpenetration conditions for known configurations of plate edges

Equilibrium problems for elastic plates with a rectilinear crack are studied. It is assumed that under the action of certain given loads, plates have deformations with a certain predetermined configuration of edges near the crack. On the crack curve, we impose a nonlinear boundary condition as an inequality describing the nonpenetration of the opposite crack faces. Assuming that the parameter $\delta$ describes the crack perturbation, the derivative of the energy functional with respect to $\delta$ is found. The results are obtained for new mathematical models with new nonlinear boundary conditions describing special character of the mechanical contact interaction of the plate edges.