Equilibrium problems for Kirchhoff–Love plates with nonpenetration conditions for known configurations of crack edges

Abstract

The paper focuses on nonlinear problems describing the equilibrium of Kirchhoff–Love plates with cracks. We assume that under an appropriate load, plates have special deformations with previously known configurations of edges near a crack. Owing to this particular case, we propose two types of new nonpenetration conditions that allow us to more precisely describe the possibility of contact interaction of crack faces. These conditions correspond to two special cases of configurations of plate edges. In each case, the nonpenetration conditions are given in the form of a system of equalities and inequalities. For initial variational statements, we prove the existence and uniqueness of solutions in an appropriate Sobolev space. Assuming that the solutions are sufficiently smooth, we have found differential statements that are equivalent to the corresponding variational formulations. The relations of the obtained differential statements are compared with the well-known setting of an equilibrium problem for a Kirchhoff–Love plate with the general nonpenetration condition on crack faces.