Non-coercive problems for Kirchhoff–Love plates with thin rigid inclusion

Abstract

In the paper, we consider a boundary value problem for an elastic plate with a thin rigid inclusion in a non-coercive case. Both vertical and horizontal displacements of the plate are considered in the frame of the considered model. The inclusion is assumed to be delaminated from the plate which provides a crack between the inclusion and the surrounding elastic body. To guarantee a mutual non-penetration between crack faces, we consider inequality type boundary conditions with unknown set of a contact. A solution existence of the equilibrium problems is proved. Displacements of the plate in the x3-direction can be fixed at one or two points. In these cases, we also prove a solution existence of the boundary value problems.