Unique solvability of an equilibrium problem for a Kirchhoff-Love plate with a crack along the boundary of a flat rigid inclusion

Abstract

A new model of an equilibrium problem for a Kirchhoff-Love plate with a flat cylindrical rigid inclusion and an interfacial crack is considered. As in previous works, we consider a rigid inclusion defined with the help of a cylindrical surface, but unlike the known models relating to the crack theory, we suppose that traces of derivatives of vertical displacements (deflections) satisfy certain boundary conditions. These conditions determine constant angles of normal fibers along an entire flat cylindrical inclusion. The interfacial crack is located on the boundary of the rigid inclusion. A condition of mutual non-penetration of opposite crack faces is given as an inequality on the crack curve. We prove the existence and uniqueness of a solution for this variational problem.