Equilibrium problem for a thermoelastic Kirchhoff–Love plate with a delaminated flat rigid inclusion

Abstract

A new mathematical model describing an equilibrium of a thermoelastic heterogeneous Kirchhoff–Love plate is considered. A corresponding nonlinear variational problem is formulated with respect to a two-dimensional domain with a cut. This cut corresponds to an interfacial crack located on a given part of the boundary of a flat rigid inclusion. The flat inclusion is described by a cylindrical surface. Due to the presence of the flat rigid inclusion in the plate, restrictions of the functions describing displacements to the corresponding curves satisfy special constraints having a linear form. Displacement boundary conditions of an inequality type are set on the crack faces that ensure a mutual non-penetration of opposite crack faces. Solvability of the problem is proved. Under the assumption that the solution of the variational problem is smooth enough, an equivalent differential formulation is found. This article is part of the theme issue ‘Non-smooth variational problems and applications’.