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

Abstract

A new variational problem on the equilibrium of a thermoelastic heterogeneous Kirchhoff–Love plate is considered in a domain with a cut. The cut corresponds to an interfacial crack located on a part of the boundary of a rigid inclusion. We suppose that the plate is under the special loads for which the configuration of crack’s edges is known a priori. This assumption allows us to rewrite the well known nonpenetration condition for Kirchhoff–Love plates in a refined form, which, in turn, leads to new relations describing the possible mechanical interaction of opposite crack edges. Displacements on the rigid inclusion satisfy special constraints having a linear form. Solvability of the problem is proved, an equivalent differential statement is found.