Equilibrium problem for an thermoelastic Kirchhoff–Love plate with a nonpenetration condition for known configurations of crack edges

Abstract

We formulate a new variational problem on the equilibrium of a thermoelastic KirchhoLove plate in a domain with a cut. It is assumed that the plate is under the special loads for which the conguration of crack's edges is known in advance. This circumstance makes it possible to write down the general boundary condition of nonpenetration in a rened form, which, in turn, leads to new relations describing the possible mechanical interaction of opposite crack edges. The initial formulation of a problem presupposes the fulllment of boundary conditions on the crack curve in the form of system of two inequalities and an equality. Solvability of the problem is proved, an equivalent dierential setting is found.

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

“…The Faedo–Galerkin method is applied to establish a solvability. The main difference from previous works [24,27] consists in the proof of suitable properties of the set scriptK, since the set scriptK additionally contains relations reflecting the connection with the space Rfalse(γfalse) and (2.1) characterizing rigid properties of the flat inclusion. Namely, we can prove convexity and closedness of K in the same way as it was proved in the work [33], where was considered the case of an elastic constitutive model for a Kirchhoff–Love plate with a flat rigid inclusion.…”

“…Thermoelastic models of plates with cracks have been studied, e.g. in [24][25][26][27]. Nonlinear thermoelastic shells were investigated, e.g.…”