Solvability of an equilibrium problem for a thermoelastic Kirchhoff-Love plate with an oblique crack

We formulate a variational problem of equilibrium for a thermoelastic Kirchhoff-Love plate with an oblique crack. In the initial state, the crack is given by a suficiently smooth surface, while opposite faces of the crack are in contact with each other. A general nonpenetration condition for oblique cracks is used, which was proposed by professor A. M. Khludnev for the Kirchhoff-Love plate in the framework of elastic constitutive relations. The peculiarity is that the condition is nonlocal. On the outer edge of the plate, conditions of rigid clamping are imposed. An initial temperature distribution is considered given. The solvability of the problem is proved under the assumption that the thermal expansion parameter is sufficiently small. The equilibrium equations are obtained in the subdomain corresponding to the part of the plate without the crack.