EQUILIBRIUM PROBLEM FOR A THERMOELASTIC KIRCHHOFF-LOVE PLATE WITH A DELAMINATED RIGID INCLUSION

EQUILIBRIUM PROBLEM FOR A THERMOELASTIC KIRCHHOFF-LOVE PLATE WITH A DELAMINATED RIGID INCLUSION

N. Lazarev, E. Sharın, G. Semenova

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Abstract

A new variational problem on the equilibrium of a thermoelastic heterogeneous Kirchho {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 con guration of crack's edges is known a priori. This assumption allows us to rewrite the well known nonpenetration condition for Kirchho {Love plates in a re ned 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 di erential statement is found.

Keywords

Thermoelastic plate, crack, nonpenetration, variational inequality, di erential setting.