On equilibrium problem for a two-layer structure in the presence of a defect

Abstract

The equilibrium problem of the structure, which consists of two elastic plates, is considered. It is assumed that the plates are flatly deformed, and the layers are modeled as elastic bodies. Plates are glued along a given line. In addition there is a defect along the gluing line in one of the layers. On the defect faces, nonlinear boundary conditions containing the damage parameter are established. Using the variational approach, the solvability of this problem is proved. In the problem, the passage to the limit is carried out when the damage parameter tends to zero and to infinity. Differential formulations for the corresponding limit problems are obtained. The case of the rigidity of one of the layers tends to infinity is considered; the obtained limit problem is analyzed.