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

摘要

The equilibrium problem of the structure, which consists oftwo elastic plates, is considered. It is assumed that the plates are flatlydeformed, and the layers are modeled as elastic bodies. Plates are gluedalong a given line. In addition there is a defect along the gluing line inone of the layers. On the defect faces, nonlinear boundary conditionscontaining the damage parameter are established. Using the variationalapproach, the solvability of this problem is proved. In the problem, thepassage to the limit is carried out when the damage parameter tends tozero and to infinity. Differential formulations for the corresponding limitproblems are obtained. The case of the rigidity of one of the layers tendsto infinity is considered; the obtained limit problem is analyzed.