Rigid Switching on in the Contact Problem for Elastic Plates

We consider a family of problems describing the contact of elastic plates located at a fixed angle to each other and, in the natural state, touching along a line. The plates are subjected only to bending. We study passage to the limit from elastic switching on to rigid switching on. We show that the limiting problems describe exactly the contact of an elastic plate with a rigid bar and the problem of the equilibrium of an elastic plate with rigid switching on. We establish the solvability of the problems, find the boundary conditions holding on the possible contact set and their precise interpretation.