A contact of two elastic plates connected along a thin rigid inclusion

A contact of two Kirchhoff—Love plates of the same shape and size is considered. The plates are located in parallel without a gap and are clamped at their outer edges. Those plates are connected to each other along a thin rigid inclusion. Three cases are considered. In the first case it is assumed that a force acts at the contact surface. This force is proportional to the difference between displacements of the contact surfaces points of two plates. In the second case a contact of two plates when that force on a contact surface equals zero is considered. The third case corresponds to an equilibrium problem of the two-layer Kirchhoff—Love plate containing thin rigid inclusion. For all three cases a solvability is studied, a variational and differential formulations of the problem are derived and their equivalence is proved. It is shown that the second and the third problems are limit cases of the first one when the value of the force acting on the contact surface tends to zero or to infinity.