Method of fictitious areas in a task about balance of a plate of Kirchhoff–Lyava

In this article we consider the problem of equilibrium of an elastic plate, which on part of the boundary in contact with a rigid obstacle. On this part of the boundary defined boundary conditions like inequalities describing the lack of penetration points of the plate and a rigid body. Equilibrium problem is set in the form of variational inequalities. Solvability of the problem is established and is proved the equivalence of the two formulations: variational and differential. By applying the method of fictitious areas proved that solutions of the family of auxiliary problems defined in the wider area, converge to the solution of the initial contact problem. In addition, each auxiliary problem in the extended area simulates the equilibrium plate with a crack.