Abstract:
Two nonlinear mathematical models on equilibrium of plates in contact with obstacles of two types are studied. It is assumed that the plate contains a bulk rigid inclusion that touches the obstacle in the initial state. The first type of obstacle limits displacements of the plates to a square-shaped section lying on the front surface. The second type of obstacle also restricts displacements on the front surface, but has a pointwise character, i.e. Signorini-type conditions are specified at one given point. The convergence of solutions of a family of variational problems is proved as the parameter that determines the area of the contact zone tends to zero. It is shown that a limit function is the solution to the problem describing the pointwise contact of the plate.
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