The Variational Problem of the Unilateral Contact between an Elastic Plate and a Beam

In the paper, we consider an unilateral contact problem for a nonhomogeneous elastic plate and a thin elastic beam. A variational formulation is given and a complete system of boundary conditions is presented consisted of a system of equations and inequalities. When the beam crosses the external boundary, a family of problems given in an extended domain with a parameter is analyzed. The convergence of these problems' solutions to the original solution is shown as the parameter vanishes. We analyse the limit case corresponding to the unbounded increase of the bending rigidity of the beam.