Contact Problem for Elastic Bodies of Different Dimensions

In this paper a variational problem describing a contact between an elastic plate and a thin elastic beam is investigated. It is assumed that the contact zone is a priori unknown and is to be defined. The given model is described by the energy functional minimization problem over a set of admissible displacements or by the equivalent variational inequality for the fourth order operator. Various formulations of problem and their equivalence are investigated. Boundary conditions, fulfilled on a set of possible contact and their exact interpretation are found.