Unilateral contact problem for two inclined elastic bodies

The paper concerns an analysis of unilateral contact problems between two inclined elastic plates and between a plate and a beam. Considered problems are characterized by a contact set having a dimension less than one of that of a domain. This property leads to a new class of free boundary problems with inequality type boundary conditions. The main attention is paid to a suitable description of boundary conditions along the contact zone. Asymptotic properties of solutions are established provided that elasticity parameters of the contacting bodies are changing, in particular, in the case when a stiffness of the elastic body goes to infinity.