Unilateral Contact Problems Between an Elastic Plate and a Beam

Abstract

It is well known that crack problems are formulated in domains with cuts. Since the beginning of 1990, the crack theory with inequality type boundary conditions, imposed at the crack faces, has been under active study. These boundary conditions describe a mutual non-penetration between crack faces. The models obtained are non-linear. From a mechanical standpoint, the non-linear models are more preferable as compared to linear ones. It turned out that contact problems for bodies of different dimensions are also described in non-smooth domains with inequality type boundary conditions imposed on sets of small dimensions. In particular, to describe a unilateral contact between elastic plates and beams we have to consider a cracked domain or a domain with a removed point. In both cases the main difficulties are related to non-smoothness of the domain. In the present paper we discuss two problems describing a unilateral contact between an elastic plate and a beam.