The detachment of an elastic strip containing absolutely rigid inclusions from a support

Abstract

A problem of the theory of elasticity for a strip containing rigid inclusions is considered. The faces of the strip are supported without friction by a rigid base and the inclusions are loaded by forces perpendicular to the faces of the strip, which leads to the appearance of a section of the strip detached from one of the supporting surfaces, in which case the problem becomes a strictly mixed one. We use the method developed in [1] for non-mixed problems in the case of non-canonical domains. It is based on the construction of matrix-valued Green's functions corresponding to simpler classical boundary value problems for canonical domains with subsequent reduction of the boundary value problems for non-canonical domains to the solution of integral equations. The method was first discussed for strictly mixed problems taking Laplace's equation as an example. It was then applied to contact problems of the theory of elasticity, including the case when the contact zones are unknown in advance.