Discontinuous contact of an anisotropic half-plane and a rigid base with disturbed surface

Abstract

A two-dimensional problem of elastic theory of discontinuous mechanical contact between an anisotropic half-plane and a rigid body having geometric perturbations of flat surface is studied. The contact is assumed to be frictionless. The approach of complex variable functions is employed to reduce the problem to a Cauchy-type singular integral equation in a height of gaps between the interacted bodies. An equation is solved analytically for the particular cases in which boundary irregularities of the rigid body are modelled by one symmetric cavity of periodic relief. It is shown that if the boundary of the rigid body is described by an even function then a gap shape and contact pressure is an even function as well despite the anisotropic material orientation. Analysis of geometric characteristics of the gaps and of stressed state of the elastic body in cases has been carried out.