On a class of exact solutions of a non-axisymmetric contact problem for an inhomogeneous elastic half-space

Abstract

A non-axisymmetric mixed boundary-value problem is considered concerning the pressure (in the absence of friction and adhesion forces) of a stiff circular-planform stamp with a base of aribitrary shape on an inhomogeneous elastic half-space. The shear modulus of the half-space material is constant while Poisson's ratio is an arbitrary piecewise-continuous function of the depth. By using the theory of dual integral equations associated with the generalized Hankel integral operator, the problem is reduced to a sequence of one-dimensional Fredholm integral equations of the second kind. It is shown that the integral equations obtained allow exact solutions to be constructed for periodic law of variation of the half-space material elastic properties with depth. The solution of a non-axisymmetric problem regarding the eccentric impression of a stamp with a flat base is presented as a example, on the basis of which the influence of inhomogeneity of the elastic material on the magnitude of the stamp displacement parameters is investigated. An asymptotic analysis is performed for the solution in the case when the elastic characteristics of the material become rapidly oscillating functions.