A Contact Problem for an Elastic Layer Indented by Multiple Rigid Annular Stamps

Abstract

This paper is concerned with a contact problem for an elastic layer on a rigid substrate indented by multiple rigid concentric-annular stamps. This problem is a mixed boundary value problem in which the surface displacement of the layer is specified inside the concentric-annular regions and the traction is zero outside. It is assumed that contact is free from friction so that the shear traction on the whole surface of the layer is zero. The problem is reduced to infinite simultaneous algebraic equations by using Fourier series expansion of the normal traction within the contact region. General solutions for the contact stress and the surface displacement are presented. Sone numerical results are given in graphical form, and the interaction of the contact stresses caused by each annulus is investigated.