A tensionless contact without friction between an elastic layer and an elastic foundation

Abstract

The plane contact problem for an infinite elastic layer lying on an elastic half space is considered. The layer is acted upon by a uniform clamping pressure po, a uniform vertical body force ρ1g due to the effect of gravity in the layer and a concentrated vertical line load P. It is assumed that the contact between the layer and the half space is frictionless and that only compressive normal tractions can be transmitted through the interface. The contact along the interface will be continuous if the value of P is less than a critical value Pcr However, for P >Pcr interface separation takes place along a certain finite region. First, the problem of continuous contact is solved and the value Pcr is determined. Then the discontinuous contact problem is formulated in terms of a singular integral equation. Two loading conditions are considered assuming that the concentrated line load P is either a tensile load or a compressive load. Numerical results for Pcr contact stress distributions, and separation regions are given for various material combinations.