An improved initial value method for a contact problem with a nonplane punch

Abstract

Solution of an axisymmetric three dimensional contact problem of a nonplane punch pressing into a finitely thick elastic layer is presented. The method consists in deriving a Cauchy system for two auxiliary functions. This initial value problem is readily solved by modern computers. Complete displacement and stress fields as well as the penetration of the center of the punch, and the force required to push it are determined. This is a direct method, and no successive approximations or series expansions are used. The results are obtained for all radii of contact of the punch with the elastic layer.