Axisymmetric frictionless contact between an elastic layer thickness and a circular base under a rigid punch

Abstract

The study presented in this work deals with analytical methods for an axisymmetric problem of an elastic layer partially reposing on a rigid circular base, and is indented along the upper surface with a rigid punch. The contact between the medium and the base is smooth. This boundary value problem is transformed into a system of dual integral equations. In contrast to the classical approach consisting in resolving the corresponding Fredholm equation of the second kind, the latter equations are obtained from an infinite algebraic system of simultaneous equations, where the particular case [Formula: see text] is verified. The results of this system are also obtained numerically. The normal displacement, normal stress, and the stress singularity factor are given analytically and shown graphically with discussion. By comparison with those predicted by the finite element method, the accuracy of the numerical method is approved.