The identation of a punch in the form of an elliptic paraboloid into the plane boundary of an elastic body

The three-dimensional contact problem for an elastic body of arbitrary geom etry with a single plane face, into which a punch in the shape of an ellipt ic paraboloid is indented, is considered. The curvilinear boundary of the b ody is partially clamped, and the remaining boundary (outside the contact r egion) is stress-free. It is assumed that the dimensions of the contact are a are small compared with the characteristic dimension of the body. Using t he method of matched asymptotic expansions a model problem of unilateral co ntact without friction is derived for the boundary layer, which is solved u sing the apparatus of Hertz's theory. Asymptotic models of the contact inte raction of different degrees of accuracy are constructed, including correct ions to the geometry and clamping conditions of the elastic body. The sensi tivity of the parameters of the elliptic region of the contact to these fac tors is investigated. (C) 1999 Elsevier Science Ltd. All rights reserved.