The asymptotic solution of a contact problem with a half-unknown boundary of the contact region

The following problem is considered: a punch, disk shaped in plan, whose ba se is an almost circular elliptical paraboloid, is pressed onto the boundar y of an elastic half-space. The friction between the bodies in contact is i gnored; the punch edges are allowed to separate from the elastic base. It i s assumed that the contact region, which is not known a priori, is almost c ircular. The solution of the problem is constructed by the method of marche d asymptotic expansions. The asymptotic form of the boundary of the contact region is presented in explicit form. (C) 2000 Elsevier Science Ltd. All r ights reserved.