Three-dimensional crack and contact problems with a general geometric configuration

A new method, based on point set theory and properties of orthogonal functions, is developed for determining exact solutions to three-dimensional crack and contact problems with complicated geometric configurations (e.g. a star-convex domain) in an infinite linear elastic medium. The governing equation is a two-dimensional Fredholm integral equation of the first kind. The central idea of this method is the chain extension of an exact solution from a regular subdomain to an irregular entire domain. Examples are given illustrating how this solution procedure can be used to obtain exact closed form solutions for a general Hertz contact problem and various crack problems in an inhomogeneous isotropic medium with an elastic modulus which is a power function of depth.