Axisymmetric mixed boundary value problems for an elastic halfspace with a periodic nonhomogeneity

This paper examines certain axisymmetric contact, crack and inclusion problems related to a nonhomogeneous elastic medium where the two elastic parameters are periodic functions of the axial variable z. A general formulation of the equations governing the axisymmetric deformations of the medium is presented. It is shown that the mixed boundary value problems can be reduced to a set of two ordinary differential equations and a Fredholm integral equation of the second kind. The ordinary differential equations are solved in a numerical fashion, and these solutions are used to evaluate the kernel function of the Fredhohn integral equation. The resulting integral equations governing the contact problem are also solved via a numerical technique to obtain the loaddisplacement relationship for a rigid circular indentor in smooth contact with a periodically nonhomogeneous elastic halfspace region. The procedures are extended to examine the problems associated with a penny-shaped crack and a rigid disc inclusion embedded in such a nonhomogeneous elastic medium. 0 1998 Elsevier Science Ltd.