AXISYMMETRICAL MIXED BOUNDARY-VALUE-PROBLEMS FOR AN ELASTIC HALF-SPACE WITH A PERIODIC NONHOMOGENEITY

This paper examines certain axisymmetric contact, crack and inclusion- problems related to a nonhomogeneous elastic medium where the two elas tic parameters are periodic functions of the axial variable z. A gener al formulation of the equations governing the axisymmetric deformation s of the medium is presented. It is shown that the mixed boundary valu e problems can be reduced to a set of two ordinary differential equati ons and a Fredholm integral equation of the second kind. The ordinary differential equations are solved ina numerical fashion, and these sol utions are used to evaluate the kernel function of the Fredholm integr al equation. The resulting integral equations governing the contact pr oblem are also solved via a numerical technique to obtain the load-dis placement relationship for a rigid circular indentor in smooth contact with a periodically nonhomogeneous elastic halfspace region. The proc edures are extended to examine the problems associated with a penny-sh aped crack and a rigid disc inclusion embedded in such a nonhomogeneou s elastic medium. (C) 1998 Elsevier Science Ltd.