A SIMPLIFIED ANALYSIS FOR AN ELASTIC QUARTER-SPACE

This analysis deals with the determination of the elastic stress and displacement fields in a quarter-space under arbitrarily applied surface loadings. The problem is formulated in terms of two coupled two-dimensional integral equations. The integral equations contain a logarithmic singularity with an unknown coefficient which varies along the edge of the quarter-space. A special solution for a half-space is developed which isolates the elastic field caused by this singularity and it is incorporated into the numerical-boundary-element solution of the integral equations. Once the equations are solved, the elastic field in the quarter-space can be found in a relatively simple fashion. The solution so developed may then be used to analyse contact problems for an elastic quarter-space. Contact is modelled with ellipsoidal distributions of pressure and traction to one or both faces. Numerical results are given for the internal elastic stress field and the von Mises yield parameter for a variety of contact loadings. © 1990 Oxford University Press.