Stress analysis of an elastic body with a wavy surface

Abstract

The purpose of this paper is to investigate the stress distribution of a half-plane solid with a wavy surface under an applied concentrated load. Orthogonal curvilinear coordinates were built-up to describe the geometry. The complex potential of stress is determined following the conformai mapping technique. It is found that the stress at the surface is proportional to ϵ γ 2 , where ϵ 2π is the ratio of the amplitude to the wavelength of the boundary and γ is the distance from the load point. Near the loading point, surface tension is found when the load is applied at a crest; compressional-type stress is found when the load is applied at a trough. In general these results are quite different from those found for stress in a half plane with a flat surface under an applied concentrated load.