Certain two-dimensional problems of stress distribution in wedge-shaped elastic solids under discontinuous load

Abstract

In this paper we consider the problem of distribution of stress in an infinite wedge of homogeneous elastic isotropic solid under the usual assumptions pertaining to plane strain in classical (infinitesimal) theory of elasticity. The wedge is supposed to occupy the region 0 ≤ ρ ≤ ∞, − α ≤ θ ≤ α (in plane polar coordinates) where the pole is taken on the apex of the wedge with the line bisecting the wedge angle as the initial line. We report here the investigations of two types of stress fields: (i) the stress field which is set up by the application of known pressure to inner surfaces of a crack situated on the bisector of the wedge angle, and (ii) the stress field generated by the indentation of the plane faces of the wedge by the rigid punch. The corresponding boundary-value problems are shown to be equivalent to the problem of solving dual integral equations involving inverse Mellin-transforms. Similar equations have been discussed by Srivastav ((l)) in a recent paper. The method of (1) is easily modified to reduce the dual equations to single Fredholm equations of the second kind which are best solved numerically. The boundary-value problems discussed here are of the mixed type and appear to have been considered only recently by Matczynski ((2)) who has investigated a contact problem. He identifies the problem with a Wiener-Hopf integral equation and solves the integral equation approximately using a method due to Koiter ((3)). The method presented here seems to have the advantage that it requires no elaborate tools of analysis which are necessary for resolving the problem of Wiener-Hopf and numerical results may be obtained comparatively easily.