Plane Stresses of the Belt which has a Discontinuity : The Case Having a Rectangular Projection with Sharp Corners and Rounded Off Corners on One Side

Abstract

It was next to impossible to solve numerically the plane problem of elasticity having discontinuities composed of straight lines e.g. rectangular notches or projections, etc. But if we use the technique of expanding the series and the method of convergence of the series because the convergence is not good, we can solve numerically such problems though the terms of the series are quite numerous. That is by using the Schwarz-Christoffel's conformal transformation we represent such shape's domain by the unit circle, and we treat the plane stress boundary value problem by the method of Goursat-Kikukawa. In this way we can solve such problems. This paper deals with the problem of the belt having a rectangular projection with sharp corners and rounded off corners on one side and the results of these numerical calculations are pretty good as compared with the results of the experiments of the photo-elasticity and the wire strain meter.