Singular Points in an Elastic Half-Plane Containing a Circular Hole, Loaded by a Normal Point Force on the Straight Boundary

Abstract

These authors published theoretical results upon the stress state induced in an elastic half-plane containing a circular hole by a point force applied on its boundary. The solutions were found in bipolar co-ordinates and by expansion of potential functions in Fourier series. The drawback is a weak convergence of stress function on the straight boundary and in its neighbourhood. This paper aims to validate the theoretical results by means of photo-elasticity. The theoretic fields of isoclinicsand of isochromatics are compared with those experimentally found. This comparison reveals an excellent agreement in the case of iso-chromatics. The analysis of isoclinics is more difficult because they loose sharpness as the observed point departures from load point. In exchange, it is easier to identify the singular points of isoclinics. Theoretically, it is difficult to identify all singular points because of the weak convergence of stress function. The authors found these points by a bi-univocal correspondence between a half-plane containing a circular hole and a circular annulus. This correspondence preserves the connection order. Because the singular points for a circular annulus are determined theoretically and experimentally, all singular points in the holed elastic half-plane are found by correspondence. These results are experimentally confirmed.