Stress concentration on the contour of a plate opening of an arbitrary corner radius of curvature

Abstract

Nowadays the title problem is usually dealt with using the finite element method (FEM). However, due to a high stress gradient an extremely fine mesh is needed in the vicinity of the contour, and even then the results obtained are of a questionable accuracy in the zones with a small radius of curvature (corners of rectangular openings). In this paper, a different—analytical—approach to the problem was applied by using Muskhelishvilli's solutions based on conformal mapping. Involving functions of a complex variable—and so being very complicated—these solutions were practically applicable for a narrow corner-radius-of-curvature spectrum only. However, after an adequate transformation and reduction to a programmable algorithm, they allowed systematic analyses for an arbitrary small corner radius of the contour and thus a more accurate formulation of its influence on the stress concentration factor (SCF) in a convenient manner.