Stress concentration around an elliptical hole in a large rectangular plate subjected to linearly varying in-plane loading on two opposite edges

Abstract

Stress concentration in plates due to geometric irregularities such as holes and cracks is a crucial factor in design. The main objective of this paper is to derive the formula for tangential stress concentration factor around an elliptical hole in a large rectangular plate subjected to linearly varying in-plane loading on two opposite edges. The problem is investigated by the two-dimensional theory of elasticity using Muskhelishvili’s complex variable method. The stress functions are evaluated using the conformal mapping method and Cauchy’s integral formula. The stress functions thus obtained are coded to compute the non-dimensional stress components in the plate. The stress concentration factors at the edge of the elliptical hole are compared for different aspect ratios under various in-plane loading conditions. The results indicate that the formula obtained for tangential stress matches to the Kang’s [1] formula when elliptical hole is reduced to a circular hole, by taking its aspect ratio equal to 1. Furthermore, the classical solutions proposed by Inglis and Kirsch are easily obtained as special cases of the problem presented in this work, which confirms the efficacy of the solution. A plane stress finite element model is prepared in ABAQUS and results are compared with present method for a particular case of linearly varying in-plane loading.