On the efficient computation of the stress components near a closed boundary in plane elasticity by using classical complex boundary integral equations

Abstract

Complex boundary integral equations (Fredholm-type regular or Cauchy-type singular or even Hadamard–Mangler-type hypersingular) have been used for the numerical solution of general plane isotropic elasticity problems. The related Muskhelishvili and, particularly, Lauricella–Sherman equations are famous in the literature, but several more extensions of the Lauricella–Sherman equations have also been proposed. In this paper it is just mentioned that the stress and displacement components can be very accurately computed near either external or internal simple closed boundaries (for anyone of the above equations: regular or singular or hypersingular, but with a prerequisite their actual numerical solution) through the appropriate use of the even more classical elementary Cauchy theorem in complex analysis. This approach has been already used for the accurate numerical computation of analytic functions and their derivatives by Ioakimidis, Papadakis and Perdios (BIT 1991; 31: 276–285), without applications to elasticity problems, but here the much more complicated case of the elastic complex potentials is studied even when just an appropriate non-analytic complex density function (such as an edge dislocation/loading distribution density) is numerically available on the boundary. The present results are also directly applicable to inclusion problems, anisotropic elasticity, antiplane elasticity and classical two-dimensional fluid dynamics, but, unfortunately, not to crack problems in fracture mechanics. Brief numerical results (for the complex potentials), showing the dramatic increase of the computational accuracy, are also displayed and few generalizations proposed. Copyright © 2000 John Wiley & Sons, Ltd.