A boundary element method for plane isotropic elastic media using complex variable technique

Abstract

A system of singular integral equations is formulated based on the theory of complex variables with Cauchy kernels for the general problem of plane isotropic elastostatics. The integral equations are represented over the image of problems in multiply-connected regions. A numerical scheme is developed by introducing suitable complex polynomial functions for a discretized boundary curve and integrations are performed exactly for any arbitrary curved boundaries using complex contour integration. This reduces to an explicit set of complex linear algebraic equations with no need for numerical integrations. The major advantage of this technique is that numerical formulations is carried out in the complex plane and does not involve real variables which depend on are length. This yields highly accurate results in the presence of strong boundary curvature with steep stress gradients. Further, this formulation does not have boundary layer effects so that accurate stresses are obtained at any interior points in contrast to previous formulations where the accuracy deteriorates near the boundary points.