Effective numerical treatment of boundary integral equations: A formulation for three‐dimensional elastostatics

Abstract

Abstract The field equations of three‐dimensional elastostatics are transformed to boundary integral equations. The elastic body is divided into subregions, and the surface and interfaces are represented by quadrilateral and triangular elements with quadratic variation of geometry and linear, quadratic or cubic variation of displacement and traction with respect to intrinsic co‐ordinates. The integral equation is discretized for each subregion, and a system of banded form obtained. For the integration of kernel‐shape function products, Gaussian quadrature formulae are chosen according to upper bounds for error in terms of derivatives of the integrands. Use of the integral formulation is illustrated by the analysis of a prestressed concrete nuclear reactor pressure vessel.