New analytical expressions in radial integration BEM for stress computation with several kinds of variable coefficients

Abstract

Abstract This paper presents a set of new analytical expressions for evaluating radial integrals appearing in the stress computation of several kinds of variable coefficient elastic problems using the radial integration boundary element method (RIBEM). The strong singularity involved in the stress integral equation is explicitly removed from the derivation of the analytical expressions. This approach can improve the computational efficiency considerably and can overcome the time-consuming deficiency of RIBEM in computing involved radial integrals. In addition, because it can solve many kinds of variable coefficient elastic problems, this approach has a very wide applicability. The fourth-order spline (Radial Basis Function) RBF is employed to approximate the unknowns appearing in domain integrals caused by the variation of the shear modulus. The radial integration method is utilized to convert domain integrals to the boundary, which results in a pure boundary discretization algorithm. Numerical examples are given to demonstrate the efficiency of the presented formulations.