Analytical expressions for evaluation of radial integrals in stress computation of functionally graded material problems using RIBEM

This paper presents a set of new analytical expressions for evaluating radial integrals appearing in the stress computation 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 in the derivation of the analytical expressions. The fourth-order spline RBF is employed to approximate unknowns appearing in domain integrals from variation of the shear modulus. Using these analytical expressions, considerable computational efficiency can be improved by overcoming the time-consuming deficiency of using the radial integration method (RIM) to convert domain integrals to the boundary which results in a pure boundary discretization algorithm in solving variable coefficient problems. Numerical examples are given to demonstrate the efficiency of the presented formulations.