An improved direct method for evaluating hypersingular stress boundary integral equations in BEM

An efficient numerical method for evaluating all kinds of singular boundary integrals presented in Ref. Gao, 2002 [16] is improved by using a newly derived formulation for computing the spatial derivative of the global distance, which is inevitably used in the finite part of radial integrals. Based on this improvement, more accurate and stable results are obtained in evaluating singular integrals on curved boundary elements. Applying this improved singular integral method to evaluate hypersingular boundary integrals in the stress boundary integral equation, and a high order accuracy of stresses is achieved. Numerical examples are given to illustrate the correctness of the proposed method, and computational results show that the accurate stresses can be obtained even on a coarse mesh, compared with other conventional techniques.