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Regularization of nearly hypersingular integrals in the boundary element method

2001; Elsevier BV; Volume: 25; Issue: 3 Linguagem: Inglês

10.1016/s0955-7997(01)00009-1

1873-197X

J. J. Quesada Granados, Rafael Gallego,

Geotechnical Engineering and Underground Structures

A critical aspect in all implementations of the boundary element method is an accurate computation of the kernels' integration. These kernels are singular or hypersingular when the collocation point belongs to the integration element, and different techniques have been devised to tackle this problem. Another important issue is the integration of the kernels when the collocation point is close to but not in the integration element. The ensuing integrals although regular are termed quasi-singular or nearly singular, and quasi-hypersingular or nearly hypersingular since the integrand varies rapidly within the integration interval, and cannot be accurately computed by standard procedures. A kernels' complex regularization procedure is presented in this paper, which leads to a decomposition of the quasi-singular and quasi-hypersingular integrals in a series of simpler terms. The method is applied to the stress boundary integral equation for two-dimensional bodies, and it is tested in both curved and straight elements. For straight elements, the method leads to closed-form formulas, which are included in the paper.