On the use of interpolative quadratures for hypersingular integrals in fracture mechanics - Korsunsky, A (Royal Society Publishing, 2002)
The implementation of finite-part integration of hypersingular boundary integrals is discussed in the context of the applications in engineering fracture mechanics. The approach uses a formulation of the Gauss-Jacobi interpolative quadrature, which can be applied in the same form and with equal success to regular Cauchy-singular and hypersingular integrals that arise in crack problems. The method therefore avoids the artificial device of separating the singularity that usually gives rise to additional numerical effort and reduced accuracy. The quadrature formulae are presented in terms of Jacobi polynomials pn(α,β) and the associated function qn(α,β). The key properties and the numerical evaluation procedures for these functions are described. The efficiency of the hypersingular Gaussian quadrature technique is demonstrated using the example of an annular crack subjected to remote tension.