Singularities in meshless implementation of the local BIE

The paper deals with the numerical integration of singular integrals occurring in the meshless implementation of the local integral equations in elasticity. Combination of the direct limit approach with an optimal transformation of the integration variable results in smooth integrands despite the singular kernels involved in the integrals existing only in the Cauchy principal value sense. Then, the sufficient accuracy can be achieved using the numerical integration by standard quadratures. The proposed technique exhibits numerical stability in contrast to the direct integration by standard Gauss quadrature.