Numerical integration of singularities in meshless implementation of local boundary integral equations

The necessity of a special treatment of the numerical integration of the boundary integrals with singular kernels is revealed for meshless implementation of the local boundary integral equations in linear elasticity. Combining the direct limit approach for Cauchy principal value integrals with an optimal transformation of the integration variable, the singular integrands are recasted into smooth functions, which can be integrated by standard quadratures of the numerical integration with sufficient accuracy. The proposed technique exhibits numerical stability in contrast to the direct integration by standard Gauss quadrature.