Approximate formulation and numerical solution for hypersingular boundary integral equations in plane elasticity

Abstract

Based on the fact that the singular boundary integrals in the sense of Cauchy principal value can be represented approximately by the mean values of two companion nearly singular boundary integrals, a vary general approach was developed in the paper. In the approach, the approximate formulation before discretization was constructed to cope with the difficulties encountered in the corner treatment in the formulations of hypersingular boundary integral equations. This makes it possible to solve the hypersingular boundary integral equation numerically in a non-regularized form and in a local manner by using conforming C0 quadratic boundary elements and standard Gaussian quadratures similar to those employed in the conventional displacement-BIE formulations. The approximate formulation is very convenient to use because the corner information is comprised naturally in the representations of those approximate integrals. Numerical examples in plane elasticity show that with the present approach, the compatible or better results can be achieved in comparison with those of the conventional BIE formulations.