A DIRECT METHOD FOR EVALUATING LINE INTEGRALS WITH ARBITRARY HIGH ORDER OF SINGULARITIES

This paper presents a new direct method for evaluating arbitrary singular boundary integrals appearing in 2D boundary element analysis. Firstly, geometry quantities on a curved line element are expressed using those projected on a tangential line. Then, singularities involved in the integrals are analytically removed by expressing the non-singular part of the integration kernel as power series. A set of formulations for computing the first and second derivatives of intrinsic coordinates with respect to local orthogonal coordinates are also presented in the paper for the first time. Since the coordinate transformation is at the real spatial scale, the operation is straightforward and convenient, and can be applied to treat arbitrary high order of singular integrals. Finally, some examples are given to verify the correctness and stability of the presented method.