A REGULARIZATION ALGORITHM FOR THE NEARLY SINGULAR INTEGRALS IN 3-D BEM
三维问题边界元法中几乎奇异积分的正则化算法

The nearly singular integrals occur in the boundary element analysis for the thin-wall structures and calculating the quantities at interior points close to the boundary. In this paper, the triangular boundary element with three nodes is considered in the three-dimensional boundary element analysis, where the relative distance from a source point to the element is introduced to measure the singularities of the integrals. The smaller the relative distance is, the more difficult the integrals are to be evaluated. The surface integrals on the triangular element are expressed in a local polar coordinate system p.Then the integrals are analytically integrated with respect to the polar variable p by means of the integral formulae of some elementary functions. Thus the nearly singular surface integrals are transformed into a series of line integrals along the contour of the element. The resulting line integrals are computed efficiently by the Gauss numerical quadrature instead of the original singular surface integrals. Moreover, the regularization algorithm can also be applied to higher order elements by subdividing the elements into several triangular sub-elements. Here, the algorithm is employed successfully to analyze the thin-walled structures of the three-dimensional elasticity problems.