A Subdivision Transformation Method for Weakly Singular Boundary Integrals in Thin-structural Problem

Abstract

Accurate and effective calculation of weakly singular integral in the boundary integral equation of the thin-structural problem is the key to the numerical implementation of the boundary element method. In this paper, a subdivision transformation method evaluated for weakly singular integrals is proposed, and the method is implemented as follows: based on the position of the source points, the shape information of the elements and the nearest distance from the source point to the integral element, a subdivision technology is constructed at first. With this subdivision technology, the integral element can be divided into several integral blocks with good shapes. And then, a simpler coordinate transformation method is constructed to remove the weak singularities of the integral blocks obtained by the subdivision technology. Compared with the conventional polar coordinate transformation method, the present transformation method does not need to calculate their integral interval, which is more simple and effective to implement. Finally, the paper gives three numerical examples to verify the accuracy and validity of the present method.