A transformation method evaluate for near singular boundary integrals in the structural analysis of thin structure

Abstract

The computational accuracy of near singular integrals is the key to determine the overall accuracy and stability of BEM in solving elastic variables, and even the success or failure of BEM analysis. In this paper, an alterative sinh transformation method is developed for solving the near singular boundary integrals in the structural analysis of thin structure. Firstly, the original sinh method is modified into the form include minimum distance and approximate expansion of local coordinates, and Newton-Raphson and cubic equation solving methods are used to obtain the position of the near singular projection point. To facilitate the implementation of the near singular integral, the integral element in the local coordinate space is mapped to the integral parameter space, and then the element integration is performed directly by sinh transformation in this space. The results of several numerical examples show that the proposed method can be used to regularize the nearly singular boundary integral effectively, and to accurately solve the elastic physical variables in the analysis of thin structures.