Analytical Algorithm of the Nearly Singular Integrals in Boundary Element Method to Orthotropic Potential Problems
Zhou Huanlin(1),Niu Zhongrong(1),Wang Xiuxi(2),Cheng Changzheng(1)
(1 Department of Engineering Mechanics, Hefei University of Technology, Hefei 230009)
(2 Department of Mechanics, University of Science and Technology of China, Hefei 230026)

Abstract: The difficulty of the treatment of the nearly singular integrals hinde red applications of Boundary Element Method(BEM). A set of new direct and analytical integral formulas are deduced with integration by parts to evaluate the nearly singular integrals in the BEM of 2D orthotropic potential problems, where the nearly singular integrals are computed exactly over the linear elements, computed approximately over the quadratic element subdivided into several linear elem ents. When an interior point is far away from a considered integral element, the conventional Gaussian numerical integral scheme is kept, otherwise, if the point is very close to this element, the Gaussian numerical integral is replaced by the new analytical integral due to the invalidation of the Gaussian integral. The numerical results of two examples demonstrate the effectiveness and accuracy of this algorithm, the results of quadratic elements are more accurate than those of linear elements.
Keywords: BEM, nearly singular integrals, analytical integral, orthotropy, potential problems.