| With the development of these years,the boundary element method has become a powerful numerical simulation technology of science and engineering,which is widely used in the potential flow,the elastic static and dynamic problems,linear problems and various kinds of heterogeneous materials and nonlinear problems.However,unlike the domain method,boundary element method needs to compute singular kernel integral,and its effective calculation is the key to the successful implementation of the boundary method.The study of this aspect is still in progress up to now,which is determined by the characteristics of the method itself.There are many methods and techniques for calculating singular integrals,which can be divided into “direct calculation method” and “ indirect calculation method ”.The former computation is to calculate the singular integrals directly on singular element.It needs to generate the integrand to the Taylor ’s series on each element.Therefore,many complicated derivations related to element parameters are required.The latter is mainly through the establishment of various rules of boundary integral equation to calculate singular integral indirectly,including the direct boundary integral equation and indirect boundary equation.The calculation of boundary gradient is quite complex no matter which method we choose to calculate singular integral..In this study,a simple solution method is presented to calculate strong singular integrals.It uses a simple solution to get strong singular integral values without direct integral calculation and the establishment of boundary element equations.The method presented has the advantages of simple theory,high calculation efficiency and accurate results and so on.The work of this paper is listed as follows:(1)2D potential problems are studied in chapter three;(2)2D elasticity problems are studied in chapter four;(3)3D potential problems are studied in chapter five;(4)3D elasticity problems are studied in chapter six. |
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