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 引用本文: 张耀明, 李小超, Vladimir Sladek, Jan Sladek. 三维边界元法中高阶单元上的几乎奇异积分[J]. 力学学报, 2013, 45(6): 908-918.
Zhang Yaoming, Li Xiaochao, Vladimir Sladek, Jan Sladek. A GENERAL ALGORITHM FOR CALCULATING NEARLY SINGULAR INTEGRALS OVER HIGH-ORDER ELEMENTS IN 3D BEM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(6): 908-918.
 Citation: Zhang Yaoming, Li Xiaochao, Vladimir Sladek, Jan Sladek. A GENERAL ALGORITHM FOR CALCULATING NEARLY SINGULAR INTEGRALS OVER HIGH-ORDER ELEMENTS IN 3D BEM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(6): 908-918.

## A GENERAL ALGORITHM FOR CALCULATING NEARLY SINGULAR INTEGRALS OVER HIGH-ORDER ELEMENTS IN 3D BEM

• 摘要: 三维边界元分析中，高阶几何单元上的几乎奇异积分计算是一个重要而且困难的问题，该文对此进行了研究。使用8节点四边形和6节点三角形曲面单元来描述几何边界；构造了新的距离函数；拓展原有的指数函数非线性变换到三维边界元法中，利用拓展的变换来消除被积函数的几乎奇异性。数值算例表明，该算法稳定，效率高，即使计算点到实际边界的距离很小，依然可获得令人满意的数值解。

Abstract: This work presents a general methodology to compute nearly singular integrals arising in 3D BEM using the eight-node second-order quadrilateral and six-node second-order triangular surface elements. The proposed method constructs a new distance function. The exponential transformation, which was proposed by present authors and is accurate and easy to implement according to extensive applications of 2D BEM, will be extended to 3D BEM to remove the near singularities of integrands. Several numerical examples are given to verify the high efficiency and the stability of the proposed scheme.

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