二维边界元法中几乎奇异积分的解析法

ANALYTICALGORITHM FOR NEARLY SINGULAR INTEGRALS IN TWO-DIMENSIONALBOUNDARY ELEMENTANALYSIS

边界元分析中的几乎奇异积分难题一直阻碍其在工程中应用。作者提出的半解析法有效计算了几乎奇异积分,在此基础上做进一步推演,得到线性单元和二次亚参元上几乎强奇异和超奇异积分的解析列式,摈弃了数值求积。该算式对高次单元也近似适用。这个算法使得边界元法能够分析弹性力学薄壁结构。

The difficulty of the evaluation of nearly singular integrals hindered the applications of the boundary element method in engineering. A semi-analytic algorithm can efficiently compute the nearly singular integrals. Based on the algorithm, exact formulations are obtained for calculating the nearly hyper-singular integrals on the linear element and a flat element. As a result, numerical quadrature is avoided. Furthermore, the strategy is applicable to some high-order elements. Consequently, the boundary element method is enabled to deal with thin-walled structures in elasticity problems. Numerical results illustrate the accuracy and effectiveness of the algorithm.