摘要
针对三维声场边界元分析的几乎奇异积分问题,将基本解中三角函数进行Taylor级数展开,分离奇异部分和非奇异部分.采用一种半解析正则化算法,计算了近边界点几乎奇异面积分,非奇异部分仍然采用Gauss数值积分,从而克服奇异积分障碍.该算法适用于三角形线性等参元,对高次单元将其细分为几个三节点三角形单元即可应用该算法.对三维声场内问题和外问题算例,计算了近边界点的声压,数值结果证明了该算法的有效性和准确性.
A semi-analytical regularization algorithm was applied to the evaluation of nearly singular surface integrals in the boundary element method （BEM） for three dimensional acoustic problems. In this method, the trigonometric function of acoustic fundamental solution was expended as Taylor series. Then the nearly singular integral parts and non-singular integral parts were separated. The semi-analytical regularization algorithm was used to solve the nearly singular integral parts and the conventional Gauss quadrature was used to solve non-singular integral parts, thus overcoming the nearly singular integral difficulty in acoustic BEM. This algorithm is applicable not only to linear triangular iso-parametric element but also to higher order element by subdividing the element into several triangular sub-elements. The sound pressures of the inner points near the boundary were computed for three dimensional acoustic interior and exterior problems. The computed results demonstrate the accuracy and the effectiveness of the present algorithm.
基金
安徽省自然科学基金(090414153)资助
作者简介
胡宗军，男，1975年生，博士生／副教授．研究方向：工程力学，计算力学．E-mail：huzongjun_1975@163．com
通讯作者：牛忠荣，博士／教授．E-mail：niu-zr@hfut．edu．cn
