边界元法中奇异积分计算的极坐标变换法
Polar Coordinate Transformation Approach for Treatment of Singular Integrals in Boundary Element Methods
-
摘要: 在边界元法中,奇异积分的处理是一个极为引人注目的问题.本文提出了一种在单元状态作极坐标变换的新的处理方法,它能显式地消除奇异积分的奇异性,使之成为常规积分,因而易于在边界元法中使用高次单元.计算实例表明,本文所提出的方法是有效的、方便的.Abstract: In boundary element methods the treatment of singular integrals, as one of the main numerical problems has been noticed seriously. In this paper, by using polar coordinate transformation for elements a new approach is proposed to remove the singularities in the integrals explicitly. The formulations for treatment of the singularities in quadrilateral boundary elements with four nodes, eight nodes and nine nodes are derived and it can be extended easily to other higher order boundary elements. Numerical examples are given. The results show the present approach is effective and efficient.
-
[1] Cruse, T.A., An improved boundary-integral equation method for three-dimensional elastic stress analysis, Computer and Structures, 4(1974), 741-754. [2] Jeng, G. and A. Wexler, Isoparametric, finite element, variational solution of integral equations for three-dimensional fields, Int. J. Num. Meth. Eng., 11(1977) 1455-1471. [3] Webster, W.C., The flow about arbitrary, three-dimensional smooth bodies, J. of Ship Research, 19, 4(1975), 206-218. [4] Oken, E.E., The potential integral for a linear distribution over a triangular domain, Int. J. Num. Meth. Eng., 18(1982), 1821-1828. [5] Lachat, J.C. and J.O. Waston, Effective numerical treatment of boundary integral equations: a formulation for three dimensional elastostatics, Int. J. Num. Meth. Eng., 10(1976), 999-1005. [6] 藏跃龙、嵇醒,三维弹性力学边界元程序的计算精度,《第一届工程中的边界元会议文集》,(1985.12), 149-155. [7] Telles, J.C.F., L.C. Wrobed and C.A. Brebbia, Boundary Element Technology Theory and Application in Engineering, Springer-Verlag(1984), 448-454. [8] Brebbia, C.A. and S. Walker, Boundary Element Techniques in Engineering, Butterworth Ltd.,(1980).中译本:张治强译,《边界元法的工程应用》,陕西科技出版社(1986) [9] Bath, K.J. and E.L. Wilson, Numerical Methods in Finite Element Analysis, Prentice-Hall, Inc.(1976), 120-123. [10] Smith, A.M.O. and J. Hess, Calculation of non-lifting potential flow about three-dimensional, bodies, Douglas Aircraft Company, Report E.S. 40622(1962). [11] Kaleff, P., A hydroelastic approach to ship vibration problems, J. of Ship Research, 27, 2(1983), 103-112.
点击查看大图
计量
- 文章访问数: 1658
- HTML全文浏览量: 70
- PDF下载量: 673
- 被引次数: 0