Advanced geometrical elements in boundary element analysis
For complex structures and analysis of the non-linear problem by using boundary element techniques, accuracy is a vital factor in a successful calculation, together with minimum computer storage and CPU time. High-order element methods are believed, in general, to give more accurate results than the lower-order method for the same computational effort, especially when singular and nearly singular integrals need to be calculated. In a high-order boundary element approach to this analysis, the body surface is discretized by a set of curved elements, and most often, using quadratic boundary elements. It should be noted, although high-order polynomial approximations of the geometry boundary are common in boundary element analysis, the efficient method for estimating nearly singular integrals defined in high-order geometrical elements is still a different problem to be solved.In this paper, three kinds of advanced geometrical elements - “circular element, “elliptic element and isoparametric quadratic element - are considerer to estimate the singular and nearly singular integrals occurring in boundary element method (BEM). In many engineering applications there are structures with circle or ellipse boundaries to avoid stress concentration. One of the big advantages of “circular and “elliptic elements is the possibility to describe the geometry of these kinds of structures exactly, even though in the sense of mathematics. Therefore, for circle or ellipse boundaries, the approximation of the geometry is absolutely accurate, and the computational accuracy of singular and nearly singular integrals will be also greatly improved.For more general geometry boundaries, isoparametric quadratic elements are employed for increased computational accuracy. Both singular and nearly singular integrals are calculated in a highly accurate and efficient way, and this is clearly demonstrated by means of representative numerical examples.
Zhang Yaoming Gu Yan Liu Zhaoyan
国际会议
南京
英文
1
2009-10-18（万方平台首次上网日期，不代表论文的发表时间）