求解三维物体波浪荷载的边界元模型-工程力学-清华大学.PDF

第22 卷第2 期 工 程 力 学 Vol.22 No.2 2005 年 4 月 ENGINEERING MECHANICS April 2005 文章编号：1000-4750(2005)02-0011-05 求解三维物体波浪荷载的边界元模型 *贺五洲，耿进柱 (清华大学水利水电工程系，北京 100084) 摘 要：建立了求解规则波中任意形状三维物体绕射问题的边界元模型。设置辐射面将流场分为内、外场，外场 中的绕射势用特征函数展开式解析表达，内场则由边界积分方程求解，所取的Green 函数为简单的1/r 形式。内 场边界采用四边形面元和轴对称面元混合布置的划分方式，轴对称面元上奇点强度沿周向为 Fourier 级数展开的 高次分布，提高了求解三维绕射问题的精度和效率。经与直立圆柱绕射的线性理论解比较，验证了数值方法的可 靠性。利用谱分析原理，将规则波中的结果拓展，得到多向不规则波中绕射物体所受波浪力的统计特性。 关键词：波浪荷载；三维绕射问题；边界积分方程；Green 函数；多向随机波 中图分类号：O353.2 文献标识码：A A BOUNDARY ELEMENT MODEL FOR CALCULATING WAVE FORCES ON 3-D BODIES * HE Wu-zhou , GENG Jin-zhu (Department of Hydraulic and Hydropower Engineering，Tsinghua University，Beijing 100084 ，China) Abstract: A boundary element model is presented for the calculation of wave forces acting on arbitrarily shaped 3-D bodies due to wave diffraction. The fluid around the body is divided into inner region and outer region by a circular cylinder interface. The diffraction potential is described by an expansion of eigenfunctions in the outer region and determined in the inner region by solving the boundary integral equation using 1/r type Green function. Axisymmetric membrane elements as well as quadrilateral membrane elements are used to discretize the boundary surface of the inner region. The distributed singularity strength on an axisymmetric membrane element is approximated as a Fourier series of higher order to enhance solution accuracy. Numerical results are in good agreement with the linear theoretical solutions in the case of diffraction by a circular cylinder