应用比例边界有限元法求解狭缝对双箱水动力的影响

Research on the hydrodynamic influence from the gap between twin caissons by a scaled boundary finite element method

比例边界有限元法(SBFEM)是一种半解析数值分析的新方法,既融合了有限元法和边界元法的优点,又有其特有的优点。用该方法可求解有限水深下狭缝对双箱水动力作用的影响,为波浪与多浮体超大型结构的相互作用探索一些规律。整个计算域划分成2个无限子域和4个有限子域,并利用加权余量法在各个子域上推导了SBFEM的积分方程;计算了4个数值算例并与边界元等其它数值方法进行了比较,验证了该方法是一种用很少单元便能得到精确结果的高效方法。应用SBFEM对不同箱体宽度、不同狭缝宽度、不同吃水深度条件的双箱作了计算,得出了狭缝对双箱水动力干涉影响的一些规律,对超大型浮体水动力分析和结构设计具有一定的参考价值。

The scaled boundary finite element method（SBFEM） is a novel semi-analytical technique, combining the advantages of the finite element and the boundary element methods with unique properties of its own. The present study aims to give some general hints about hydrodynamic interactions for water wave action on a super large floating structure composed of a large number of box-shaped modules with many small gaps between them. The entire computational domain is divided into several sub-domains, and a weighted residual approach is used to derive the scaled boundary finite element equations in each sub-domain. The problem of wave action with twin caissons in a water of finite depth is computed and compared with BEM and other numerical methods. The results show that the present method yields excellent results with less unknowns and quick convergence. Numerical experiments are carried out for different twin caissons with various drafts and gap widths to study the resonance phenomena on the hydrodynamic interaction between modules due to the im＇luence of gaps between twin blocks. The present results are of practical significance to the design of links of modules for supper large floating structures.