1、中文 3040 字 出处： Ocean engineering, 2007, 34(11): 1516-1531 外文 Hydroelastic analysis of flexible floating interconnected structures Three-dimensional hydroelasticity theory is used to predict the hydroelastic response of flexible floating interconnected structures. The theory is extended to take into a
2、ccount hinge rigid modes, which are calculated from a numerical analysis of the structure based on the finite element method. The modules and connectors are all considered to be flexible, with variable translational and rotational connector stiffness. As a special case, the response of a two-module
3、interconnected structure with very high connector stiffness is found to compare well to experimental results for an otherwise equivalent continuous structure. This model is used to study the general characteristics of hydroelastic response in flexible floating interconnected structures, including th
4、eir displacement and bending moments under various conditions. The effects of connector and module stiffness on the hydroelastic response are also studied, to provide information regarding the optimal design of such structures. Very large floating structures (VLFS) can be used for a variety of purpo
5、ses, such as airports, bridges, storage facilities, emergency bases, and terminals. A key feature of these flexible structures is the coupling between their deformation and the fluid field. A variety of VLFS hull designs have emerged, including monolithic hulls, semisubmersible hulls, and hulls comp
6、osed of many interconnected flexible modules. Various theories have been developed in order to predict the hydroelastic response of continuous flexible structures. For simple spatial models such as beams and plates, one-, two- and three-dimensional hydroelasticity theories have been developed. Many
7、variations of these theories have been adopted using both analytical formulations (Sahoo et al., 2000； Sun et al., 2002； Ohkusu, 1998) and numerical methods (Wu et al., 1995； Kim and Ertekin, 1998； Ertekin and Kim, 1999； Eatock Taylor and Ohkusu, 2000； Eatock Taylor, 2003； Cui et al., 2007). Specifi
8、c hydrodynamic formulations based on the modal representation of structural behaviour, traditional three-dimensional seakeeping theory, and linear potential theory have been developed to predict the response of both beam-like structures (Bishop and Price, 1979) and those of arbitrary shape (Wu, 1984
9、), through application of two-dimensional strip theory and the three-dimensional Green s function method, respectively. Other hydroelastic formulations also exist based upon two-dimensional (Wu and Moan, 1996； Xia et al., 1998) and three-dimensional nonlinear theory (Chen et al., 2003a). Finally, se
10、veral hybrid methods ofhydroelastic analysis for the single module problem have also been developed (Hamamoto, 1998； Seto and Ochi, 1998； Kashiwagi, 1998； Hermans, 1998). To predict the hydroelastic response of interconnected multi-module structures, multi-body hydrodynamic interaction theory is usu
11、ally adopted. In this theory, both modules and connectors may be modelled as either rigid or flexible. There are, therefore, four types of model: Rigid Module and Rigid Connector (RMRC), Rigid Module and Flexible Connector (RMFC), Flexible Module and Rigid Connector (FMRC) and Flexible Module and Fl
12、exible Connector (FMFC). By adopting two-dimensional linear strip theory, ignoring the hydrodynamic interaction between modules, and using a simplified beam model with varying shear and flexural rigidities, Che et al. (1992) analysed the hydroelastic response of a 5-module VLFS. Che et al. (1994) la
13、ter extended this theory by representing the structure with a three-dimensional finite element model rather than as a beam. Various three-dimensional methods (in both hydrodynamics and structural analysis) have been developed using source distribution methods to analyse RMFC models (Wang et al., 199
14、1； Riggs and Ertekin,1993； Riggs et al., 1999； Cui et al., 2007). These formulations account for the hydrodynamic interactions between each module by considering the radiation conditions corresponding to the motion of each module in one of its six rigid modes, while keeping the other modules fixed.
15、By employing the composite singularity distribution method and three-dimensional hydroelasticity theory, Wu et al. (1993) analysed the hydroelastic response of a 5-module VLFS with FMFC. Riggs et al. (2000) compared the wave-induced response of an interconnected VLFS under the RMFC and FMFC (FEA) mo
16、dels.They found that the effect of module elasticity in the FMFC model could be reproduced in a RMFC model by changing the stiffness of the RMFC connectors to match the natural frequencies and mode shapes of the two models. The methods considered so far deal with modules joined by connectors at both
17、 deck and bottom levels, so that there is no hinge modes existed, or all the modules are considered to be rigid. In a structure composed of serially and longitudinally connected barges, Newman (1997a, b, 1998a) explicitly defined hinge rigid body modes to represent the relative motions between the m
18、odules and the shear force loads in the connectors (WAMIT； Lee and Newman, 2004). In addition to accounting for hinged connectors, modules can be modelled as flexible beams (Newman, 1998b； Lee and Newman, 2000； Newman, 2005). Using WAMIT and taking into account the elasticity of both modules and con
19、nectors, Kim et al. (1999) studied the hydroelastic response of a five-module VLFS in the linear frequency domain, where the elasticity of modules and connectors is modelled by using a structural three-dimensional FE modal analysis, and the hinge rigid modes are explicitly defined following Newman (
20、1997a, b) and Lee and Newman (2004). When it comes to the more complicated interconnected multi-body structures, composed of many flexible modules that need not be connected serially, it will become very difficult to explicitly define the hinge modes of rigid relative motion and shear force. In part
21、icular, it is difficult to ensure that the orthogonality conditions of the hinge rigid modes are satisfied with respect to the other flexible and rotational rigid modes. The purpose of this paper is to demonstrate a method of predicting the hydroelastic response of a flexible, floating, interconnect
22、ed structure using general three-dimensional hydroelasticity theory (Wu, 1984), extending previous work to take into account hinge rigid modes. These modes are calculated through a numerical analysis of the structure based on the finite element method, rather than being explicitly defined to meet or
23、thogonality conditions. All the modules and connectors are considered to be flexible. The translational and rotational stiffness of the connectors is also considered. This method is validated by a special numerical case, where the hydroelastic response for very high connector stiffness values is sho
24、wn to be the equivalent to that of a continuous structure. Using the results of this test model, the hydroelastic responses of more general structures are studied, including their displacement and bending moments. Moreover, the effect of connector and module stiffness on the hydroelastic response is
25、 studied to provide insight into the optimal design of such structures. 2. Equations of motion for freely floating flexible structures Using the finite element method, the equation of motion for an arbitrary structural system can be represented as ,. PUKUCUM （ 1） where M, C and K are the global mass
26、, damping and stiffness matrices, respectively； U is the nodal displacement vector； and P is the vector of structural distributed forces. All of these entities are assembled from the corresponding single element matrices Me, Ce, Ke, Ue, and Pe using standard FEM procedures. The connectors are modele
27、d by translational and rotational springs, and can be incorporated into the motion equations using standard FEM procedures. Neglecting all external forces and damping yields the free vibration equation of the system: UM + KU =0 (2) Assuming that Eq. (2) has a harmonic solution with frequency o, this
28、 then leads to the following eigenvalue problem: 02 DKMW （ 3） Provided that M and K are symmetric and M is positive definite, and that K is positive definite (for a system without any free motions) or semi-definite (for a system allowing some special free motions), all the eigenvalues of Eq. (3) will be non-negative and real. The
