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1、外文Hydroelastic analysis of flexible floating interconnected structuresThree-dimensional hydroelasticity theory is used to predict the hydroelastic response of flexible floating interconnected structures. The theory is extended to take into account hinge rigid modes, which are calculated from a numer
2、ical 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 interconnected structure with very high connector stiffness
3、 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 their displacement and bending moments under various conditio
4、ns. 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 purposes, such as airports, bridges, storage facilities, emergenc
5、y 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 composed of many interconnected flexible modules.Various theorie
6、s 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 variations of these theories have been adopted using both ana
7、lytical 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). Specific hydrodynamic formulations based on the modal representation
8、 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), through application of two-dimensional strip theory and th
9、e three-dimensional Greens 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, several hybrid methods ofhydroelastic analysis for the single mo
10、dule 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 usually adopted. In this theory, both modules and connectors may
11、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 Flexible Connector (FMFC). By adopting two-dimensional linear st
12、rip 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) later extended this theory by representing the structure with a
13、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., 1991; Riggs and Ertekin,1993; Riggs et al., 1999; Cui et al., 200
14、7). 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. By employing the composite singularity distribution method and
15、 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) models.They found that the effect of module elasticity in the FM
16、FC 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 deck and bottom levels, so that there is no hinge modes existe
17、d, 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 modules and the shear force loads in the connectors (WAMIT; Lee
18、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 connectors, Kim et al. (1999) studied the hydroelastic response of
19、 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 (1997a, b) and Lee and Newman (2004). When it comes to the more
20、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 particular, it is difficult to ensure that the orthogonality condit
21、ions 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, interconnected structure using general three-dimensional hydroelasticity th
22、eory (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 orthogonality conditions. All the modules and connectors are cons
23、idered 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 shown to be the equivalent to that of a continuous structure. Usin
24、g 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 studied to provide insight into the optimal design of such str
25、uctures.2. Equations of motion for freely floating flexible structuresUsing the finite element method, the equation of motion for an arbitrary structural system can be represented as （1）where M, C and K are the global mass, damping and stiffness matrices, respectively; U is the nodal displacement ve
26、ctor; 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 modeled by translational and rotational springs, and can be incorporated into the mo
27、tion equations using standard FEM procedures. Neglecting all external forces and damping yields the free vibration equation of the system:+=0 (2)Assuming that Eq. (2) has a harmonic solution with frequency o, this then leads to the following eigenvalue problem: （3）Provided that M and K are symmetric
28、 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. Theeigenvalues (r=1,2,3，.6n) represent the squared natural frequencie
29、s of the system:0. (4)where 0 when K is positive definite, and 0 when K is semi-definite. Each eigenvalue is associated with a real eigenvector Dr, which represents the rth natural mode: (5)where is the eigenvector of the ith node which contains 6 degree of freedoms, and i runs over the n nodes of t
30、he structural FE model system. , a sub-matrix of , consists of the rth natural mode components of all the nodes associated with one particular element. The rth modal shape at any point in that element can be expressed as = (6)where L is a banded, local-to-global coordinate transform matrix composed
31、of diagonal sub-matrices l, each of which is a simple cosine matrix between two coordinates. N is the displacement interpolation function of the structural element.For freely floating, hinge-connected, multi-module structures, Eq. (3) has zero-valued roots corresponding to the 6 modes of global rigi
32、d motion and the hinge modes describing relative motion between each module. According to traditional seakeeping theory, the rigid modes of the global system can be described by three translational components (uG, vG, wG) and three rotational components (yxG, yyG, yzG) about the center of mass in th
33、e global coordinate system coincident with equilibrium. Thus, the first six rigid modes (with zero frequency) at any point j on the freely floating body can be expressed by,， , (7),These vectors correspond to the six rigid motions of the global structure: surge, sway, heave, roll, pitch and yaw, whe
34、re (x, y, z) and (xG, yG, zG) are the coordinates of a point in the floating body and the center of mass, respectively. To obtain the zero-frequency hinge modes describing the relative motion between different modules, we transform the eigenvalue problem into a new one by introducing an additional a
35、rtificial stiffness proportional to the mass, gM where g can be non-zero artificial real number close to the first non-zero eigenvalue of the system. Then we have (8)Where (9) (10)From Eq. (8) we can get the corresponding positive eigenvalues l and eigenvectors X. The orthogonality conditions with r
36、espect to K gM and M are automatically satisfied in Eq. (8). Thus, these also can satisfy the orthogonality conditions with respect to K and M for the original interconnected structure. This means that eigenvalues and eigenvectors of the original system can therefore be expressed as , (11) （12）Since
37、 usually only the first several oscillatory modes dominate the structural dynamic response, we assume that the nodal displacement of the structure can written as a superposition of the first m modes, (13)where pr(t) refers to the rth generalized coordinate. For r 16, Dr represents the vector of the
38、first six rigid modes and pr(t) the magnitude of rigid displacement about the center of mass (xG, yG, zG). Substituting (13) into (1) and premultiplying by DT, the generalized equation of motion is as follows: (14)with （15）a, b and c are the generalized mass, damping and stiffness matrices respectiv
39、ely; Z is the generalized distributed force and can be expressed as. (16)In general, the generalized coordinates p in Eq. (14) separate naturally into two groups, which can be denoted by respectively, that is to say (17)where (18)refers to the rigid body modes of the global structure as defined by E
40、q. (7) and (19)refers to the distortion modes, including both rigid hinge modes and structural distortional modes.外文翻译水弹性分析关于柔性的浮动互连结构文摘三维水弹性理论是用来预测的水弹性对于柔性浮动互连结构的影响。这个理论扩展到考虑铰刚性模式，它是基于有限元方法从数值分析计算结构的。模块和连接构件都认为是的连接刚度柔性的，比如有平移和小角度的旋转。例如一个特殊的情况,当两个模块的互联结构具有很高的连接刚度我们可以发现他是可以和实验连续结构比较吻合的。这个模型是用来研究水弹性对柔
41、性浮动互连结构的一般特点。水弹性对柔性浮动互连结构的影响包括他们的位移和弯矩。水弹性对连接和模块影响的研究,为最优设计提供了相关信息。1.介绍非常大的浮动结构(VLFS循环使用)有很多用途,如机场、桥梁、存储设施、应急基地,和终端。这些灵活的结构的一个关键特性是他们变形和流体场之间的耦合。各种VLFS循环使用船体设计的出现,包括单片船体、半潜式外壳,外壳由许多相互联系的灵活的模块。各种理论发展是为了预测水弹性对连续柔性结构的影响。对于简单的空间模型,例如梁和板，一维、二维，三维水弹性理论已被应用。这些各种各样的理论都采用这两种方法:分析配方(Sahooet al., 2000; Sun et
42、al., 2002; Ohkusu, 1998)和数值方法(Wu et al.,1995; Kim and Ertekin, 1998; Ertekinand Kim, 1999; Eatock Taylor and Ohkusu, 2000; EatockTaylor, 2003; Cui et al., 2007)。特定的水动力学构想是基于结构行为传统的三维耐波性理论、线性势理论表示的模态,这个理论被用来预测对像梁一样的结构(Bishop and Price, 1979)和各种形状的结构(Wu, 1984)的影响，分别通过应用二维带理论和三维格林函数方法。最后,一些用混合的水弹性分析来解决
43、单一模块问题的方法被开发出来(Hamamoto, 1998; Seto and Ochi,1998; Kashiwagi, 1998; Hermans, 1998).其他水弹性构想也是基于二维(Wu and Moan, 1996;Xia et al., 1998)和三维(Chen et al., 2003a)非线性理论。通常采用多体水动力相互作用理论来预测水弹性对互联多模块结构的影响。在这个理论中,两个模块和连接可以建模为要么刚性或柔性的。因此共有四种类型的模型：刚性模块和刚性连接器(RMRC),刚性模块和柔性的连接器(RMFC),柔性的模块和刚性连接器(FMRC)和柔性模块和柔性连接器(FM
44、FC)。采用二维线性带理论,忽略了模块之间水动力相互作用使用一个简化的受不同剪切和弯曲梁模型，Che et al. (1992)分析了水弹性对一个5模块VLFS循环使用的影响。Che et al.(1994)后来扩展这一理论，他是通过用的代表的结构三维有限元模型来说明而不是用一个梁。各种三维方法(两种流体动力学和结构分析)被开发出来并使用源分布的方法来分析RMFC模型(Wang et al., 1991; Riggs and Ertekin,1993; Riggs et al., 1999; Cui et al., 2007).在保持其他模块固定的情况下，通过考虑六个刚性模块中的一个运动相对应
45、的辐射条件。来说明在模块之间的水动力的相互作用。利用复合奇点分布方法和三维水弹性理论,Wu et al. (1993)分析了水弹性响应的一个5模块与FMFC VLFS循环使用。Riggs et al. (2000)对比了波浪诱导对在柔性连接器下对一个循环使用相互关联的影响和FMFC(有限元分析)模型。他们发现的影响弹性的模块，FMFC模型可以被复制在一个柔性连接器模型，它是通过改变刚度的RMFC连接器来匹配自然频率与模型的形状。到目前为止这个方法被认为是处理通过连接器加入模块在甲板和底部的水平，所以，没有铰链模式存在,或所有的模块被认为是是刚性的。一个结构由串行和纵向连接的驳船,Newman
46、(1997a, b,1998a)明确地定义的铰链刚体模，铰链刚体模代表着相对运动模块和在剪切力加载在连接器 (WAMIT; Lee andNewman, 2004).。另外考虑到铰接连接器,模块可以建模为柔性梁(Newman, 1998b; Lee and Newman, 2000; Newman,2005). 使用WAMIT和考虑弹性的两个模块和连接器,Kim et al.(1999)研究了水弹性对五个模块在线性频域VLFS循环使用的影响,在那个实验中应用弹性为模板的模块和连接器使用结构三维有限元模态分析,正如Newman(1997a, b) and Lee and Newman (2004
47、)明确定义铰链刚性模式.当涉及到更复杂的互连多体结构,由许多可以移动的模块组成，那他们不一定需要连续连接,它将变得非常很难明确定义，铰链的模式；刚性相对运动和剪切力。特别是，很难确保正交性条件的铰链刚性模式是严格满足就其柔性的和旋转刚性模式。本文的目的是演示的方法预测了水弹性对柔性、漂浮、互连结构的影响。使用通用三维水弹性理论(Wu, 1984)拓展之前的工作来考虑铰链刚性模式。基于有限元素的方法通过计算数值分析的结构的方法计算这些模块而不是完全满足正交性条件。所有的模块和连接器被认为是有弹性的。也需要连接器的平动和转动刚度。这种方法是由一个特殊的数值案例验证的，水弹性对非常高接头刚度的影响和对一个连续结构的影响是一样的。使用这个测试模型的,结果，对水弹性影响一般的结构进行了研究,，它们包括他们的位移和弯矩。此外,对水弹性影响连接器和模块刚度的研究，为优化设计结构提供深入的理论支持。2.对于具有自由浮动弹性的结构运动方程使用有限元方法，对于一个任意的结构系统的运动方程可以表示为： (1)下面个符号M,C和K是分别表示总体质量、阻尼和刚度矩阵,是节点位移向量;是所有的分布小向量向量的矢量和。这些单元素矩阵
