水弹性分析关于柔性的浮动互连结构毕业论文外文翻译

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 account 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 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 their 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 purposes, 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 composed 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 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). Specific 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), 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, several 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 usually 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 Flexible 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) later 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., 1991; 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. 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) models.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 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 modules 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 connectors, 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 (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 particular, 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, interconnected 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 orthogonality 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 shown 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 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, 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 modeled 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 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 eigenvalues 2r (r=1,2,3， .6n) represent the squared natural frequencies of the system: 0 21 22 . 26n (4) where 2r 0 when K is positive definite, and 2r 0 when K is semi-definite. Each eigenvalue is associated with a real eigenvector Dr, which represents the rth natural mode: ,., rn21 Trjrrr DDDDD ， (5) where riDis the eigenvector of the ith node which contains 6 degree of freedoms, and i runs over the n nodes of the structural FE model system. rd , a sub-matrix of rD , consists of the rth natural mode components of all the nodes associated with one particular element. The rth modal shape ru at any point in that element can be expressed as rU =TI N L rd = Trr WVU r, (6) where L is a banded, local-to-global coordinate transform matrix composed 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 rigid 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 the 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 TjD 0,0,0,0,0,11 , 0,0,0,0,1,02 jD ， 0,0,0,1,0,03 jD, (7) ,0,0,1),(),z(,04 TGGj yyzD TGGj xxzD 0,1,0),(,0),z(5 , TgGj xyyD 1,0,0,0),x(),(6 These vectors correspond to the six rigid motions of the global structure: surge, sway, heave, roll, pitch and yaw, where (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 artificial 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 0- XKM (8) Where 2W (9) MKK (10) From Eq. (8) we can get the corresponding positive eigenvalues l and eigenvectors X. The orthogonality conditions with respect 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 2 , (11) rXDr （ 12） Since 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, PDtPPU mr )(r1 r(13) where pr(t) refers to the rth generalized coordinate. For r 1 6, Dr represents the vector of the 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: Zpcpbp a (14) with ,DKDCDCDbDMDaTTT m21 . ZZZDDZ T ， （ 15） a, b and c are the generalized mass, damping and stiffness matrices respectively; Z is the generalized distributed force and can be expressed as PUZ Trr . (16) In general, the generalized coordinates p in Eq. (14) separate naturally into two groups, which can be denoted by DR PandP respectively, that is to say , TDR PPP (17) where TR PPPP 621 .， (18) refers to the rigid body modes of the global structure as defined by Eq. (7) and TMD PPPP .,87 ， (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 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; Eatock Taylor, 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 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 (FMFC)。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 (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)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 ： ,. PUKUCUM (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 , U 是节点位移向量 ; P 是 所有的分布小向量 向量 的矢量和 。 这些 单元素矩 阵 PeUKCMe eee 使用标准的有限元程序 组成相应的字符实体 。连接器 可以 通过平移和 弹性 旋 转 建立模型， 使用标准的有限元程序 ,可以 将模型运动要素 纳入到运动方程 。 忽视所有的外部力量和阻尼 的 自由振动方程的系统 : UM + KU =0 (2). 假设 (2)式有 有频率为 w 谐波的解 ,那么这将导致特征值的问题： 02 DKMW (3). 如果 M和 K和 M是对称的 , M 正定 ,K是正定的 (系统没有任何 自由的运动 )或半正定的 (系统允许一些特殊的自由运动 ),方程式 3 所有的特征值将 是 非负的和实 数 的。 这个特征值 2r (r=1,2,3， .6n)代表系统的固有频率 的