水彈性分析關(guān)于柔性的浮動互連結(jié)構(gòu)畢業(yè)論文外文翻譯

中文 3040 字 出處： 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. 外文翻譯 水彈性分析關(guān)于柔性的浮動互連結(jié)構(gòu) 文摘 三維水彈性理論是用來預(yù)測的水彈性 對于柔性 浮動互連結(jié)構(gòu) 的影響 。這個理論擴展到考慮 鉸剛性模式 ，它是 基于有限元方法從數(shù)值分析計算結(jié)構(gòu)的。模塊和連接 構(gòu)件 都認為是 的連接剛度柔性的，比如有 平移和 小角度的 旋轉(zhuǎn)。 例如 一個特殊的情況 ,當兩個模塊 的互聯(lián)結(jié)構(gòu)具有很高的連接剛度 我們可以發(fā)現(xiàn)他是可以和實驗 連續(xù)結(jié)構(gòu) 比較吻合的。 這個模型是用來研究水彈性 對柔性 浮動互連結(jié)構(gòu)的一般特點 。 水彈性 對柔性 浮動互連結(jié)構(gòu) 的影響 包括他們的位移和彎矩。水彈性 對 連接和模塊 影響的 研究 ,為 最優(yōu)設(shè)計提供 了 相關(guān)信息。 1.介紹 非常大的浮動結(jié)構(gòu) (VLFS 循環(huán)使用 )有很多用途 ,如機場、橋梁、存儲設(shè)施、應(yīng)急基地 ,和終端 。 這些靈活的結(jié)構(gòu)的一個關(guān)鍵特性是他們變形和流體場之間的耦合 。 各種 VLFS 循環(huán)使用船體設(shè)計的出現(xiàn) ,包括單片船體、半潛式外殼 ,外殼由許多相互聯(lián)系的靈活的模塊。 各種理論發(fā)展 是 為了預(yù)測水彈性 對 連續(xù)柔性結(jié)構(gòu) 的影響 。對于簡單的空間模型 ,例如梁和板 ， 一維 、 二維， 三維水彈性理論 已被應(yīng)用。 這些 各種各樣的 理論 都采用 這兩種 方法 :分析配方 (Sahooet al., 2000; Sun et al., 2002; Ohkusu, 1998)和數(shù)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)。特定的水動力 學(xué)構(gòu)想是 基于結(jié)構(gòu)行為傳統(tǒng)的三維耐波性理論、 線性勢理論表示的模態(tài) ,這個理論被用來 預(yù)測 對像梁一樣的結(jié)構(gòu) (Bishop and Price, 1979)和各種形狀的結(jié)構(gòu) (Wu, 1984)的影響， 分別通過應(yīng)用二維帶理論和三維格林函數(shù)方法。 最后 ,一些 用 混合的水彈性分析 來解決 單一模塊問題 的 方法被開發(fā)出來 (Hamamoto, 1998; Seto and Ochi,1998; Kashiwagi, 1998; Hermans, 1998).其他水彈性 構(gòu)想 也 是 基于二維 (Wu and Moan, 1996;Xia et al., 1998)和三維 (Chen et al., 2003a)非線性理論 。 通常采用多體水動力相互作用理論 來 預(yù)測水彈性 對 互聯(lián)多模塊結(jié)構(gòu) 的影響。 在這個理論中 ,兩個模塊和連接可以建模為要么剛性或 柔性 的。因此 共有 四種類型的模型 ： 剛性模塊和剛性連接器 (RMRC),剛性模塊和 柔性 的連接器 (RMFC),柔性 的模塊和剛性連接器 (FMRC)和柔性模塊和 柔性 連接器 (FMFC)。采用二維線性帶理論 ,忽略了模塊之間水動力相互作用使用一個簡化的 受 不同剪切和彎曲梁模型 ， Che et al. (1992)分析了水彈性 對 一個 5 模塊 VLFS 循環(huán)使用 的影響 。 Che et al.(1994)后來擴展這一理論 ，他是通過用 的代表的結(jié)構(gòu)三維有限元模型 來說明 而不是 用 一個梁。各種三維方法 (兩種流體動力學(xué)和結(jié)構(gòu)分析 )被 開發(fā) 出來并 使用源分布的方法來分析RMFC 模型 (Wang et al., 1991; Riggs and Ertekin,1993; Riggs et al., 1999; Cui et al., 2007).在 保持其他模塊固定 的情況下，通過考慮六個剛性模塊中的一個運動相對應(yīng)的輻射條件。來說明在模塊之間的 水動力的相互作用 。 利用復(fù)合奇點分布方法和三維水彈性理論 ,Wu et al. (1993)分析了水彈性響應(yīng)的一個 5 模塊與 FMFC VLFS 循環(huán)使用。 Riggs et al. (2000)對比 了 波浪誘導(dǎo) 對在 柔性連接器 下對 一個 循環(huán)使用相互關(guān)聯(lián)的 影響 和 FMFC(有限元分析 )模型 。 他們發(fā)現(xiàn)的影響彈性的模塊 ， FMFC 模型可以被復(fù)制在一個 柔性連接器 模型 ，它是通過 改變剛度的 RMFC 連接器來匹配自然頻率與模 型的形狀。 到目前 為止這個方法被認為是處理通過連接器加入模塊 在 甲板和底部的水平 ， 所以 ， 沒有鉸鏈模式存在 ,或所有的模塊被認為是是剛性 的。 一個結(jié)構(gòu)由串行和縱向連接的駁船 , Newman (1997a, b,1998a)明確地 定義的鉸鏈剛體模 ， 鉸鏈剛體模代表 著 相對運動 模塊 和在剪切力加載在連接器 (WAMIT; Lee andNewman, 2004).。 另外考慮到 鉸接連接器 ,模塊可以建模為柔性梁(Newman, 1998b; Lee and Newman, 2000; Newman,2005). 使用 WAMIT 和考慮彈性的兩個模塊和連接器 ,Kim et al.(1999)研究了水彈性 對 五個模塊在線性頻域 VLFS 循環(huán)使用的 影響 ,在那個實驗中應(yīng)用 彈性為模板的模塊和連接器使用結(jié)構(gòu)三維有限元模態(tài)分析 ,正如 Newman(1997a, b) and Lee and Newman (2004)明確定義鉸鏈剛性模式 . 當涉及到更復(fù)雜的互連多體結(jié)構(gòu) ,由許 多可以移動 的模塊 組成， 那 他們 不 一定 需要連續(xù)連接 ,它將變得非常很難明確定義 ， 鉸鏈的模式 ； 剛性相對運動和剪切力。特別是 ， 很難確保正交性條件的鉸鏈剛性模式是 嚴格滿足 就其 柔性的 和旋轉(zhuǎn)剛性模式。本文的目的是演示的方法預(yù)測了水彈性 對柔性 、漂浮、互連結(jié)構(gòu) 的影響。 使用通用三維水彈性理論 (Wu, 1984)拓展 之前的工作 來 考慮鉸鏈剛性模式。基于 有限元素的方法通過計算數(shù)值分析的結(jié)構(gòu) 的方法計算這些模塊 而不是 完全 滿足正交性條件。所有的模塊和連接器被認為是 有彈性 的。 也需要 連接器 的 平動和轉(zhuǎn)動剛度 。 這種方法是由一個特殊的數(shù)值 案例 驗證 的， 水彈性 對 非常高接頭剛度 的影響和對 一個連續(xù)結(jié)構(gòu) 的影響是一樣的 。 使用這個測試模型 的 ,結(jié)果 ，對 水彈 性影響 一般的結(jié)構(gòu)進行了研究 ,，它們 包括他們的位移和彎矩。此外 ,對 水彈性 影響連接器和模塊剛度的研究 ，為 優(yōu)化設(shè)計結(jié)構(gòu)提供深入 的理論支持 。 2.對于具有 自由浮動 彈性 的結(jié)構(gòu)運動方程 使用有限元方法 ， 對于一個任意的結(jié)構(gòu)系統(tǒng)的運動方程可以表示為 ： ,. PUKUCUM (1) 下面?zhèn)€符號 M,C和 K是 分別表示總體 質(zhì)量、阻尼和剛度矩陣 , U 是節(jié)點位移向量 ; P 是 所有的分布小向量 向量 的矢量和 。 這些 單元素矩 陣 PeUKCMe eee 使用標準的有限元程序 組成相應(yīng)的字符實體 。連接器 可以 通過平移和 彈性 旋 轉(zhuǎn) 建立模型， 使用標準的有限元程序 ,可以 將模型運動要素 納入到運動方程 。 忽視所有的外部力量和阻尼 的 自由振動方程的系統(tǒng) : UM + KU =0 (2). 假設(shè) (2)式有 有頻率為 w 諧波的解 ,那么這將導(dǎo)致特征值的問題： 02 DKMW (3). 如果 M和 K和 M是對稱的 , M 正定 ,K是正定的 (系統(tǒng)沒有任何 自由的運動 )或半正定的 (系統(tǒng)允許一些特殊的自由運動 ),方程式 3 所有的特征值將 是 非負的和實 數(shù) 的。 這個特征值 2r (r=1,2,3， .6n)代表系統(tǒng)的固有頻率 的