支撑条件对浮动式厚弹性板水弹性行为的影响分析（英文）

The hydroelastic response of very large floating structures(VLFS) under the action of ocean waves is analysed considering the small amplitude wave theory. The very large floating structure is modelled as a floating thick elastic plate based on TimoshenkoMindlin plate theory, and the analysis for the hydroelastic response is performed considering different edge boundary conditions.The numerical study is performed to analyse the wave reflection and transmission characteristics of the floating plate under the influence of different support conditions using eigenfunction expansion method along with the orthogonal mode-coupling relation in the case of finite water depth. Further, the analysis is extended for shallow water depth, and the continuity of energy and mass flux is applied along the edges of the plate to obtain the solution for the problem. The hydroelastic behaviour in terms of reflection and transmission coefficients, plate deflection, strain, bending moment and shear force of the floating thick elastic plate with support conditions is analysed and compared for finite and shallow water depth. The study reveals an interesting aspect in the analysis of thick floating elastic plate with support condition due to the presence of the rotary inertia and transverse shear deformation. The present study will be helpful for the design and analysis of the VLFS in the case of finite and shallow water depth.     

Simplified estimation for the dynamic behavior and reliability analysis of very large floating structures under wave-induced loads

This paper deals with the dynamic response and strength of very large floating structures (VLFS) in regular and irregular waves, considering the propagation of the hydroelastic deflection wave of the structure. First, a simplified estimation method is presented for the dynamic response and strength of the structure in regular waves. Then, the validity of the method is demonstrated by comparing its results with analytical results and experimental results for a mat-type floating structure model. Next, a simplified estimation method for dynamic responses under long crested irregular wave conditions is presented by using the above results and by combining them with irregular sea wave spectra. Finally, the applicability of the method is investigated through numerical examples carried out for a 4,800-m class VLFS under trial design. Characteristics of the hydroelastic waves, short-term responses, and reliability levels are numerically identified. Received for publication on April 14, 1999; accepted on Sept. 10, 1999     

Hydroelastic analysis of oblique irregular waves with a pontoon-type VLFS edged with dual inclined perforated plates

The fluid-structure interaction of oblique irregular waves with a pontoon-type very large floating structure (VLFS) edged with dual horizontal/inclined perforated plates has been investigated in the context of the direct time domain modal expansion theory. For the hydroelastic analysis, the boundary element method (BEM) based on time domain Kelvin sources is implemented to establish water wave model including the viscous effect of the perforated plates through the Darcy’s law, and the finite element method (FEM) is adopted for solving the deflections of the VLFS modeled as an equivalent Mindlin thick plate. In order to enhance the computing efficiency, the interpolation-tabulation scheme is applied to assess rapidly and accurately the free-surface Green function and its partial derivatives in finite water depth, and the boundary integral equation of a half or quarter VLFS model is further established taking advantage of symmetry of flow field and structure. Also, the numerical solutions are validated against a series of experimental tests. In the comparison, the empirical relationship between the actual porosity and porous parameter is successfully applied. Numerical solutions and model tests are executed to determine the hydroelastic response characteristics of VLFS with an attached anti-motion device. This study examines the effects of porosity, submerged depth, inclined angle and gap distance of such dual perforated anti-motion plates on the hydroelastic response to provide information regarding the optimal design. The effects of oblique wave angle on the performance of anti-motion and hydroelastic behavior of VLFS are also emphatically examined.     

基于离散模块梁单元水弹性理论的复杂连接处建模方法

[目的]在离散模块?梁单元(DMB)水弹性理论框架下,提出针对连接形式复杂的超大型浮体结构(VLFS)的新的建模方法,并与已有方法进行对比分析.[方法]首先,概述基于DMB的水弹性分析方法,给出求解连续VLFS结构在波浪作用下的动力响应步骤;然后,针对VLFS复杂连接处进行建模,通过定义连接处的刚度矩阵,对与连接处相邻...     

Numerical calculation method for the hydroelastic response of a pontoon-type very large floating structure close to a breakwater

This paper presents an effective scheme for calculating the wave-induced hydroelastic response of a pontoon-type very large floating structure (VLFS) when it is near a breakwater. The basic numerical calculation method is the one previously developed by the same author for a VLFS in the open sea (no breakwater), which is expanded to include the effect of the hydrodynamic mutual interaction between the breakwater and the floating structure. The efficiency and accuracy of the proposed method are validated through comparisons with other numerical results and with existing experimental results. After that confirmation, various numerical calculations were conducted, paying special attention to the resonance phenomena which will occur depending on the relation between the wavelength and the clearance between the breakwater and the floating structure. The irregular frequency phenomenon which appears in the calculation of the fluid dynamic problem is discussed in the appendices, including a method for its elimination. Received: October 31, 2000 / Accepted: December 19, 2000     

On the hydroelastic responses of a very large floating structure in waves

New numerical methods are presented for hydroelastic analyses of a very large floating structure (VLFS) of several kilometers length and width. Several methods are presented that accelerate computation without an appreciable loss of accuracy. The accuracy and efficiency of the proposed methods are validated through comparisons with other numerical results as well as with existing experimental results. After confirming the effectiveness of the methods presented, various characteristics of the hydroelastic behavior of VLFSs are examined, using the proposed methods as numerical tools. Received for publication on Dec. 3, 1999; accepted on Dec. 15, 1999     

超大型浮体结构考虑非线性项的波浪力响应计算

为求解超大型浮体结构波浪响应问题,将其简化成弹性梁板模型。以有限元软件为基础来建立超大型浮体结构的弹性梁板模型,在势流理论的基础上,将速度势分解为入射势、绕射势和辐射势三部分,并利用格林函数法推导出一阶、二阶波浪速度势的表达式。以此为理论基础,编制了相应的计算程序来计算浮体结构所受到的二阶波浪力,最后建立了梁板模型的水弹性响应方程,对非线性波浪力作用下的浮体结构的水弹性响应进行求解分析,并分析了波向对响应振幅的影响。     

A B-spline Galerkin scheme for calculating the hydroelastic response of a very large floating structure in waves

This paper presents an effective scheme for computing the wave-induced hydroelastic response of a very large floating structure, and a validation of its usefulness. The calculation scheme developed is based on the pressure-distribution method of expressing the disturbance caused by a structure, and on the mode-expansion method for hydroelastic deflection with the superposition of orthogonal mode functions. The scheme uses bi-cubic B-spline functions to represent unknown pressures, and the Galerkin method to satisfy the body boundary conditions. Various numerical checks confirm that the computed results are extremely accurate, require relatively little computational time, and contain few unknowns, even in the region of very short wavelengths. Measurements of the vertical deflections in both head and oblique waves of relatively long wavelength are in good agreement with the computed results. Numerical examples using shorter wavelengths reveal that the hydroelastic deflection does not necessarily become negligible as the wavelength of incident waves decreases. The effects of finite water depth and incident wave angle are also discussed.     

Hydroelastic analysis of a very large floating plate with large deflections in stochastic seaway

The hydroelasticity of a very large floating plate with large deflections in multidirectional irregular waves is discussed. After a brief introduction on wave loads on a flexible structure, the paper derives the generalised fluid force acting on a floating structure in multidirectional irregular waves. The nonlinear sectional forces induced by the membrane forces in the plate are deduced. The hydroelastic response equations of a floating plate with large deflections in multidirectional irregular waves are established, and a solution method in the frequency domain is discussed including extreme value statistics. A very large floating structure is chosen as an example. The numerical results show that the influence of the membrane forces on the vertical displacements and the bending moments is noticeable but not that large.     

预报超大型浮式结构物水弹性响应方法的比较

超大型海洋浮式结构物(VLFS)在利用海洋空间和开发海洋资源方面有着很大的实用价值.但如何精确有效地计算和预报其在波浪中的水弹性响应是设计过程中的一个非常重要的技术问题.目前,很多学者提出了不同的简化方法来预报VLFS的水弹性响应.文章全面地介绍了关于计算VLFS水弹性响应的解析方法和数值方法的研究现状,并将相应的数值结果与已有的试验数据相比较,进行了分析讨论.     

Hydroelastic responses and interactions of floating fuel storage modules placed side-by-side with floating breakwaters

This paper is concerned with the hydroelastic responses and hydrodynamic interactions of two large floating fuel storage modules placed side-by-side with the presence of floating breakwaters. These modules and breakwaters form the floating fuel storage facility (FFSF). The floating storage modules and breakwaters are modeled as plates and the linear wave theory is used to model the water waves in the numerical model. The numerical model is verified with existing numerical results and validated with experimental test. Numerical simulations are performed to determine the hydroelastic behavior and hydrodynamic interactions of floating storage modules placed adjacent to each other and enclosed by floating breakwaters under various incident wave angles. The effects of breakwaters, drafts, channel spacing formed by the two adjacent modules and water depth on the hydroelastic responses of the modules are investigated. The wave induced responses of multiple floating storage modules enclosed by floating breakwaters are also examined.     

Time-domain numerical and experimental analysis of hydroelastic response of a very large floating structure edged with a pair of submerged horizontal plates

This paper is concerned with the hydroelastic problem of a pontoon-type, very large floating structure (VLFS) edged with the perforated plates, non-perforated plates or their combination anti-motion device both numerically and experimentally. A direct time domain modal expansion method, taking amount of the time domain Kelvin sources in hydrodynamic forces, in which the fluid flows across the perforated anti-motion plate by applying the Darcy's law, is applied to the fluid–structure interaction problem. A quarter of numerical model is built based on the symmetry of flow field and structure in hydrodynamic forces, and special care is paid to the rapid and accurate evaluation of time domain free-surface Green functions and its spatial derivatives in finite water depth by using interpolation–tabulation method. Using the developed numerical tools and the model tests conducted in a wave basin, the response-reduction efficiency of the perforated plates is systematically assessed for various wave and anti-motion plate parameters, such as plate width, porosity and submergence depth. As a result of the parametric study, the porosity 0.11 is selected as the optimal porosity, and the relationship between the porosity and the porous parameter is developed by using the least-squares fitting scheme. After simulation and verification, the dual anti-motion plates which are the perforated-impermeable-plate combination attached to the fore-end and back-end of the VLFS, are designed for more wave energy dissipation and added damping. Considering variation of the water depths in offshore, discussion on the effectiveness of these anti-motion devices at different water depths is highlighted.     

三维水弹性力学中的结构广义质量计算

该文给出了三维水弹性力学中弹性模态位移振型归一化时广义质量的计算方法，并应用三维有限元方法计算了箱式大型浮体结构的固有频率和广质量，经与均匀梁解析解的比较表明，两种方法差异不大，因此，采用均匀染解析解来计算这种结构的固有频率和广义质量是完全可行的，简化了计算工作。     

Fluid-structure-material coupling analysis for a floating laminated structure consisting of high-stiffness panels and a soft core

This paper presents a fluid-structure-material coupling analysis for the interaction between water waves and a very large floating laminated structure (VLFLS), which is consisted of two enhanced ultrahigh-performance concrete (UHPC) panels and a middle lightweight foamed rubber core. The representative volume element (RVE) method is used to design the mechanical properties of enhanced UHPC and foamed rubber, and the parameterized formulas are presented to reveal the dependency between macroscale mechanical properties and mesoscale hierarchical characteristics. By idealizing the rubber core as a uniformly distributed spring layer, an eighth-order differential equation of motion of the laminated structure is derived. In the context of linear potential flow theory, a hydroelastic analytical model is developed for the floating laminated structure with finite length under wave action. In the process of solving velocity potentials, a complicated dispersion equation for the wave motion below the laminated structure is derived, and this equation contains two pairs of conjugate complex roots with positive real parts. The various hydrodynamic quantities, including reflection coefficient, transmission coefficient, deflection, shear force, and bending moment, are calculated. The hydroelastic model is confirmed by considering the convergence of calculation results and the energy conservation of wave propagation. The coupled effects of wave action, material characteristics, structural parameters, and edge conditions on the hydroelastic and mechanical response of the floating laminated structure are clarified to provide important information regarding the optimal design of such structures.     

浸没式穿孔板对超大型浮体的水弹性响应影响（英文）

Scattering of oblique flexural-gravity waves by a submerged porous plate in a finite water depth is investigated under the assumptions of linearized surface waves and small-amplitude structural response. The study is carried out using eigenfunction expansions and the corresponding orthogonal mode-coupling relations associated with flexural-gravity waves in uniform water depth. The characteristics of the roots of the complex dispersion relation are examined using the principle of counting argument and contour plot. Characteristics of the flexural-gravity waves are studied by assuming both the floating elastic plate and the submerged porous plate are infinitely extended in horizontal directions. The effectiveness of the submerged porous structure on the reflection, transmission, and dissipation coefficients is analyzed for various wave and structural parameters.     

Time-domain,shallow-water hydroelastic analysis of VLFS elastically connected to the seabed

In order to ensure the safe operation of a VLFS, a combination of mooring, breakwater and other motion reducing systems is employed. In the present work, the transient hydroelastic response of a floating, thin elastic plate, elastically connected to the seabed, is examined. The plate is modelled as an Euler-Bernoulli strip, while the linearized shallow water equations are used for the hydrodynamic modelling. Elastic connectors are approximated by a series of simple spring-dashpot systems positioned along the strip. A higher order finite element scheme is employed for the calculation of the hydroelastic response of the strip-connector configuration over the shallow bathymetry. After the definition of the initial-boundary value problem, its variational form is derived and discussed. Next, on the basis of the aforementioned formulation, an energy balance expression is obtained. The effect of variable bathymetry on the response of a two connector-strip system is examined by means of three seabed profiles featuring a flat bottom, an upslope and a downslope environment. For the flat bottom case, the strip response mitigating effect exerted by the employment of two and three elastic connectors is considered. Finally, by means of the derived energy balance equation, the energy exchange is monitored, providing a valuable insight into the transient phenomena that take place in the studied configurations.     

Overview: Research on hydroelastic responses of VLFS in complex environments

In the past several decades, extensive investigations have been carried out on the hydroelastic responses of Very Large Floating Structures (VLFS) in the deep open sea by researchers around the world. However, when tackling the hydroelastic problems of VLFS used as the protection and exploitation of marine resources near offshore and islands, the effects of complex environments, such as the seabed profile and inhomogeneous wave conditions should be taken into account. Based on the development history of VLFS and the process of classical hydroelasticity of VLFS, the research results of hydroelastic responses of VLFS in complex environments have been systematically summarized in this paper, so as to provide a basis for the further research.     

Transient responses of a VLFS during landing and take-off of an airplane

The transient elastic deformation of a pontoon-type very large floating structure (VLFS) caused by the landing and take-off of an airplane is computed by the time-domain mode-expansion method. The memory effects in hydrodynamic forces are taken into account, and great care is paid to numerical accuracy in evaluating all the coefficients appearing in the simultaneous differential equations for the elastic motion of a VLFS. The time-histories of the imparted force and the position and velocity of an airplane during landing and take-off are modeled with data from a Boeing 747-400 jumbo jet. Simulation results are shown of 3-D structural waves on a VLFS and the associated unsteady drag force on an airplane, which is of engineering importance, particularly during take-off. The results for landing show that the airplane moves faster than the structural waves generated in the early stage, and the waves overtake the airplane as its speed decreases to zero. The results for take-off are essentially the same as those for landing, except that the structural waves develop slowly in the early stage, and no obstacle exists on the runway after the take-off of airplane. The additional drag force on an airplane due to the elastic responses of the runway considered in this work was found to be small in magnitude.     

波浪作用下带式舟桥的水弹性响应研究

对于设计和使用在波浪和流作用下作业的浮桥,充分了解其水弹性性能尤为重要.就在国防和桥梁工程中极为重要的带式舟桥而言,预报其在波浪中的水弹性响应在实际工程中就显得十分必要.该文主要研究带式舟桥在波浪作用下的水弹性性能.首先,简要地介绍了预报浮桥动力响应的不同方法及它们与试验比较的结果;其次,在三维水弹性理论的基础上采用模态叠加法对带式舟桥的有限元模型进行了水弹性分析,同时与十分之一模型试验结果做了比较(该试验由上海交通大学海洋工程国家重点实验室承担).研究表明,文中的方法计算分析波浪中浮桥的水弹性响应是可行的.     

Structural safety assessment of a pontoon-type VLFS considering damage to the breakwater

 A structural safety assessment of a pontoon-type very large floating structure (VLFS) surrounded by a gravity-type breakwater was carried out for extreme wave conditions by considering the damage to the breakwater. Bending and shear collapses are considered to be a failure mode of the floating structure, while overturning damages the breakwater. The probability of the breakwater overturning, and the transmitted wave height before and after damage to the breakwater, are evaluated using design formulae for port and harbor facilities in Japan. The ultimate bending and shear strengths of the floating structure are calculated by the idealized structural unit method (ISUM) and FEM, respectively. The calculated failure probability for the floating structure is compared with the specified target safety level. It was found that the floating structure under consideration is most likely to fail by bending in transverse waves, and that the corresponding failure probability satisfies the target level. Received: September 12, 2002 / Accepted: October 4, 2002 Acknowledgment. The authors are grateful to Dr. Shigeo Ohmatsu, National Maritime Research Institute, Japan, for allowing us to use the program of hydroelastic response analysis. Address correspondence to: M. Fujikubo (e-mail: fujikubo@naoe.hiroshima-u.ac.jp) Updated from the Japanese original, which won the 2002 SNAJ prize (J Soc Arthit Jpn 2002;190:337–345)