A multiscale material-structure-hydroelasticity coupled analytical model for floating sandwich structures with hierarchical cores

A novel material-structure-hydroelasticity coupling analytical model is proposed for marine structures, which is utilized for the calculation and optimization of a very large floating sandwich structure (VLFSS) with a hierarchical ultrahigh-performance concrete (UHPC) core in this study. For the coupling material and structure analysis, three-dimensional representative volume element and self-consistent methods are developed to reveal the physical relations between the UHPC core's macroscale mechanical properties (e.g., modulus and density) and mesoscale hierarchical characteristics (e.g., aggregate and porosity) and to obtain the corresponding parameterized formulas. For the coupling material-structure-hydroelasticity analysis, a sixth-order dynamical equation for the potential flow model of the VLFSS, in which the hierarchical core's parameters are introduced through the material-structure coupling formulas, is developed. The hydroelasticity equations containing multiscale parameters are solved, and the mechanical responses are calculated. Using this coupled multiscale method, the shear force in the representative VLFSS is optimized for a smaller amplitude, which relies on the interactivity of the hierarchical structural parameters and wave conditions. These results demonstrate the potential of the multiscale coupling methodology to achieve the physically significant optimization of a floating composite structure in ocean engineering.     

On the dispersion relation of hydroelastic waves in a plate

This paper deals with the dispersion relation of hydroelastic waves in pontoon-type very large floating structures (VLFS) using a simple beam modeling, where the term hydroelastic waves means propagation of deflection vibrations in VLFS. The purpose of this paper is to show the properties of the hydroelastic waves. The dispersion relation of hydroelastic waves propagating in an infinite plate floating on the water is derived based on the linear water wave theory. The effects of the water depth and of the bending rigidity of the floating plate on the wavelength, phase velocity, and group velocity of the hydroelastic waves are shown theoretically or numerically. Then, the dispersion relation of hydroelastic waves in a finite plate floating on shallow water is investigated. It is shown that the wavelength or the phase velocity of the hydroelastic waves varies with the location in the plate. Received for publication on April 7, 1999; accepted on Aug. 20, 1999     

Connection design for two-floating beam system for minimum hydroelastic response

This paper is concerned with the connection design for a two-floating beam system for minimum hydroelastic response. The frequency domain approach is used for the hydroelastic analysis. The fluid is modelled as an ideal fluid, and the floating beams are modelled by the Euler–Bernoulli beam theory. The boundary element method (BEM) and the finite element method (FEM) are applied to solve the governing equation of the fluid motion and the beam equation of motion, respectively. The study aims to investigate the optimum location and rotational stiffness of the connection for the two-floating beam system with the view to minimize the compliance. The study also investigates the effects of relative beam stiffnesses on the hydroelastic response of the two-floating beam system.     

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.     

Combining low- and high-frequency loads acting on large floating structures

Loads acting on large floating structures usually consist of high-frequency and low-frequency loads. The high-frequency loads are associated with the hydroelastic behavior of the structure and excitation of the natural frequency modes. The low-frequency loads are associated with the body motion of the structure and the wave profile. In design analysis, extreme values of these loads must be combined taking into consideration the correlation between them. This paper discusses a methodology for combining the extreme loads, and proposes a simple formulation suitable for use in reliability analysis. A proposed load combination factor K was found to depend on the correlation coefficient of the two loads, the ratio of their standard deviations and the frequency content of the processes from which the loads are determined. The correlation coefficient was found to depend on the complex frequency response functions of the loads and the input wave spectrum. The paper also discusses characteristic extreme values of slightly nonlinear loads acting on large floating structures.Extreme loads may be based on a storm condition with a specified return period. Since very large floating structures are expected to have a long operational lifetime, the return period must be selected carefully. The paper discusses a method for selecting return periods based on the expected operational life of the structure and encounter probability.     

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.     

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.     

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 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.     

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。     

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.     

A study on the estimation of the seaquake response of a floating structure considering the characteristics of seismic wave propagation in the ground and the water

 Seaquakes, which are characterized by the propagation of vertical earthquake motion at the sea bottom as a compression (longitudinal) wave, are reported to cause damage to ships, and their effect on floating structures is a matter of great concern. To comprehend the basic properties of seaquakes, we first discuss a method to calculate the displacement of the seabed when it is subjected to hydrodynamic pressure. To investigate the interrelationship between the vibration of a floating structure and the deformation of the seabed, a new boundary integral equation is derived which assumes that the seabed is a semiinfinite homogeneous elastic solid in order to analyze the seaquake-induced hydrodynamic pressure acting on the floating structure. By considering the propagation of the seismic wave in the ground and in the water, the incident wave potential in seaquake problems is also deduced and its characteristics are discussed. Finally, the response of a very large floating structure in a seaquake is investigated using a fluid force analysis method, and considering the interrelationship between the vibration of the floating structure and the deformation of the seabed. Received: August 19, 2002 / Accepted: November 11, 2002 Address correspondence to: H. Takamura (hiroaki_takamura@nishimatsu.co.jp) Updated from the Japanese original, which won the 2002 SNAJ prize (J Soc Nav Archit Jpn 2001;189:87–92,93–100 and 190:381–386)     

Hydroelastic analysis of a nonlinearly connected floating bridge subjected to moving loads

In this paper, the motion equations for the nonlinearly connected floating bridge, considering the nonlinear properties of connectors and vehicles’ inertia effects, are proposed. The super-element method is used to condense the whole calculation scale, and the direct integration and Newton–Raphson iteration method are applied to solve the reduced equations. Based on the modal and static analyses, the dynamic displacement and connection forces characteristics of a floating bridge with nonlinear connectors subjected to moving loads are investigated. It is found that nonlinearity and initial gap of the connectors are important for the hydroelastic response of a nonlinearly connected floating bridge.     

The influence of water depth on the hydroelastic response of a very large floating platform

The hydroelastic response of a two-dimensional very large floating platform to plane incident wave is investigated for three different cases: infinite, finite and shallow water depth. An integro-differential equation is presented to describe the deflection of the platform due to incident waves. Reflection and transmission coefficients are obtained as well. We consider the case of a strip and a half-plane. Numerical results are obtained for various values of the parameters. The results for the strip and for the semi-infinite platform are compared for different values of depth.     

Inhomogeneous wave load effects on a long,straight and side-anchored floating pontoon bridge

In this paper, we present a numerical study on the hydroelastic response of a 4.6 km long fjord crossing floating bridge subjected to wave loads. The bridge is straight in design and supported by 35 pontoons along its full length. To limit the response to horizontal loads, four clusters of deep water mooring lines are engaged to increase the transverse stiffness of the bridge. Owing to the very large span across the fjord, inhomogeneity in the wave field exists. This study examines the various effects of inhomogeneous wave loads on the dynamic responses of the floating bridge. These include the spatial variations of the wave direction, significant wave height and peak period as well as the coherence and correlation of waves along the entire length of the floating bridge. For the purpose of comparison, the dynamic bridge responses under homogeneous wave load cases are also studied. In addition, the effects of wave load components and short-crestedness are presented and discussed.     

Hydroelastic Analysis of a Flexible Floating Body for the Variation of Incident Wave

As for the hydroelastic response of a flexible floating body, various kinds of simplified analytical and numerical methods based on the different assumption have been developed, however, the most versatile and applicable approach is the three-dimensional hydroelasticity theory. Currently, most studies mainly focused on the wave condition of head seas without taking the differences for the variation of the incident wave angle into account. In this paper, based on the three-dimensional hydroelasticity theory, an investigation into the variation of the hydroelastic response for different incident wave angles is presented; also some comparisons are demonstrated and discussed.     

Hydroelasticity of large container ships

The importance of hydroelastic analysis of large and flexible container ships of today is pointed out for structure design. A methodology for investigation of this challenging phenomenon is drawn up and a mathematical model is worked out. It includes the definition of ship geometry, mass parameters, structure stiffness, and combines ship hydrostatics, hydrodynamics, wave load, ship motion and vibrations. The modal superposition method is employed. Based on the presented theory, a computer program is developed and applied for hydroelastic analysis of a large container ship. The transfer functions for heave, pitch, roll, vertical and horizontal bending and torsion are presented. Rigid body and elastic responses are correlated.     

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.     

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)     

Simplified analysis for estimation of the behavior of a submerged floating tunnel in waves and experimental verification

To achieve rational design in waves for a submerged floating tunnel which has emerged as a new offshore transportation infrastructure, it's necessary to understand its hydrodynamic behavior. For simple but accurate estimation of hydrodynamic forces, a theoretical method is proposed and the tests with physical models in a wave flume were carried out for verification. Morison's equation was used to estimate wave loads composed of inertia force and drag force. Forces calculated by applying the linear wave theory to Morison's equation coincided well with those measured by the tests. The test results showed that mooring systems played a significant role in the movement of the submerged floating tunnel in waves. A pendulum model could be used to describe the motion of the submerged floating tunnel with a single vertical mooring. Based on the verified relations, a simple slack condition which causes the submerged floating tunnel to be unstable was also proposed. The simplified approach proposed by this study proved to be useful in designing the submerged floating tunnel in the initial stage.