Reducing Hydroelastic Response of Very Large Floating Structure: A Literature Review
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paper_title: Time Domain Analysis on the Dynamic Response of a Flexible Floating Structure to Waves

paper_content:

A time-domain numerical method is developed to analyze the hydroelastic responses of flexible floating structures to waves; in which, the boundary element method is applied to evaluate the fluid motion and the finite-element method to analyze the elastic deformation of structure. The dynamic wave-structure interaction is simulated by prescribing the conditions on a wave generation boundary for each time step and by satisfying the continuity of the pressure and displacement on the fluid-structure interface. A time-domain solution is obtained in a predictor-corrector scheme and through a time-stepping computation. The effect of space and time discretizations on the convergence and stability of solution for regular, random and solitary waves is discussed by comparing among numerical solutions. The validity of the present method is verified by comparing it with the experimental results for the three kinds of waves mentioned. Further, the fission of a solitary wave under a flexible floating structure is observed both in numerical analysis and experiments.
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paper_title: The influence of water depth on the hydroelastic response of a very large floating platform

paper_content:

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.
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paper_title: A geometrical-optics approach for the deflection of a floating flexible platform

paper_content:

In an earlier paper, see [J Fluids Struct 14 (2000) 943], a derivation of an integro-differential equation for the determination of the deflection of a large floating flexible platform, excited by waves, is given. In this paper, we investigate the possibility to derive a short wave formulation for this problem. It will be shown that for a flexible half-plane and a strip in deep water, the integral equation can be used to find such a formulation. The asymptotic results shall be compared with the numerical results obtained earlier.
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paper_title: The response of ice floes to ocean waves

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A precise linear mathematical theory is reported to model the response of a solitary ice floe in ocean waves, allowing the floe to bend with the passing wave. Both infinite and finite water depths are considered, and the model is also extended to include a pair of separated floes of different length, the case of n-floes then being a natural and straightforward development. For a single ice floe, perfect transmission is achieved whenever the wavelength beneath the ice couples perfectly to the length of the ice floe. Then the strains induced in the bending ice floe reach a maximum, and because multiple-cycle tuning can occur in floes which are long compared to the wavelength, strain response amplitude operators (RAOs) are complicated. By considering the case of infinite stiffness, heave and roll RAOs are also found for typical ocean wave periods, and these agree well with two-dimensional rigid-body models. Finally, ice floes of different diameters but constant 1-m thickness are subjected to spectral forcing, and the strain spectral density for each is found. Spectral density envelopes increase gradually with floe diameter, achieving a maximum value for a floe of about 102m. Thereafter strains never decrease below those for the 80-m curve owing to multiple-cycle tuning. This may explain the presence of zones within an ice field where floe size never exceeds some prescribed value. Results obtained from the complete theory for two adjacent floes do not differ significantly from those found by applying the single-floe model serially except when the separation is very small.
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paper_title: FEM For Time Domain Analysis of Hydroelastic Response of VLFS With Fully Nonlinear Free-surface Conditions

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A finite element method (FEM) is developed for the time domain analysis of the hydroelastic deformation of a pontoontype very large floating structure (VLFS) with fully nonlinear free-surface conditions. A 3-dimensional free-surface flow is formulated in the scope of potential flow theory with the nonlinear free-surface conditions. To describe the motion of VLFS, the Mindlin plate modeling is adopted. The equation of plate motion is discretized by finite elements using the virtual work principle and integrated by the Newmark method. To consider the fluid-structure interaction, the nonlinear free-surface motion and the plate motion are numerically solved through an iterative method at each time step.
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paper_title: Three-Dimensional Time-Domain Analysis of Very Large Floating Structures Subjected to Unsteady External Loading

paper_content:

The strong interest in very large floating structure (VLFS) is a result of a need to utilize effectively the ocean space for transportation, industrial use, storage, habitats, and military bases, among others. The VLFS has great width and length and relatively small flexural rigidity, therefore, investigation of its hydroelastic behavior including fluid-structure interaction is of greater importance than studies of its motion as rigid bodies. In addition to the most important wave-induced responses, the operation of the VLFS also requires determination of its dynamic responses with respect to the effect of unsteady external loading due to intense traffic, load movement, takeoffs and landings of airplanes, missile takeoffs, etc. Therefore, the transient responses of a VLFS to impulsive and moving loads must be studied by a reliable calculation method. In this study, a finite element procedure developed directly in time domain for solution of transient dynamic response of the coupled system consists of a VLFS and a fluid domain subjected to arbitrary time-dependent external loads is presented. The hydrodynamic problem is formulated based on linear, inviscid, and slightly compressible fluid theory and the structural response is analyzed under the thin plate assumption. For numerical calculations, a scaled model of the Mega-Float is exemplified. Three tests-weight pull-up test, weight drop test, and weight moving test which idealize the airplane landing and takeoff-are carried out and compared with published experimental data. The overall agreement was favorable which indicates the validation of the present method.
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paper_title: Numerical calculation method for the hydroelastic response of a pontoon-type very large floating structure close to a breakwater

paper_content:

Abstract 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.
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paper_title: Very large floating structures

paper_content:

1. Colonization of the Ocean and VLFS Technology 2. Wave Phenomenon and Properties 3. Hydroelastic Analysis of VLFS 4. Structural Analysis and Design of VLFS 5. Analysis and Design of Station Keeping Systems 6. Analysis and Design of Breakwaters 7. Model Experiments for VLFS 8. Maintenance and Anti-Corrosion Systems 9. Research and Developments of VLFS
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paper_title: Time Domain Analysis on the Dynamic Response of a Flexible Floating Structure to Waves

paper_content:

A time-domain numerical method is developed to analyze the hydroelastic responses of flexible floating structures to waves; in which, the boundary element method is applied to evaluate the fluid motion and the finite-element method to analyze the elastic deformation of structure. The dynamic wave-structure interaction is simulated by prescribing the conditions on a wave generation boundary for each time step and by satisfying the continuity of the pressure and displacement on the fluid-structure interface. A time-domain solution is obtained in a predictor-corrector scheme and through a time-stepping computation. The effect of space and time discretizations on the convergence and stability of solution for regular, random and solitary waves is discussed by comparing among numerical solutions. The validity of the present method is verified by comparing it with the experimental results for the three kinds of waves mentioned. Further, the fission of a solitary wave under a flexible floating structure is observed both in numerical analysis and experiments.
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paper_title: The influence of water depth on the hydroelastic response of a very large floating platform

paper_content:

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.
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paper_title: Hydroelastic behaviour of compound floating plate in waves

paper_content:

The paper deals with the plane problem of the hydroelastic behaviour of floating plates under the influence of periodic surface water waves. Analysis of this problem is based on hydroelasticity, in which the coupled hydrodynamics and structural dynamics problems are solved simultaneously. The plate is modeled by an Euler beam. The method of numerical solution of the floating-beam problem is based on expansions of the hydrodynamic pressure and the beam deflection with respect to different basic functions. This makes it possible to simplify the treatment of the hydrodynamic part of the problem and at the same time to satisfy accurately the beam boundary conditions. Two approaches aimed to reduce the beam vibrations are described. In the first approach, an auxiliary floating plate is added to the main structure. The size of the auxiliary plate and its elastic characteristics can be chosen in such a way that deflections of the main structure for a given frequency of incident wave are reduced. Within the second approach the floating beam is connected to the sea bottom with a spring, the rigidity of which can be selected in such a way that deflections in the main part of the floating beam are very small. The effect of the vibration reduction is quite pronounced and can be utilized at the design stage.
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paper_title: An anti-motion device for a very large floating structure

paper_content:

We proposed a simple anti-motion device, which is a box-shaped body attached to an edge of VLFS. The performance of this device is investigated theoretically and experimentally in the present work. The theory is based on the eigen-function expansion method and the extension of this method to the oblique sea case is presented. The experiment is carried out in a wave tank with small-scale models. Both experimental results and the theoretical results show that the anti-motion performance of this device is very good at the design period in the case of beam-sea. The theory also demonstrates that this device reduces not only the deformation but also the shearing force and the moment of the platform and it also works well in the oblique sea.
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paper_title: Investigation of the Effect of Stiffness Distribution And Structure Shape On Hydroelastic Responses of Very Large Floating Structures

paper_content:

This paper investigates the influences of stiffness distribution and structure shape on hydroelastic responses of very large floating structures (VLFS). Direct method is employed as a numerical tool to calculate hydroelastic responses such as displacements and stresses. Higher order boundary element method (HOBEM) is employed for the analysis of fluid flow. Structural stiffness and mass matrices and force vector are obtained by finite element method (FEM) employing Mindlin plate elements. A 1 km-long VLFS with uniform stiffness is considered in numerical example. To investigate the effect of stiffness distribution, modified VLFSs with nonuniform stiffness and mass distributions are analyzed. Discussions on response reduction by stiffening, setting moon pools and hinge linking are also included.
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paper_title: Connection design for two-floating beam system for minimum hydroelastic response

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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.
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paper_title: Wave interaction with multiple articulated floating elastic plates

paper_content:

Flexural gravity wave scattering by multiple articulated floating elastic plates is investigated in the three cases for water of finite depth, infinite depth and shallow water approximation under the assumptions of two-dimensional linearized theory of water waves. The elastic plates are joined through connectors, which act as articulated joints. In the case when two semi-infinite plates are connected through a single articulation, using the symmetric characteristic of the plate geometry and the expansion formulae for wave-structure interaction problem, the velocity potentials are obtained in closed forms in the case of finite and infinite water depths. On the other hand, in the case of shallow water approximation, the continuity of energy and mass flux are used to obtain a system of equations for the determination of the full velocity potentials for wave scattering by multiple articulations. Further, using the results for single articulation and assuming that the articulated joints are wide apart, the wide-spacing approximation method is used to obtain the reflection coefficient for wave scattering due to multiple articulated floating elastic plates. The effects of the stiffness of the connectors, length of the elastic plates and water depth on the propagation of flexural gravity waves are investigated by analysing the reflection coefficient.
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paper_title: Evaluation of bending moments and shear forces at unit connections of very large floating structures using hydroelastic and rigid body analyses

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This paper investigates the characteristics of bending moments, shear forces and stresses at unit connections of very large floating structures (VLFS) under wave loads. The responses of VLFS are calculated by solving multi-body motion equation considering hydroelasticity and connection stiffness. Hydroelastic responses are calculated by the direct method. Higher-order boundary element method (HOBEM) is used for fluid analysis and finite element method (FEM) is introduced for structural analysis. The equation of motion is modified to describe the unit connections by employing spring elements. Bending moments and shear forces at the connections are obtained from the dynamic equilibrium condition for pressures and inertia forces. Two types of VLFS units such as tandem arranged units and side-by-side arranged units are considered in the numerical examples. The influences of connection stiffness, wave frequency and heading angle on responses of VLFS are investigated through the numerical examples. Rigid body analysis along with hydroelastic analysis is also carried out in the numerical analysis and comparison of those two approaches is discussed.
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paper_title: AN ASSESSMENT OF HYDROELASTICITY FOR VERY LARGE HINGED VESSELS

paper_content:

A computational analysis is presented for the effects of waves on very large hinged vessels consisting of several modules, connected by simple hinges. Two generic types of modules are considered: rectangular barges similar to the Megafloat prototype and semi-submersibles similar to those proposed for mobile offshore bases. Most of the computations are for configurations with five modules, each of length 300 m. The results include vertical motions, structural deflections, and hinge shear forces in head and oblique waves. A range of structural stiffness parameters is considered, to permit a quantitative assessment of the importance of hydroelasticity.
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paper_title: Time Domain Analysis on the Dynamic Response of a Flexible Floating Structure to Waves

paper_content:

A time-domain numerical method is developed to analyze the hydroelastic responses of flexible floating structures to waves; in which, the boundary element method is applied to evaluate the fluid motion and the finite-element method to analyze the elastic deformation of structure. The dynamic wave-structure interaction is simulated by prescribing the conditions on a wave generation boundary for each time step and by satisfying the continuity of the pressure and displacement on the fluid-structure interface. A time-domain solution is obtained in a predictor-corrector scheme and through a time-stepping computation. The effect of space and time discretizations on the convergence and stability of solution for regular, random and solitary waves is discussed by comparing among numerical solutions. The validity of the present method is verified by comparing it with the experimental results for the three kinds of waves mentioned. Further, the fission of a solitary wave under a flexible floating structure is observed both in numerical analysis and experiments.
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paper_title: Hydroelastic responses and drift forces of a very-long floating structure equipped with a pin-connected oscillating-water-column breakwater system

paper_content:

Abstract The hydroelastic responses of a very-long floating structure (VLFS) in waves connected to a floating oscillating-water-column (OWC) breakwater system by a pin are analyzed by making use of the modal expansion method in two dimensions. The Bernoulli–Euler beam equation for the VLFS is coupled with the equations of motions of the breakwater taking account of the geometric and dynamic boundary conditions at the pin. The Legendre polynomials are employed as admissible functions representing the assumed modes of the VLFS with pinned-free-boundary conditions. It has been shown numerically that the deflections, bending moments and shear forces of the VLFS in waves can be reduced significantly by a pin-connected OWC breakwater. The time-mean horizontal drift forces of the VLFS equipped with the breakwater calculated by the near-field method are also presented.
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paper_title: Wave Response Analysis of VLFS With an Attached Submerged Plate

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This paper presents a wave response analysis of an elastic floating plate, of which a submerged horizontal plate is attached at the fore-end. The whole model is analyzed rigorously within the framework of the linear potential theory and the linear elasticity. The eigenfunction expansion matching method is employed to solve the hydrodynamic problem. The analytical results are compared with the experimental results. The agreement between the analytical results based on the linear potential theory and the experiment has been shown to be satisfactory, showing the significant effect of the submerged plate.
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paper_title: Reduction of hydroelastic responses of a very-long floating structure by a floating oscillating-water-column breakwater system

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Abstract The hydroelastic responses of a very-long floating structure (VLFS) placed behind a reverse T-shape freely floating breakwater with a built-in oscillating water column (OWC) chamber are analyzed in two dimensions. The Bernoulli–Euler beam equation is coupled with the equations of rigid and elastic motions of the breakwater and the VLFS. The interaction of waves between the floating rigid breakwater and the elastic VLFS is formulated in a consistent manner. It has been shown numerically that the structural deflections of the VLFS can be reduced significantly by a suitably designed reverse T-shape floating breakwater.
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paper_title: Experimental study on anti-heaving devices for very large floating structure

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This article presents an experimental study on various anti-heaving devices for a longish very large floating structure (VLFS). To reduce the heaving motion, a device in the form of a submerged plate is attached to the fore-end of the VLFS. We proposed a simple anti-heaving device, which is a submerged inclined plate. The performances of this device as well as three devices proposed in other previous studies, namely a horizontal plate, a vertical plate and an L-shaped plate, are investigated experimentally in the present work. A small scale model of VLFS with the plate attachments was tested in a wave-tank to assess their effectiveness in reducing the heaving motion. Experimental results show that the devices could significantly reduce the heaving motions of the VLFS. Among the four anti-heaving devices, the newly proposed inclined plate attachment seems to offer the best performance.
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Title: Reducing Hydroelastic Response of Very Large Floating Structure: A Literature Review
Section 1: INTRODUCTION
Description 1: Introduce the concept of Very Large Floating Structures (VLFS), their types, uses, and the need for addressing hydroelastic response in these structures.

Section 2: VLFS APPLICATION, ASSUMPTION
Description 2: Discuss the historical developments and various applications of VLFS, such as floating airports, bridges, storage facilities, and floating cities.

Section 3: HYDROELASTIC RESPONSE
Description 3: Describe the factors affecting the hydroelastic response of floating structures, including wave period, water depth, and structural rigidity.

Section 4: Hydroelastic Analysis
Description 4: Explain the methodologies used to perform hydroelastic analysis, including thin plate theory, frequency domain approach, time domain approach, and the different solution methods.

Section 5: Hydroelastic reduction
Description 5: Review various techniques for reducing the hydroelastic response of VLFS, such as increasing structural stiffness, using breakwaters, semi-rigid connections, and anti-motion devices.

Section 6: CONCLUSION REMARK
Description 6: Summarize the importance of reducing hydroelastic response for VLFS design, mention the methods discussed, and highlight potential benefits of implementing these methods.