Time Domain Simulation of Transient Responses of Very Large Floating Structures Under Unsteady External Loads

A time domain finite element method （FEM） for the analysis of transient elastic response of a very large floating structure （VLFS） subjected to arbitrary time-dependent external loads is presented. This method is developed directly in time domain and the hydrodynamic problem is formulated based on linear, inviscid and slightly compressible fluid theory and the structural response is analyzed on the thin plate assumption. The time domain finite element procedure herein is validated by comparing numerical results with available experimental data. Finally, the transient elastic response of a pontoon-type VLFS under the landing of an airplane is computed by the proposed time domain FEM. The time histories of the applied force and the position and velocity of an airplane during landing are modeled with data from a Boeing 747-400 jumbo jet.

Hydroelastic Analysis of Very Large Floating Structures Using Plate Green Functions

Great attention has been paid to the development of very large floating structures. Owing to their extreme large size and great flexibility, the coupling between the structural deformation and fluid motion is significant. This is a typical problem of hydroelasticity. Efficient and accurate estimation of the hydroelastic response of very large floating structures in waves is very important for design. In this paper, the plate Green function and fluid Green function are combined to analyze the hydroelastic response of very large floating structures. The plate Green function here is a new one proposed by the authors and it satisfies all boundary conditions for free-free rectangular plates on elastic foundations. The results are compared with some experimental data. It is shown that the method proposed in this paper is efficient and accurate. Finally, various factors affecting the hydroelastic response of very large floating structures are also studied.

Time Domain Calculation of Connector Loads of a Very Large Floating Structure

Loads generated after an air crash, ship collision, and other accidents may destroy very large floating structures （VLFSs） and create additional connector loads. In this study, the combined effects of ship collision and wave loads are considered to establish motion differential equations for a multi-body VLFS. A time domain calculation method is proposed to calculate the connector load of the VLFS in waves. The Longuet-Higgins model is employed to simulate the stochastic wave load. Fluid force and hydrodynamic coefficient are obtained with DNV Sesam software. The motion differential equation is calculated by applying the time domain method when the frequency domain hydrodynamic coefficient is converted into the memory function of the motion differential equation of the time domain. As a result of the combined action of wave and impact loads, high-frequency oscillation is observed in the time history curve of the connector load. At wave directions of 0° and 75°, the regularities of the time history curves of the connector loads in different directions are similar and the connector loads of C1 and C2 in the X direction are the largest. The oscillation load is observed in the connector in the Y direction at a wave direction of 75° and not at 0° This paper presents a time domain calculation method of connector load to provide a certain reference function for the future development of Chinese VLFS

Reliability-Based Optimal Design for Very Large Floating Structure

Costs and losses induced by possible future extreme environmental conditions and difficulties in repairing post yielding damage strongly suggest the need for proper consideration in design rather than just life loss prevention. This can be addressed through the development of design methodology that balances the initial cost of the very large floating structure (VLFS) against the expected potential losses resulting from future extreme wave induced structural damage. Here, the development of a methodology for determining optimal, cost effective design will be presented and applied to a VLFS located in the Tokyo bay. Optimal design criteria are determined based on the total expected life cycle cost and acceptable damage probability and curvature of the structure, and a set of sizes of the structure are obtained. The methodology and applications require expressions of the initial cost and the expected life cycle damage cost as functions of the optimal design variables. This study includes the methodology, total life cycle cost function, structural damage modeling, and reliability analysis.

Free-Surface Wave Interaction with a Very Large Floating Structure

The free-surface wave interaction with a pontoon-type very large floating structure(VLFS) is analyzed by utilizing a modal expansion method. The modal expansion method consists of separating the hydrodynamic analysis and the dynamic response analysis of the structure. In the dynamic response analysis of the structure,the deflection of the structure with various edge conditions is decomposed into vibration modes that can be arbitrarily chosen. Free-free beam model, pinned-free beam model and fixed-free beam model are three different types of edge conditions considered in this study. For each of these beam models, the detailed mathematical formulations for calculating the corresponding eigenvalues and eigenmodes have been given, and the mathematical formulations corresponding to the beam models of pinned-free beam and fixed-free beam are novel. For the hydrodynamic analysis of the structure, the boundary value problem(BVP) equations in terms of plate modes have been established, and the BVP equations corresponding to the beam models of pinned-free beam and fixedfree beam are also novel. When these BVP equations are solved numerically, the structure deflections and the wave reflection and transmission coefficients can be obtained. These calculation results point out some findings valuable for engineering design.

Linear and quadratic damping coefficients of a single module of a very large floating structure over variable bathymetry:Physical and numerical free-decay experiments

The linearity assumption is widely used when acquiring the hydrodynamic coefficients of a floating structure.However,the linear damping is frequently underestimated,especially for the natural frequency.To investigate the sloping seafloor effects on the damping terms of a single module of a semi-submersible Very Large Floating Structure(VLFS),this paper revisits the conventional formulation and further proposes the direct integration method for obtaining the linear and quadratic damping coefficients from free-decay tests.Numerical free-decay simulations of the single module over variable bathymetry are carried out by the CFD numerical tank.Corresponding model tests are also implemented to verify and validate against the numerical solutions.The effects of the sloping seafloor,as well as the water depth,on the hydrodynamic coefficients are investigated based on the validated CFD modeling.Both numerical and experimental results indicate that the acquisition of the linear and quadratic damping coefficients is sensitive to the data-processing and identification approaches.For the case studied in present paper,the identification errors introduced by the conventional method are 1.5%while they are 0.5%using the direct integration method.The quadratic damping coefficient for heave mode decreases about 10.4%when the sloping angle increases from 0 to 6 deg.

A method to Estimate Dynamic Responses of VLFS Based on Multi-Floating-Module Model Connected by Elastic Hinges

Based on the elastic foundation beam theory and the multi-floating-module hydrodynamic theory,a novel method is proposed to estimate the dynamic responses of VLFS(Very Large Floating Structure).In still water,a VLFS can be simplified as an elastic foundation beam model or a multi-floating-module model connected by elastic hinges.According to equivalent displacement of the two models in static analysis,the problem of rotation stiffness of elastic hinges can be solved.Then,based on the potential flow theory,the dynamic responding analysis of multi-floatingmodule model under wave loads can be computed in ANSYS-AQWA software.By assembling the time domain analysis results of each module,the dynamic responses of the VLFS can be obtained.Validation of the method is conducted through a series of comparison calculations,which mainly includes a continuous structure and a three-part structure connected by hinges in regular waves.The results of this paper method show a satisfactory agreement with the experiment and calculation data given in relative references.

Hydroelastic interaction between water waves and thin elastic plate floating on three-layer fluid

The wave-induced hydroelastic responses of a thin elastic plate floating on a three-layer fluid, under the assumption of linear potential flow, are investigated for two-dimensional cases. The effect of the lateral stretching or compressive stress is taken into account for plates of either semi-infinite or finite length. An explicit expression for the dispersion relation of the flexural-gravity wave in a three-layer fluid is analytically deduced. The equations for the velocity potential and the wave elevations are solved with the method of matched eigenfunction expansions. To simplify the calculation on the unknown expansion coefficients, a new inner product with orthogonality is proposed for the three-layer fluid, in which the vertical eigenfunctions in the open-water region are involved. The accuracy of the numerical results is checked with an energy conservation equation, representing the energy flux relation among three incident wave modes and the elastic plate. The effects of the lateral stresses on the hydroelastic responses are discussed in detail.

A Novel Conceptual Telescopic Positioning Pile for VLFS Deployed in Shallow Water:Structure Design

A conceptual design of using novel telescopic piles to position a multi-modular very large floating structure(VLFS),which is supposed to be severed as a movable floating airport,is proposed.The telescopic piles can automatically plug in the soil to resist the environmental loads and pull out from the soil to evacuate or move on to the next operational sea.The feasibility demonstration of the conceptual design includes two parts:function verification and structure design.In the latter part of the conceptual design,a time-domain structural analysis is firstly conducted by using Abaqus software.The simulation results suggest that the preliminary structure scheme is not optimum due to the insufficient structure utilization,although both structure safety of the piles and positioning accuracy are guaranteed.To realize a cost reduction of construction and installation,a Genetic Algorithm-Finite Element Analysis(GA-FEA)method is employed to perform structural optimization.After optimization,31 percent of the weight of each pile is reduced and higher structure utilization is maintained.The difference of the self-weight and allowable buoyancy of a single module(SMOD)of a semisubmersible-type VLFS is much larger than the weight of the piles.Combined with the function verification in our previous work,the conceptual design of using the novel telescopic pile to position VLFS is demonstrated to be feasible.

超大浮体与OWC集成系统的水动力性能:半解析研究

Responses of the very large floating Structures(VLFS)can be mitigated by implementing oscillating water columns(OWCs).This paper explores the fundamental mechanism of present wave interactions with both structures and examines the hydrodynamic performance of VLFS equipped with OWCs(VLFS-OWCs).Under the linear potential flow theory framework,the semi-analytical model of wave interaction with VLFS-OWCs is developed using the eigenfunction matching method.The semi-analytical model is verified using the Haskind relationship and wave energy conservation law.Results show that the system with dual-chamber OWCs has a wider frequency bandwidth in wave power extraction and hydroelastic response mitigation of VLFS.It is worth noting that the presence of Bragg resonance can be trigged due to wave interaction with the chamber walls and the VLFS,which is not beneficial for the wave power extraction performance and the protection of VLFS.

Comparison of Linear Level I Green-Naghdi Theory with Linear Wave Theory for Prediction of Hydroelastic Responses of VLFS

Very Large Floating Structures (VLFS) have drawn considerable attention recently due to their potential significance in the exploitation of ocean resources and in the utilization of ocean space. Efficient and accurate estimation of their hydroelastic responses to waves is very important for the design. Recently, an efficient numerical algorithm was developed by Ertekin and Kim (1999). However, in their analysis, the linear Level I Green-Naghdi (GN) theory is employed to describe fluid dynamics instead of the conventional linear wave (LW) theory of finite water depth. They claimed that this linear level I GN theory provided better predictions of the hydroelastic responses of VLFS than the linear wave theory. In this paper, a detailed derivation is given in the conventional linear wave theory framework with the same quantity as used in the linear level I GN theory framework. This allows a critical comparison between the linear wave theory and the linear level I GN theory. It is found that the linear level I GN theory can be regarded as an approximation to the linear wave theory of finite water depth. The consequences of the differences between these two theories in the predicted hydroelastic responses are studied quantitatively. And it is found that the linear level I GN theory is not superior to the linear wave theory. Finally, various factors affecting the hydroelastic response of VLFS are studied with the implemented algorithm.

On the Interaction of Surface Waves with An Elastic Plate of Finite Length in Head Seas

An eigen-function expansion method based on a new orthogonal inner product is proposed by Sahoo et al. (2000) for the study of the hydroelastic response of mat-type VLFS in head seas. However, their main emphasis is on the effect of edge conditions and they assume that the plate is of a semi-infinite length. In reality, the plate is of finite length. For consideration of the finite length effect, the reflection and transmission from the other end must be considered. The effect of this reflection and transmission on the hydroelastic response of VLFS is of interest for practical application. Furthermore, the physical meaning of the new inner product was not given in their paper. In this paper, it is shown that the new inner product can he derived from the governing equation and the bottom boundary conditions. Then the same eigen-function expansion method is adopted for the study of the hydroelastic response of an elastic plate of finite length in surface waves. Detailed comparisons are made between the present finite length model and the semi-infinite model and between the present model predictions and the experimental results. It is found that that the finite length effect is significant and the accuracy of present model is higher than the semi-infinite model. Furthermore, a new phenomenon, which is not mentioned in Sahoo et al. (2000), is found. Taht is, for larger L/h ratios, the reflection and transmission coefficients will oscillate with the non-dimensional parameter k(0) h. Further study is needed for full understanding of this phenomenon.

An Improved Simplified Method for Predicting the Hydroelastic Response of Mat-Like VLFS

Very Large Floating Structures (VLFS) have received considerable attention recently. Efficient and accurate estimation of their hydroelastic responses in waves is very important for the design. The most efficient approach would obviously be the analytical one, Within the category of analytical approaches, the simplified method proposed by Ohkusu and his colleague are of special characteristics. However, when one studies their methods, several questions arise. The purpose of this paper is to critically study the simplified methods proposed by Ohkusu and his colleague in order to answer these questions. Some problems in their original methods have been found and possible improvements are suggested. It is concluded that the improved simplified method using the same idea of Ohkusu and his colleague could provide a reasonable estimate of the hydroelastic response of mat-like VLFS in a certain range of incident angles of waves.

Transient Hydroelastic Response of VLFS by FEM with Impedance Boundary Conditions in Time Domain

A time-dependent finite element method (FEM) is developed to analyze the transient hydroelastic responses of very large floating structures (VLFS) subjected to dynamic loads. The hydrodynamic problem is formulated based on the linear theory of fluid and the structural response is analyzed based on the thin plate theory. The FEM truncates the unbounded fluid domain by introducing an artificial boundary surface, thus defining a finite computational domain. At this boundary surface an impedance boundary conditions are applied so that no wave reflections occur. In the proposed scheme, all of the procedures are processed directly in time domain, which is efficient for nonlinear analyses of structure floating on unbounded fluid. Numerical results indicate acceptable accuracy of the proposed method.

Hydroelastic Response Analysis of Mat-Like VLFS over A Plane Slope in Head Seas

Very large floating structures (VLFS) have an extremely large size of several kilometers in length, thus, the environment at one end of the platform may be different from that at the other end. The importance of such an inhomogeneous environment to the hydroelastic response of a VLFS is of obvious concern for practical application. Some studies have been carried out to investigate the effects of shoreline proximity, breakwaters and harbor walls. In this paper, the impact of the variable depth on the hydroelastic responses of a VLFS is investigated. For simplicity, an ascending plane slope is taken to simulate the varying bottom although the method is capable of treating a bottom of arbitrary variation. The long wave theory and the thin plate theory are employed to model the wave field and the mat-like VLFS respectively. The finite difference method is used to numerically solve the boundary value problem. The results for the zero inclination slope are compared with experimental data and an analytical method to validate the present numerical method. Finally the effect of the inclination of the slope on reflection and transmission coefficients and plate deflections are investigated thoroughly.

Oblique Wave-Induced Responses of A VLFS Edged with A Pair of Inclined Perforated Plates

This paper is concerned with the hydroelastic responses of a mat-like, rectangular very large floating structure(VLFS) edged with a pair of horizontal/inclined perforated anti-motion plates in the context of the direct coupling method. The updated Lagrangian formulae are applied to establish the equilibrium equations of the VLFS and the total potential formula is employed for fluids in the numerical model including the viscous effect of the perforated plates through the Darcy’s law. The hybrid finite element-boundary element(FE-BE) method is implemented to determine the response reduction of VLFS with attached perforated plates under various oblique incident waves.Also, the numerical solutions are validated against a series of experimental tests. The effectiveness of the attached perforated plates in reducing the deflections of the VLFS can be significantly improved by selecting the proper design parameters such as the porous parameter, submergence depth, plate width and inclination angle for the given sea conditions.

A direct coupling analysis method and its application to the Scientific Research and Demonstration Platform

Design of a very large floating structure(VLFS)deployed near islands and reefs,different from those in the open sea,inevitably faces new technical challenges including numerical analysis methods.In this paper,a direct coupling analysis method(DCAM)has been established based on the Boussinesq equations and the three-dimensional hydroelasisity theory with Rankine source method to analyze the responses of a VLFS in shallow sea with complicated geographical environment.Model tests have been carried out to validate the DCAM.To further verify the numerical methods and investigate the performance of such a VLFS,a“Scientific Research and Demonstration Platform(SRDP)”was built and deployed in 2019 at the site about 1000 m off an island with water depth around 40m in South China Sea.It is a simplified small model of a two-module semi-submersible-type VLFS.The numerical simulation of its responses on severe waves with focus on motions and connector forces is conduct by DCAM,and compared with the on-site measurements.Good agreement has been achieved.This approves the DCAM as a feasible tool for design and safety assessment of a VLFS deployed near islands and reefs.

Power enhancement of pontoon-type wave energy convertor via hydroelastic response and variable power take-off system

Wave energy has gained its popularity in recent decades due to the vast amount of untapped wave energy resources.There are numerous types of wave energy convertor(WEC)being proposed and to be economically viable,various means to enhance the power generation from WECs have been studied and investigated.In this paper,a novel pontoon-type WEC,which is formed by multiple plate-like modules connected by hinges,are considered.The power enhancement of this pontoon-type WEC is achieved by allowing certain level of structural deformation and by utilizing a series of optimal variable power take-off(PTO)system.The wave energy is converted into useful electricity by attaching the PTO systems on the hinge connectors such that the mechanical movements of the hinges could produce electricity.In this paper,various structural rigidity of the interconnected modules are considered by changing the material Young’s modulus in order to investigate its impact on the power enhancement.In addition,the genetic algorithm optimization scheme is utilized to seek for the optimal PTO damping in the variable PTO system.It is observed that under certain condition,the flexible pontoon-type WEC with lesser connection joints is more effective in generating energy as compared to its rigid counterpart with higher connection joints.It is also found that the variable PTO system is able to generate greater energy as compared to the PTO system with constant/uniform PTO damping.