Very large floating structures

... 1.1.1 Definition and types of VLFS Floating structures are broadly classified as pontoon type and semi-submersible floating structures Semi-submersible type floating structures are partly raised above... porosity Hence instead of building large structures in deep water region and soft seabed conditions, floating structures are an economical option Also, due to their floating nature, the foundation... VLFS (e) Floating infrastructures: Two of the major infrastructural applications of floating structures have been covered above, viz bridges and airplane runways Other applications include floating

ASPECT RATIO AND SLOPING SEABED ON HYDROELASTIC RESPONSE OF VLFS

MRINALINI PATHAK

NATIONAL UNIVERSITY OF SINGAPORE

2014

EFFECTS OF WAVELENGTH, WATER DEPTH,

ASPECT RATIO AND SLOPING SEABED ON HYDROELASTIC RESPONSE OF VLFS

MRINALINI PATHAK

B.Tech (Civil Engineering), Sardar Vallabhbhai National Institute of Technology, Surat, India

A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING

DEPARTMENT OF CIVL AND ENVIRONMENTAL ENGINEERING

NATIONAL UNIVERSITY OF SINGAPORE

2014

I hereby declare that the thesis is my original work and has been written by me in

Dedicated to

My parents

I wish to express my deep gratitude to Professor Wang Chien Ming for his guidance, encouragements

and invaluable suggestions throughout this research His enthusiasm and research acumen have

inspired me immensely and greatly shaped my reasoning ability Over the period of last two years, the

knowledge gained and lessons learnt under his supervision are invaluable to me and I believe that

they will enormously help me in my future endeavors

I would also like to extend my sincere thankfulness to Dr Gao Ruiping for his patience and

persistent cooperation and help throughout the research He has been a great support during my

course of study and helped me with the tiniest doubts I encountered with utmost patience I will be

always grateful to him for sharing his knowledge and experience with me

I would also like to extend my thanks to the faculty members of Civil Engineering

department who have taught me various courses which have helped me in research

I would like to thank National University of Singapore for giving me the opportunity to study

here and I appreciate the staff of Civil Engineering department for addressing and helping with

administrative matters

Last but not least, I am immensely grateful to my parents for providing all the love and

support It is due to their belief on me and their constant encouragement that I have successfully

completed my study in Singapore I would also like to thank my friends and loved ones for their

constant support and understanding

Mrinalini Pathak

Table of Contents

Acknowledgements i

Table of Contents iii

Summary v

List of Tables vii

List of Figures ix

List of Notations xiii

Chapter 1 INTRODUCTION 1

1.1 Background information on VLFS 1

1.1.1 Definition and types of VLFS 2

1.1.2 Advantages of VLFS 4

1.1.3 Applications of VLFS: Past to present and future 5

1.2 Literature survey 8

1.3 Research objectives 13

1.4 Thesis layout 14

Chapter 2 HYDROELASTIC ANALYSIS OF VLFS 17

2.1 Plate-water model 18

2.2 Governing equations of motions 19

2.2.1 Equations of motion of plate 19

2.2.2 Equations of motions of water 22

2.3 Numerical solutions of fluid-structure system 25

2.3.1 Finite element method for solving plate deflections 25

2.3.2 Boundary element method for solving velocity potentials 30

2.3.3 Constant panel method to calculate velocity potential 32

2.4 Modal expansion method 34

2.5 Summary 38

Chapter 3 EFFECT OF WAVELENGTH ON HYDROELASTIC BEHAVIOUR OF VLFS 39

3.1 Numerical model 39

3.2 Effect of wavelength on hydroelastic behaviour of VLFS 41

3.3 Effect of water depth on hydroelastic behaviour of VLFS 43

3.4 Upstream and downstream deflections of VLFS 45

3.5 Summary 47

Chapter 4 EFFECT OF ASPECT RATIO ON HYDROELASTIC BEHAVIOUR OF VLFS 49

4.1 Numerical model 49

4.2 Effect of aspect ratio (B/L) on hydroelastic behaviour of VLFS 51

4.3 Effect of water depth on hydroelastic behaviour of VLFS with different aspect ratios 55

4.4 Effect of aspect ratios on upstream and downstream deflections of VLFS 59

4.4.1 Effect of water depth 63

4.4.2 Effect of wavelength 65

4.5 Summary 66

Chapter 5 EFFECT OF SEABED SLOPE ON HYDROELASTIC BEHAVIOUR OF VLFS 67

5.1 Numerical model 67

5.2 Effect of seabed slope on hydroelastic behaviour of VLFS 70

5.3 Summary 76

Chapter 6 CONCLUSIONS AND RECOMMENDATIONS 77

6.1 Conclusions 77

6.2 Recommendations 79

References 81

Appendix A Finite Element Formulation of Mindlin Plate 87

Appendix B Boundary Integral Equation 97

Summary

Very Large Floating Structures (VLFS) is a promising technology that facilitates ocean space

colonization, a sustainable and environmental friendly technological innovation which enables

creation of land on water without disturbing marine environment, polluting coastal waters and

disrupting ocean currents VLFS are becoming a popular choice in a wide range of applications like

floating bridges, walkways, recreational structures, storage facilities and offshore platforms Owing to

their large size and small depth, the VLFS deforms under the action of waves Hence, their

hydroelastic deformations should be checked for serviceability limits In order to understand the

hydroelastic behaviour of VLFS under various sea states and seabed conditions, parametric studies

are undertaken in this thesis Owing to the purpose and function, a VLFS can take many shapes and

orientations In this thesis, the behaviour of the most commonly used, rectangular VLFS of different

aspect ratios subjected to different wavelengths and water depths is studied in detail Since a VLFS is

generally connected to the land and deployed in near-shore regions, the effect of varying seabed

topography also becomes significant Therefore studies investigating the effect of sloping seabed

topography are also presented herein In addition to overall hydroelastic responses of VLFS, the end

deflections which are usually largest in magnitude are also studied for different situations The ends

of a VLFS are particularly important because they are also the connecting interface between the

VLFS and land-masses

To idealize the physical VLFS system, an equivalent numerical model is considered in terms

of a plate floating on a fluid domain The VLFS is modelled as an isotropic, elastic and flat Mindlin

plate with free edges The fluid is assumed to be ideal, incompressible, inviscid and irrotational so

that the velocity potential exists Linear wave potential theory is used to model the fluid-motion by

using the velocity potential, i.e single frequency velocity potential of water which satisfies the

Laplace’s equation The wave potential satisfies boundary condition at the seabed, linearized kinematic boundary condition on the fluid structure interface, linearized dynamic boundary condition

on free surface of water and Somerfield radiation condition at artificial boundary condition at infinity

The main objective of the hydroelastic analysis is to determine the fluid velocity potentials and plate

displacements In order to decouple the fluid–structure interaction problem, the modal expansion

method is adopted for the hydroelastic analysis which is carried out in the frequency domain

Boundary element method is used to solve the Laplace equation for the velocity potential and finite

element method is employed for solving the equations of motion of the floating plate

In Chapter 1, a general introduction of VLFS and their past, present and future applications in

different fields are presented Chapter 2 describes the hydroelastic analysis of a floating structure and

present method for solving the fluid-structure interaction problem Chapters 3, 4 and 5 present and

discuss the results obtained from the formulation as well as parametric studies to comprehend the

behaviour of VLFS Chapter 6 presents the summary and key points of this thesis and also the

suggested future studies related to the present research

The studies carried out in the thesis provide an insight to the hydroelastic behaviour of a

VLFS in different sea conditions and on constant and sloping seabed topographies The solutions to

the fluid structure interaction problems in this thesis may serve as benchmark solutions for structural

and offshore engineers in analysis of VLFS

List of Figures

Figure 1 1 Components of VLFS system 3

Figure 1 2 Two phase floating runway project, the Mega-Float, in Japan (Suzuki et al 2005) 6

Figure 1 3 (a) World’s longest floating bridge, Governor Albert D Rossellini Bridge (aka

Evergreen Point Bridge) (b) Yumemai Bridge, Japan (c) Dubai floating bridge,

(source: bridge-info.org, Wikipedia) 7

Figure 1 4.(a) Ujina’s floating pier (b) Floating walkway made of High Density

Poly-Ethylene (HDPE) modules 7

Figure 1 5 (a) Keppel-built 6th Generation Semi-Submersible (b) FPSO vessel in Angola

(source: energy-pedia news) (c) Kamigoto Floating Oil Storage Base, Nagasaki

Prefecture, Japan (d) Floating nuclear power plant in Russia (source: RIA novosti) (e) Hexicon, a Swedish design for wind energy farm (source:Main(e) Consulting

Ltd.) (f) 125 MWE OTEC Plant designed by Dr Alfred Yee 11

Figure 1 6.(a) Performing stage at Marina Bay, Singapore (b) Floating breakwater, Monaco

seawall, in Monaco (source: FCC const.) (c) Jumbo restaurant in Hong Kong (d) Prof Wang’s proposed floating crab restaurant (e) Lilipads – floating

cities(sourc:vincent.callebaut.org) (f) Proposed Greenstar floating hotel and

convention centre 12

Figure 2 1 Plan and elevation views of plate-water problem domain 19

Figure 2 2 Mindlin plate element in physical coordinates and its isoparametric transformation

in natural coordinates 27

Figure 3.1 Plan and elevation views of plate-water problem domain 40

Figure 3.2 Centre-line deflections of VLFS in four different wavelengths (a) α=0.2 (b) α=0.4

(c) α=0.5 and (d) α=0.6 in water depth and H=58.5m 41

Figure 3.3 Centre-line deflection of VLFS subjected to different wavelengths, α=0.2,0.4,0.5

and 0.6 in water depths (a) H=20m (b) H=58.5m and (c) H=100m 42

Figure 3.4 Centre-line deflections of VLFS in three different water depths, H=20m, 40m,

58.5m and 100m for (a) α=0.2 (b) α=0.4 (c) α=0.5 and (d) α=0.6 44

Figure 3.5 Variations of (a) upstream and (b) downstream deflections of VLFS with respect to

water depth, H , in different wavelengths (α=0.1, 0.2, 0.3, 0.4, 0.5 and 0.6) 47

Figure 4.1 Plan and elevation views of plate-water problem domain 50

Figure 4.2 Centre-line deflections of VLFS with five aspect ratio, B/L= 1/5,1/3,1,3/2 and 3, in

water depth, H=20m for (a) α=0.2 (b) α=0.4 (c) α=0.5 and (d) α=0.6 52

Figure 4.3 Centre-line and edge-line response of VLFS of aspect ratio, B/L=1/5 subjected to

wavelength of α=0.2 and 0.6 in water depth, H=20m 54

Figure 4.4 Centre-line and edge-line response of VLFS of aspect ratio, B/L=1 subjected to

wavelength of α=0.2 and 0.6 in water depth, H=20m 54

Figure 4.5 Centre-line and edge-line response of VLFS of aspect ratio, B/L=3 subjected to

wavelength of α=0.2 and 0.6 in water depth, H=20m 55

Figure 4.6 Centre-line and edge-line response of VLFS of aspect ratio, B/L=1/5 subjected to

wavelength of α=0.2 and 0.6 in water depth, H=100m 56

Figure 4.7 Centre-line and edge-line response of VLFS of aspect ratio, B/L=1 subjected to

wavelength of α=0.2 and 0.6 in water depth, H=100m 56

Figure 4.8 Centre-line and edge-line response of VLFS of aspect ratio, B/L=3 subjected to

wavelength of α=0.2 and 0.6 in water depth, H=100m 57

Figure 4.9 Centre-line deflection of VLFS of different aspect ratio (a) B/L=1/5 (b) B/L=1 (c)

B/L=3, in four water depths, H=20m, 40m, 58.5m and 100m subjected to two

wavelength α=0.2 and 0.6 58

Figure 4.10 Displacement of upstream point of VLFS in different water depths and

wavelengths for aspect ratio (a) B/L=1/5 (b) B/L=1 and (c) B/L=3 61

Figure 4 11.Displacement of downstream point of VLFS in different water depths and

wavelengths for aspect ratio (a) B/L=1/5 (b) B/L=1 and (c) B/L=3 62

Figure 4.12 Ratio of upstream and downstream deflections of aspect ratio B/L=1/5, 1/3, 1, 3/2

and 3 v/s water depth in different wavelengths (a) α=0.2 (b) α=0.4 (c) α=0.5 and (d) α=0.6 64

Figure 4.13 Ratio of upstream and downstream deflections of aspect ratio B/L=1/5, 1/3, 1, 3/2

and 3 v/s wavelengths in different water depths (a) H=20m (b) H=30m (c) H=50m and (d) H=100m 65

Figure 5.1 Plan and elevation views of plate-water problem domain 68

Figure 5.2 Validation against Kyoung et al (2005) in three different cases of seabed slope

configurations, (a) H 1 , H 2 =15m, 7.5m (b) H 1 , H 2 =30m, 15m (c) H 1 , H 2=58.5m,

29.25m for wavelengths α=0.2, 0.6 69

Figure 5.3 Various seabed topographies used by Kyoung et al (2005) (a) slope from upstream

point of VLFS to mid-ship of structure (b) slope from mid-ship of structure to

downstream point of VLFS (c) slope from upstream to downstream points of VLFS (d) seabed cosine hump 70

Figure 5.4 Centre-line deflections of VLFS on sloping seabed when H1=20m, 30m, 58.5m and

100m and H 2 =20m in four wavelengths (a) α=0.2 (b) α=0.4 (c) α=0.5 and (d) α=0.6 73

Figure 5.5 Variation in Wd with respect to the wavelength for (a) =20m (b) =30m (c)

=40m and (d) =50m in different upstream water depths H 1 74

Figure 5.6 Variation in Wd with respect to the water depth for =20m, 30m, 40m and 50m in

wavelength (a) α=0.2 (b) α=0.4 (c) α=0.5 and (d) α=0.6 75

w, , Plate deflection, rotations about x and y axes

( ) Modal functions and complex amplitudes of the l-th mode of the plate x,y,z Cartesian coordinates

x=(x,y,z) Field points

( ) Source points

G(x, ) Three-dimensional free surface Green function

R(x, ) Distance between source and field point

α Incident wavelength-to-structure length ratio

Shear correction factor

Plate material density, kg/m 3

Water density, kg/m 3

Incident, diffraction, radiated and scattered potential

Radiation potential corresponding to the unit-amplitude motion of l-th modal

function

W u Upstream plate deflection per unit amplitude

W d Downstream plate deflection per unit amplitude

Normal strains

Shear strains

Normal stresses

Shear stresses

The e-th element in the plate mesh

(g,h) Natural coordinates of parametric element

( ) Shape functions of 8-node serendipity element

[ ] Shear-strain-displacement matrix due to assumed shear strain field

[ ] Global flexural stiffness matrix

[ ] Global hydrostatic stiffness matrix

Chapter 1

INTRODUCTION

This chapter introduces Very Large Floating Structures (VLFS) as an emerging technology and solution for land creation from the sea In this chapter, a brief introduction, literature survey and thesis outline are given The brief introduction describes the VLFS system in general, its applications

in the past and the present and its inherent advantages over the traditional land reclamation technique for birthing land from sea Also, examples of prominent VLFS systems from around the world are mentioned as evidence of their emerging importance A literature review on various studies, methods and results of VLFS by different researchers is presented It also shows the gaps between the studies undertaken till now and the real world problems and also provides the backdrop for the present study as a solution to the problem Lastly, the research objectives of the thesis and its layout are given

1.1 Background information on VLFS

Population explosion and lifestyle preferences for coastal areas are leading to lack of space and

amenities In order to alleviate these demands of coastal land pressure and land scarcity, near shore

and ocean space are now emerging as potential frontiers for colonization Also, oceans offer a

plethora of opportunities in terms of renewable energy, food resources, minerals and hydrocarbons

Countries like Japan, Singapore, Monaco, the Netherlands have extended their land mass by land

reclamation processes These methods have numerous topographical limitations and resulted in

boundary disputes, environmental disruptions and are cost inefficient Therefore, VLFS emerged as a

promising technology which facilitates ocean space colonization, a sustainable and environmental

friendly technological innovation which enables creation of land on water without disturbing marine

environment, polluting coastal waters and disrupting ocean currents

With numerous inherent advantages, VLFS technology is adopted by various countries, viz

Japan, Singapore, United States of America, the Netherlands, Monaco, South Korea and many more

densely populated cities and countries around the world In view of inevitable growing needs of

VLFSs, researchers and engineers have studied their behaviour, developed and implemented

innovative ideas to make this technology popular and mainstream Following sub-topics present a

general description of VLFS, their applications in different fields and some of their inherent

advantages

1.1.1 Definition and types of VLFS

Floating structures are broadly classified as pontoon type and semi-submersible floating structures

Semi-submersible type floating structures are partly raised above the sea level using column tubes or

watertight ballast structural compartments at the bottom/hull to minimize the effects of waves while

maintaining a constant buoyant force Therefore they are suitably deployed in deep seas with large

waves Floating oil drilling platforms used for drilling and production of oil and gas and

semi-submersible type floating wind farms are typical examples of semi-semi-submersible-type floating

structures Some semi submersibles are transported using outside vessels such as tugs or barges, and

some have their own propulsion system for transport and are then properly moored to the sea beds

When these floating structures are attached to the seabed using vertical tethers with high pretension as

provided by additional buoyancy of the structure, they are referred as tension-leg platforms This

particular type of floating structures is currently believed to be one of the few serviceable solutions

for areas further away from shorelines where waves are larger and have been exploited as early as the

1970s

Pontoon-type floating structures are in direct contact to the water surface and utilize larger

area than semi-submersibles, making them prone to wave motion Thus the hydroelastic deformations

are more significant than rigid deformations, making them more suitable in calm waters They are

basically simple box type structures which float on the surface of the water body and feature high

stability for calm sea conditions, e.g., a cove or a lagoon or near the shoreline In rough sea

conditions, being prone to roll and pitch due to large waves and swells, they are installed along with

breakwaters or other protective installations To restrain their movements in horizontal direction, they

are anchored to the seabed with the help of mooring lines which can be chains, ropes, sinkers, anchors

or tension legs depending on the requirement of the structure For greater restrain, either the pier/quay

wall method or the dolphin-frame guide mooring system may be adopted The pontoon type floating

structures are very cost effective with low manufacturing costs and easy to repair and maintain

As mentioned above, a pontoon type VLFS typically has five major components (see Fig

1.1), namely (1) an access bridge or a floating walkway from land (2) very large pontoon-type

floating structure, VLFS (3) superstructure and facilities (4) a mooring system or a station keeping

system (5) a breakwater

Figure 1.1.Components of VLFS system

A floating structure can be classified as a VLFS depending on two parameters First is its

length with respect to the wavelength of the incoming wave and second is its characteristic length

Characteristic length, defined by Suzuki et al (1996), is a parameter of the structure which is

equivalent to the length of the structure influenced due to an equivalent point load applied on it For a

larger than its characteristic length and also the wavelength of the incoming wave Once the floating

structure is classified as a VLFS, it is essential to conduct a hydroelastic analysis due to its flexibility

under wave action

1.1.2 Advantages of VLFS

Apart from alleviating pressure on land demand, VLFS has many inherent advantages over the

traditional land reclamation technique in creating land from sea These advantages are (Wang et al

2008):

(a) Environmental friendly: Construction and installation of VLFS do not require reclamation and

dredging of sand, hence saving the marine habitat and restoring the marine ecosystems

(b) Cost effective: The principle behind working of VLFS is buoyancy which is unaffected by the

water depth and seabed porosity Hence instead of building large structures in deep water region

and soft seabed conditions, floating structures are an economical option Also, due to their

floating nature, the foundation systems needed for them are limited to foundations of moorings

(c) Easy and fast construction: VLFS can be constructed as a single module or multiple modules

connected together Different modules can be constructed at different locations simultaneously

and can be towed to the desired location and assembled together thereby reducing time and

money Also they can be dismantled or retracted or moved to facilitate other operations or

transport them to different places

(d) Protection from seismic shocks: Superstructures and people on VLFS are insulated from seismic

shocks as the VLFS is inherently base-isolated

(e) Internal spaces: Empty watertight spaces in the hull of VLFS create the necessary buoyancy of

the VLFS which can be used as a storage space, parking spaces or offices

Next section is dedicated to some prominent VLFS systems around the world and their applications in

numerous fields

1.1.3 Applications of VLFS: Past to present and future

Floating structures have been a part of various cultures in the forms of floating homes and villages

and floating docks and bridges They were an innovative idea to create and connect different

landmasses or landmass to marine vessels, alleviate traffic pressures, enable movement of equipment

and soldiers in the time of war etc The use of floating structures began in offshore industry when a

semi-submersible rig was accidently invented in Gulf of Mexico by Blue Water Drilling Company

Floating structures have evolved in last 50 years in terms of size and serviceability VLFS technology

is now opted other infrastructural areas like floating air base, emergency centre, recreational centre,

performing stage, barges and FPSOs Following is a summary of VLFS’s functional areas and their

examples

(a) Floating Air-base: Japan adopted the VLFS technology to build the Mega-float, a one kilometre

long and 60 m wide pontoon type floating airplane runway The near to shore runway is cheaper

in comparison to reclaimed landmass Fig 1.2 shows two phases of the project undertaken by

Japan Government

Figure 1.2.Two phase floating runway project, the Mega-Float, in Japan (Suzuki et al 2005)

(b) Floating bridges: These longish VLFS enable both road and marine traffic as they are easy to

construct and deploy and are an economical alternative in calm waters Largest floating bridge in

the world is in United States of America, Evergreen Point Bridge which is 4750m long and has

four lanes of vehicular traffic (Fig 1.3) Very recent example of floating bridge is in Dubai,

which is a temporary arrangement for an upcoming mega-project and can handle 3000 vehicles

per hour of vehicular traffic flow in each direction It is 365m long and 22m wide It was

constructed in a record time of 300 days An inherited advantage of floating bridges is that they

can be constructed in segments which can be retracted, hence allowing marine traffic too

(c) Floating docks and bases: Floating docks have been an important part in army operations and as

a connecting link between landmasses and marine vessels Ujina’s floating pier (see Fig 1.4(a))

in Hiroshima, Japan is a concrete floating pier which extends in the water and facilitates docking

of vessels and movement of goods Alaska’s floating concrete terminal in Valdez provide services

to 50,000 tonnes capacity ships and 5000 tonnes capacity barges Watertight containers in the

concrete units of floating piers provide buoyancy and maintain required freeboard Small scale

floating walkways are used very frequently for recreational purposes on the shore and rivers as

shown in Fig 1.4b Rescue emergency bases such as in Osaka, Tokyo and Ise bays in Japan,

country which is in an earthquake-prone geographical region, are also floating structures which

are immune to seismic forces and are designed to accommodate gravity and wave loads

(a)

Figure 1 3 (a) World’s longest floating bridge, Governor Albert D Rossellini Bridge (aka

Evergreen Point Bridge) (b) Yumemai Bridge, Japan (c) Dubai floating bridge, (source:

bridge-info.org, Wikipedia)

Figure 1 4 (a) Ujina’s floating pier (b)Floating walkway made of High Density Poly-Ethylene

(HDPE) modules

(d) Floating offshore structures and facilities: With oil exploration moving to deeper waters, VLFS,

both semi-submersible and pontoon types, have emerged like FPSO (floating production storage

and offloading) vessels and oil storage units such as Kamigoto storage facility in Nagasaki in

Japan which has storage capacity of 7,00,000 kl of fuel and oil storage facility at Pulao Sebarok

in Singapore, which holds 3,00,000 cubic meters of fuel Apart from offshore structure related to

hydrocarbon industries, offshore structures like wind-farms, ocean thermal energy conversion

(OTEC) platforms, floating wave-energy converters, floating nuclear power plants are also

successfully in operation in different parts of world harnessing other sources of energy Fig 1.5

encompasses some major offshore VLFS

(e) Floating infrastructures: Two of the major infrastructural applications of floating structures have

been covered above, viz bridges and airplane runways Other applications include floating

entertainment facilities like Marina Bay performing stage in Singapore and Jumbo restaurant in

Hong Kong, floating breakwaters like Monaco seawall in Monaco, serving as a breakwater and

vehicle parking arena simultaneously Many architects and engineers around the world have

proposed various sustainable floating cities Some examples are shown in Fig 1.6

1.2 Literature survey

Hydroelastic analysis of a pontoon type VLFS can be regarded as a fluid-structure interaction

problem Therefore both the fluid part and the structure part have to be modelled in order to simulate

the VLFS system The fluid part, water, is usually assumed to be an ideal fluid, i.e incompressible,

inviscid and has irrotational motion, thereby a velocity potential exists The motion of the water is represented by velocity potential which is governed by Laplace’s equation The structure part, VLFS, can be modelled as a one dimensional beam or two dimensional plate structure Its deflection and

stresses denotes its hydroelastic response to wave forces Early studies to solve the motion of rigid

plate using boundary value problem were undertaken by John (1949; 1950) He used Green’s function

for boundary integral formulation to account for wave scattering by rigid bodies Wehausen and

Laitone (1960), on the other hand have studied in detail the linear wave theory and published their study in the famous article ‘Surface Waves’ Their article provided one of the pioneering solutions of

the wave-structure interaction problems Significant work by Bishop et al (1986) in hydroelastic

analysis of floating and fixed offshore structures included three dimensional fluid-structure modelling

using of Green’s function method and finite element method These developments made the feasibility and popularity of VLFS possible In recent times, major contributors to the development of

hydroelastic theory of VLFS are Etekin et al (1993), Suzuki (1996; 2005), Yago and Endo (1996),

Kashiwagi (1998; 2000), Utsunomiya et al (1998), Ohmatsu (1998; 1999) and Belibassakis (2008)

Similar ice-floe problems were studied by Meylan and Squire (1996)

Early research includes approximation of a longish VLFS structure as a one-dimensional

structure Longish VLFS denotes that one horizontal dimension of the VLFS is significantly larger

than the other one Such simplistic model can be used to model runways, bridges, walkways and

piers However, such models are overestimated as the wave effects from the edges perpendicular to

wave direction is neglected (Yamashita et al 2003) Also, such models are inadequate to model

square type VLFS More refined model consists of modelling a two-dimensional plate structure on a three dimensional fluid domain This model has the structure based on Kirchhoff’s plate theory and

zero draft assumption (Watanabe et al 2004) Kirchhoff’s theory assumes that the horizontal

dimensions of the structure are very large compared to its depth The use of such model is proven to

be accurate by various researchers like Kashiwagi (1998), Meylan (2001) and Watanabe et al (2000)

But the drawback of this method is that the stress resultants are not accurately predicted at the free

edges as they are calculated from approximate deflection derivatives Also the effects of shear

deformation and rotary inertia are neglected These may lead to erroneous predictions in high

frequency vibration and shorter wavelengths In order to overcome these difficulties, researchers

turned to Mindlin plate theory to model the structure (Wang et al 2001) In this thesis, the Mindlin

plate theory is used

Boundary element method (BEM) and finite element method (FEM) have been widely used

to model the fluid part BEM is more suitable and accurate for linear problems and give almost same

level of accuracy as FEM BEM uses lesser elements and nodes in hydroelastic analysis than FEM

which reduces computation time and data storage capacity Researchers, like Becker (1992), Hermans

(2000), popularly use BEM whereas others like Sannasiraj et al (2000), Kyoung et al (2005), have

used FEM in their formulation of fluid part Due to linear nature of problem, BEM is used in this

thesis as it gives fairly accurate results in a lesser time Moreover, Belibassakis and Athanassoulis

(2005) used coupled-mode model for hydroelastic analysis of large floating bodies Belibassakis

(2008) used hybrid technique of solving the problem using boundary element method and

coupled-mode coupled-model

While designing the VLFS, it is important to fulfil its functional requirements and

serviceability, which are directly related to the hydroelastic response of VLFS Hence understanding

the hydroelastic response of the structure in different conditions is important The behaviour of

semi-infinite and strip VLFP (Very Large Floating Platform) in shallow, finite and semi-infinite water depths has

been studied by Andrianov and Hermans (2003) They investigated the behaviour of VLFP with

different flexural rigidities in different wavelengths and water depths Xia et al (2000) studied the

effects of incoming wave frequencies on multi-module infinite and semi-infinite two dimensional

VLFS They also investigated the displacements of the plate at the free edges and found that they

edge displacements were much larger than that in the middle of the plate However, main drawback is

their assumption of a semi-infinite plate to represent a finite VLFS which may be inaccurate.Yago

and Endo (1996) have also studied the effect of different wavelengths and wave angles on the

hydroelastic behaviour of a finite two dimensional plate modelled as VLFS resting on two

dimensional fluid domain

designed by Dr Alfred Yee

(a) (b)

Figure 1 6 (a) Performing stage at Marina Bay, Singapore (b) Floating breakwater, Monaco

seawall, in Monaco (source: FCC const.) (c) Jumbo restaurant in Hong Kong (d) Prof

Wang’s proposed floating crab restaurant (e) Lilipads – floating cities(sourc:vincent.callebaut.org) (f) Proposed Greenstar floating hotel and convention centre

The aforementioned studies are largely based on constant seabed configuration Studies on

variable seabed topographies have been done by various researchers like Kyoung et al (2005),

Belibassakis (2008), Wang and Meylan (2002) in both time and frequency domains Kyoung et al

(2005) studied the effects of different seabed topographies on two dimensional finite VLFS resting on

three dimensional fluid domain and used FEM for both structure and fluid part to solve the problem

Studies involving BEM for hydrodynamic analysis of floating bodies in two and three dimensional

fluid domains with variable bathymetry region are undertaken by Belibassakis (2008) and

Belibassakis and Athanassoulis (2005) However, they considered a semi-infinite thin plate to idealize

a floating structure A more refined model which comprises modelling of the floating structure as a

finite thick plate resting on a fluid domain modelled using hybrid FE-BE method (finite

element-boundary element method) in frequency domain is presented in this thesis Such model makes the

problem more practical and realistic

1.3 Research objectives

In line with the above studies, the objective of the present research is to refine the VLFS model to

make it more generic and carry out parametric studies to understand the hydroelastic behaviour of

VLFS in more depth Therefore the main objectives of this research are:

 to investigate the effect of wavelength, water depth and aspect ratios of VLFS on hydroelastic behaviour of pontoon-type VLFS resting on three dimensional fluid domain with constant seabed;

 to solve the hydroelastic problem of pontoon-type longish VLFS resting on fluid domain with sloping seabed topography

The parametric study in this thesis involving different parameters like wavelength, water depth and

aspect ratios is very important to understand the behaviour of VLFS in a given set of sea state

conditions This study can be used as a benchmark to predict the hydroelastic response of a VLFS in a

given set of parameters Studies relating to the most sensitive regions of a VLFS are also explained

Also, the hydroelastic behaviour of a longish VLFS modelled as a Mindlin plate on a sloping seabed

topography will provide researchers and engineers a deeper insight to design near-shore longish

VLFS like runways, bridges and walkways

1.4 Thesis layout

In Chapter 1, the definition and concept of VLFS are explained and the major advantages and their

applications are discussed A brief literature review on different VLFS problems and their modelling

and computational methods is given thereafter Finally, the objectives of the research in this thesis are

presented

In Chapter 2, a description of the numerical model is given and the assumptions adopted for

the model as stated Formulations of the floating plate and water are presented and the method of

solution, i.e finite element method for solving the plate deflections and boundary element method for

solving the velocity potential are given afterwards The constant panel method is used to implement

boundary element method on the fluid boundaries Formulations for both uneven and constant seabed

topographies are presented and accordingly the solutions are derived Also, the modal expansion

method to decouple and solve the coupled plate-water interaction problem is explained

In Chapter 3, results are obtained from the mathematical formulation The hydroelastic

responses of a longish VLFS in a constant water depth are studied and interpreted to reveal the effects

of different wavelengths and water depths Then, the hydroelastic response at the most sensitive

regions of VLFS, i.e upstream and downstream ends, are studied

In Chapter 4, the hydroelastic behaviours of VLFS with different aspect ratios are studied

The responses of longish, square and widish VLFS differ from each other The variations of these

differences with various wavelengths of incoming wave and different water depths are studied The

overall responses of all VLFS which include their edge deflection and upstream and downstream

deflections are studied in detail

In Chapter 5, the numerical model with irregular seabed condition is used to derive results for

a sloping seabed condition This type of seabed condition is very pertinent to near-shore zones and

hence in the design of floating structures like bridges and walkways The effect of different depths

and wavelengths on hydroelastic response of VLFS on sloping seabed is studied

Chapter 6presents the conclusions of the present studies and recommendations for future

research work relating to the present problem