CHAPTER ONE Introduction ‘’ World population is projected to grow from 6.1 billion in 2000 to 8.9 billion in 2050, increasing therefore by 47 per cent.” United Nations, 2004 The growth in urbanisation due to the continuous increase of world population and rural-urban migration problem has exerted great pressure on the urban cities The American Association for the Advancement of Science (AAAS) 1996 annual meeting has reported that about two-third of the humanity are crowded in the coastal cities resulting in these cities becoming over-developed, over-crowded and over-exploited Ultra high-rise structures as well as underground space solution are sought in order to fully utilise the lands in these highly urban cities However, with the world population growth keeps on expanding at an alarming rate and expected to reach 75% of the humanity by year 2025 (AAAS annual meeting, 1996), land scarcity problems are expected to increase dramatically in the near future The conventional way of expanding the land mass for land scarce countries such as Japan, the Netherlands, Monaco and Singapore through aggressive land reclamation programs Introduction are not cost effective or even feasible as the water depth gets larger than 20m or when the seabed is extremely soft Moreover, land reclamation works generally have a negative environmental impact on the coastlines and the marine eco-system Upadhayay et al (2002) and Padma (2004) claimed that the mangrove forest that plays a significant role in reducing the devastating impact of tsunamis that struck the southern India on 26 December 2004 is among the most threatened habitat in the world due to deliberate land reclamation for urban and industrial development The Reef Ecology Study Team of NUS also reported that Singapore has lost up to 65% of their live coral cover since 1986 due to major land reclamation activity As a solution to pursuing environmental friendly yet sustainable technology in creating additional land, Japanese engineers have propounded the construction of Very Large Floating Structure (VLFS) – a technology that allows the creation of artificial land from the sea without destroying marine habitats, polluting coastal waters and altering tidal and natural current flow (Wang et al., 2008) VLFSs have advantages over the traditional land reclamation solution in the following respects: they are cost effective when the water depth is large and the seabed is soft; environmentally friendly as they not damage the marine eco-system, or silt-up deep harbours or disrupt the ocean currents; they are easy and fast to construct and therefore the investment may be monetised more rapidly; they can be easily removed or expanded; and the structure on VLFS is protected from seismic shocks since VLFSs are inherently base isolated Examples of these pontoon-type VLFS are the Mega Float (a runway test model in Tokyo Bay, see Fig 1.1a), the emergency Introduction rescue bases (moored at Tokyo Bay, Ise Bay and Osaka Bay), the floating oil storage bases (in Shirashima and Kamigoto Islands, see Fig 1.1b), the floating ferry piers (at Ujina Port, Hiroshima, see Fig 1.1c), the floating bridges (in Dubai, UAE and Seattle, USA, see Fig 1.1d) and the floating performance stage (at Marina Bay, Singapore, see Fig 1.1e) (a) Mega-Float at Tokyo Bay, Japan (b) Floating oil storage base at Kamigoto Island, Japan (c) Floating ferry pier at Ujina Port, Hiroshima, Japan (d) Lacey V Murrow Bridge and the Third Washington Bridge at Seattle, USA (Photo courtesy of Prof E Watanabe Kyoto University) (e) Floating performance stage at Marina Bay, Singapore Fig 1.1 Applications of pontoon-type VLFSs Introduction The application of VLFSs as floating farms in urban cities may also emerge as an innovative solution to provide arable land in supplying food to the increasing growth of human population while maintaining the integrity of the ecosystem The sustainable engineering science barge (Fig 1.2a) – a prototype floating urban farm powered by sustainable energy that raises vegetables through water-saving hydroponic technology, is constructed by the New York Sun Works Center on the Hudson River in Manhattan to demonstrate that urban agriculture on floating structure is possible without causing damage to the environment In salmon producing countries such as Norway, the United States of America, Canada and Chile, marine salmon farm (Fig 1.2b) – a floating structure of one to twenty individual netpens (cages) that is anchored relatively close to shore, is constructed to ensure continuous supply of fresh fish even during the off-season of the species (Per Heggelund, 1989) (a) Sustainable engineering science barge at Hudson River, Manhattan, USA (source: http://nysunworks.org) (b) Salmon farms north of Vancouver, Canada (source: http://www.democracyinaction.org) Fig 1.2 Application of VLFSs as floating farms Introduction With the increase in the human population coupled with land-scarcity in cities and global warming problems, VLFS technology has emerged as a new option for future human habitation The Lilypad Floating Ecopolis (Fig 1.3a), proposed by the Belgium architect Vincent Callebaut, is an example of a visionary proposition to house part of the city population in a huge floating city With more than half of the Netherlands’s land area now below sea level, the Dutch have also proposed the concept of a floating town (Fig 1.3b), which is a visionary integrated town consisting of greenhouses, commercial centre and residential area Prof Wang Chien Ming from the National University of Singapore has also proposed the use of VLFS as a floating-type cruise terminal (Fig 1.3c) and a mega floating crab restaurant (Fig 1.3d) as opposed to the conventional onshore design in order to create iconic structures for Singapore to attract tourists The examples shown above show that the feasibility of using the VLFS technology as an attractive alternative to create additional lands for development In this thesis, we will focus on the use of VLFS for storing fuel in the sea Inspired by the successful construction and operation of the floating oil storage bases in Kamigoto and Shirashima Islands in Japan, Singapore is proposing the use of an offshore-based floating fuel storage facility (FFSF) to expand her fuel storage capacity The role of Singapore as the 3rd largest oil hub in the world and the advantages of the offshore-based floating fuel storage facility will be further discussed in the following section Introduction (a) Lilypad floating ecopolis (source: www.vincent.callebaut.org) (b) Visionary semi-aquatic town in the Netherlands (source: http://www.resosol.org) (c) Proposed floating cruise terminal in Singapore (d) Proposed mega floating crab restaurant in Singapore Fig 1.3 Proposed future VLFSs Introduction 1.1 Focusing on VLFS as Floating Fuel Storage Facility (FFSF) “Race is on to build storage facilities and add capacity Amid the huge global demand for oil, Singapore as the world’s 3rd largest trading hub has hit a snag – where to put the stuff? Its storage facilities are almost full and while additional space is coming up, the problem will resurface, an industry expert has warned…“ The Straits Times, 18 July 2005, page H21 World’s trade and development have increased rapidly with globalisation triggered by the information, communication and transportation technology Correspondingly, the demand for oil consumption has increased sharply Being the 3rd largest oil hub in the world, Singapore is facing an urgent need to increase its oil storage capacity with all the land for oil tank farms being almost exhausted Its conventional land-based oil tank farms are not amenable for further expansion due to land scarcity Industry feedback has indicated that Singapore is at least million cubic metres shortage of oil storage, which would require more than 100 hectares of land to accommodate (Yap, 2008) Innovative underground cavern-type storage facility for crude oil is currently being constructed in Jurong Island, Singapore Yet, more storage capacity for fuel is needed This need prompted the consideration of the floating type fuel storage facilities Introduction The presence of sterile sea spaces around various islands in Singapore makes the floating offshore storage facilities an enticing alternative A joint research project between Jurong Town Corporation (JTC), Maritime and Port Authority (MPA) and the National University of Singapore (NUS) was conducted with the objectives of producing a practical yet cost effective floating fuel storage system The proposed floating fuel storage facility comprises mega box-like floating storage modules that are placed side-by-side and held in position by mooring dolphin-rubber fender system to restrain its horizontal movement but allowing vertical movement with the waves and tidal changes, as well as with the varying payloads Floating breakwaters such as the one found in the Kanon Marina in Hiroshima, Japan (see Fig 1.5) could be constructed around the floating storage modules in order to attenuate the wave forces The floating breakwater can also double up as an oil fence as well as acting as a collision barrier Fig 1.4 Design concept of floating fuel storage facility (Picture courtesy of Jurong Consultants Pte Ltd.) Introduction Floating concrete breakwaters Fig 1.5 Floating concrete breakwaters at Kanon Marina, Hiroshima The feasibility studies for the FFSF, co-funded by JTC, MPA and NUS, have reported that for the storage of 300,000 cubic metres, the FFSF only requires hectares of foreshore land, a significant reduce of land by times as compared to that required for the land based storage facility (Yap, 2008) Moreover, such floating storage facilities also assist in providing relief to tanker traffic congestion and crowded anchorage spaces at Singapore harbours since these floating fuel storage facilities may double up as a bunkering cum mooring station for ships The FFSF also has the advantages of scalability and mobility Should the storage capacity of the FFSF needs to be increased, more storage modules may be added It can also be easily dismantled, removed or even relocated elsewhere The floating structures being afloat in the sea are also environmental friendly as they not affect the water quality and disrupting the water flow underneath the floating modules as well as causing irreversible damage to the marine habitat Introduction The FFSF does not only augment the oil storage capacity significantly but it also increases its waterfront for oil carriers and bunker ships The construction of the FFSF next to the land-based pumping control station will serve as the hub between the floating modules and the fuel supply vessels Petrochemical products such as processed and/or crude oil and feedstock petrochemicals (e.g ethylene, benzene, etc.) may also be stored in the floating modules This cutting-edge innovation by using the VLFS as a floating storage facility will continue to aid in bolstering the country’s standing in the oil trading and bunkering industry The storage of hydrocarbon and petrochemical out in the sea by ultilising the VLFS technology raises wonderful challenges in the design of the FFSF As FFSFs have a large surface area and a relatively small depth, they behave elastically under wave action The fluid-structure interaction has been termed as hydroelasticity Hydroelastic analysis that takes into account the elastic vibration modes of the structure is thus necessary to be carried out for the FFSF in order to assess the dynamic motion and stresses due to wave action for design (Suzuki and Yoshida, 1996) This PhD thesis focuses on the hydroelastic responses and interactions of two box-like floating storage modules by using the frequency domain approach The hydroelastic interaction behaviors of the floating storage modules when they are placed side-by-side are critical factors that affect the responses of the structures under wave actions The interactions between the modules under different loading combinations might also affect the loading/offloading operations Besides that, the enhanced wave elevations along the channel formed by the adjacently placed 10 Introduction Kashiwagi (1998), Utsunomiya et al (1998), Hermans (2000), Meylan (2001) and Watanabe et al (2000) However, the stress resultants (such as the twisting moments and shear forces) are not accurately predicted and they not satisfy the free-edge boundary conditions (Wang et al., 2001) The inaccuracy is due to the stress resultants being computed from second and third derivatives of the approximate deflections In addition, the effects of shear deformation and rotary inertia are neglected in the classical thin plate theory Also, these effects become significant in high frequencies of vibration and should be included when the floating structure is subjected to wavelength shorter than twenty times the thickness or when the thickness-length ratio of the floating structure is greater than 0.005 as reported by Mindlin (1951) and Petyt (1990) As the mega floating storage module such as the one shown in Fig 1.4 has a larger thickness to length ratio compared to the pontoon-type VLFS, the classical thin plate theory could no longer predict the deflections and stress resultants correctly Furthermore, the zero-draft assumption made on the VLFS in the hydroelastic analysis could no longer be applied to the FFSF due to its larger draft under loaded condition The hydroelastic responses based on the zero-draft assumption are found to be inaccurate when the draft of the floating modules gets larger or when the VLFS is operating in shallow water condition (Suzuki et al., 2006; Riggs et al., 2008) Watanabe et al (2000) adopted the Mindlin plate theory (thick plate theory) where the motion of the plate is represented not only by its deflection but also its bending rotations They derived an exact hydroelastic solution for a circular VLFS 14 Introduction under wave action Recently, Wang and Wang (2006) used the 4-node Mindlin plate element to model the elastic plate Computational results from Wang and Wang (2006) agreed well with the exact solution They found that the predicted stress resultants better satisfy the free-edge natural boundary conditions when compared to the Kirchhoff plate However, on closer examination of the transverse shear forces, it was found that these forces not vanish completely at the free edges of the plates as they should Kim and Choi (1992) and Bathe (1996) investigated the inadequacy of the numerical Mindlin plate model in obtaining the correct shear forces distribution as the thickness of the plate gets smaller Hence the plate does not bend easily due to excessive shear stiffness on the plate Such a phenomenon is known as shear locking and it prevents the stresses from vanishing at the free edges To overcome the shear locking problem, Bathe (1996) suggested the use of reduced integration, selective interpolation or mixed interpolation methods that will increase the flexibility of the element In contrast, Choi (1986) superposed non-conforming modes on the basis functions of a 9-node element in order to restore the real flexural deformation to avoid shear locking phenomena Kim and Choi (1992) claimed that their 9-node element can avoid shear locking phenomenon when the interpolated shear strain function contains more variables than the number of equations obtained This means that either the number of variables has to be increased or the number of equations relating the shear strains has to be decreased Therefore, they proposed the coupling of reduced integration method with additional non-conforming modes 15 Introduction Note that the Kirchhoff plate theory assumes that the normal to the middle surface remains normal to the deformed surface This assumption is tantamount to neglecting the effect of transverse shear deformation This means that shear force has to be calculated from the equilibrium equation since it is zero if calculated from the constitutive relation Thus, the shear force expression in the Kirchhoff plate theory involves the third derivative of the transverse deflection which of course will not be accurate Unlike the Kirchhoff plate theory, the Mindlin plate theory allows the normal to the undeformed middle surface to rotate (albeit in a constant rotation) with respect to the deformed midsurface This assumption admits a constant shear strain and hence a constant shear stress through the plate thickness In order to compensate for the error due to the violation of the statical condition of zero stress at the free surfaces, a shear correction factor is introduced to factor the shear force in the Mindlin plate theory (given later as κ in the Mindlin plate theory Eqs 2.9a-c) Notwithstanding, the shear force expression in the Mindlin plate theory involves the constant bending rotation ψ x ,ψ y (which is a new variable) and only the first derivative of the deflection function (see Eqs 2.13c in Chapter 2) So it is clear that the shear forces calculated using the Mindlin plate theory should be more accurate than its Kirchhoff plate counterpart Therefore, the methods proposed by Kim and Choi (1992) and Bathe (1996) are highly contributory in predicting the stress distribution on the slabs of the mega floating fuel storage modules correctly In order to reduce the computational time, their modified 9-node element could be simplified to an 8-node element without loss of accuracy in the stress distribution This 16 Introduction designated 8-node NC-QS Mindlin plate element will be used in modelling the floating storage modules in order to access the hydroelastic responses and interactions behaviour of the floating storage modules when they are placed side-by-side 1.2.3 Hydroelastic Responses and Interactions of Adjacently Placed Floating Modules Extensive hydroelastic analyses had been carried out on the VLFS under wave actions by modelling the floating structure as a solid plate as presented in the previous section The hydroelastic responses computed on the equivalent solid plate were found to be in good agreement with the experimental test results (Yago and Endo, 1996; Kashiwagi, 1998; Utsunomiya, 1998) However, there have been relatively few studies conducted on the hydroelastic responses and hydrodynamic interactions of multiple VLFS when they are placed side-by-side and with the presence of floating breakwater Koo and Kim (2005) studied the hydrodynamic interactions between the adjacent storage modules of LNG gas terminals in the Gulf of Mexico, but their calculations were carried out by assuming rigid body motions of the floating structures, i.e neglecting the elastic deformations of the modules They found that the safety and operability of the side-by-side loading and offloading operation are greatly influenced by the relative motions between the adjacent modules due to wave action 17 Introduction A comprehensive review on the research and development of the Mega-Float project from 1995-2001, as well as its legal aspect and environment impact have been reported by Suzuki (2005) Ohmatsu (2000) presented an effective method for calculating the wave induced hydroelastic response of a pontoon-type VLFS when the VLFS is near a breakwater Based on his study, he found that the response of the VLFS decreases when the reflected coefficient of the breakwater is small Utsunomiya et al (1998) also presented a wave response analysis of a box-like VLFS near a breakwater by employing the higher order boundary element method (HOBEM) The influence of a breakwater on the response was determined and its effectiveness in reducing the response of the VLFS was confirmed However, these researchers have not studied the hydrodynamic interactions of the floating storage modules when placed adjacent to each other and with floating breakwaters in place It is to be noted that the breakwater considered in the previous researchers’ studies are of the bottom-founded type In the literature, there are studies focusing on the hydrodynamic properties of floating breakwaters by treating the breakwater as a separate part of the structure instead of investigating the influence of floating breakwater towards the response of the floating structures Therefore, investigations on the hydroelastic responses and interactions of the adjacently placed floating storage modules enclosed by floating breakwater are the focus of the present study 18 Introduction 1.2.4 Wave Propagation along Channel Formed by Two Adjacently Placed Floating Modules While the hydroelastic interactions between the floating storage modules are significant towards the structural responses as reviewed in the previous section, the significant effect of the interactions towards the wave field surrounding the floating structures should not be neglected as well In the literature, although extensive research investigations (Molin et al., 2002; Chen, 2004; Chau and Eatock Taylor, 1992; Issacson and Cheung, 1996; Bai and Eatock Taylor, 2006) have been made on wave diffraction and radiation by floating bodies such as barges, vessels and cylinders (in which their motions are dominated by rigid body modes), only a few researchers such as Wang and Meylan (2002) and Utsunomiya and Watanabe (2006) have studied the wave reflection by a VLFS under regular wave action Furthermore, to date, there have been relatively few studies conducted on wave diffraction and radiation along the channel formed by VLFS-type floating bodies which are deformable under wave action Molin et al (2002) and Chen (2004) showed that the free surface elevations are large as the wave propagates through the channel formed by barges placed side-by-side The enhanced wave elevations along the channel formed by the two floating storage modules significantly govern the design of the floating storage modules As green water adversely affects the stability of the floating storage modules, adequate freeboard should be designed when the storage modules are fully loaded with fuel 19 Introduction 1.2.5 Steady Drift Forces on Adjacently Placed Floating Modules When the floating modules are placed close to each other with a relatively small gap, hydrodynamic interactions between two bodies are expected to be large and complex Owing to the hydrodynamic interaction, large repulsion and drift forces may be exerted on the storage modules, resulting in damage to the mooring system The consequences due to the failure of the mooring system when typhoon and tsunami occurred were addressed by Suzuki (2001) Suzuki (2001) reported that an upper limit of casualty of 10,000 lives was estimated from the fatal failure scenario of the VLFS used as a floating airport during heavy storms This vast numbers of casualty lives highlight the importance of designing the mooring dolphin system correctly In doing so, the steady drift forces have to be computed for the design of the mooring dolphin fenders There are two well known methods for computing the wave interaction problems which are respectively the near-field method based on the direct pressure integration method and the far-field method based on the momentum-conservation principle Kagemoto and Yue (1986), Chakrabarti (2000), Maruo (1960) and Newman (1967) applied the far-field method to solve the wave interaction problems The far-field method gives only the total forces on all floating modules that are included by fictitious vertical circular cylinder located far from the ships The wave interaction theory proposed by Kagemoto and Yue (1986) and Chakrabarti (2000) is applicable to any number of modules of arbitrary geometry and in a general spatial arrangement 20 Introduction with the assumption that the fictitious bottom-mounted vertical cylinder circumscribing one module does not intersect any part of the other modules (see Fig 1.6) Kashiwagi et al (2005) showed that the results of the wave forces in the surge response may still be accurate although the assumption stated in Fig 1.6 is violated but it is not the case for the wave forces in the heave response (a) valid (b) not valid Fig 1.6 Validity of the far-field method based on wave interaction theory proposed by Kagemoto and Yue (1986) (a) Valid when fictitious cylinder circumscribing one module does not intersect any part of the other module (b) Invalid when the fictitious cylinder intersects part of the other module On the other hand, the near-field method proposed by Pinkster (1979) gives individual forces on each floating structure but the computations are rather complicated because various components must be evaluated, such as the flow velocity on the wetted surface of a ship and the relative wave height along the waterline of a ship (Kashiwagi et al., 2005) Fang and Chen (2002) and Kashiwagi et al (2005) adopted the near-field method to compute the interaction of two ships which are arranged side-by-side in waves Relative good agreement is found between Kashiwagi et al.’s (2005) computed and experimental results As the prediction of the steady forces on each floating module of the FFSF is a requisite, the near-field 21 Introduction method must be used Analysis of steady drift force acting on a single VLFS by the near-field method had been carried out by researchers such as Namba et al (1999) and Utsunomiya et al (2001) The numerical scheme presented by these authors could be extended for the evaluation of steady drift forces acting on adjacently placed mega floating storage modules 1.3 Objectives and Scope of Study The foregoing literature reviews provide insights in identifying the research gaps that need further investigation for the hydroelastic analysis and design of the FFSF For the hydroelastic analysis, we only consider the FFSF that comprises two floating storage modules placed side-by-side and enclosed by floating breakwater under operation condition We used the linear potential wave theory to model the regular wave whereas the floating fuel storage module is modelled as an equivalent solid plate without considering the effect of fluid sloshing in the modules towards the wave-structure interaction The objectives of this thesis are to: i develop numerical models and solution techniques for solving hydroelastic interactions problem of very large floating structures ii develop robust computer codes in MATLAB that are capable of determining: • the hydroelastic interaction behavior of adjacently placed floating storage modules (this knowledge is important for designing the appropriate 22 Introduction spacing for the modules), • the flow field especially the wave elevations in the channel formed by the storage modules (this knowledge is needed to design the necessary freeboard for the modules to avoid green water on deck), and • the steady drift forces, allowing for the interaction of floating storage modules (this knowledge is needed to design the mooring dolphin rubber fender system) iii verify the formulation, solution technique and computer code using existing results obtained from other researchers as well as to validate the computed results by carrying out experimental tests of floating structural models in a water basin iv conduct parametric studies to investigate the effect of: • floating breakwater, channel spacing, draft, water depth and wave angle on the responses and interactions of the floating modules • wave angle, channel spacing, attachment of parapet wall around the perimeter deck, floating breakwater and water depth on the wave elevations along the channel • channel spacing and floating breakwater on the steady drift forces 23 Introduction The key developments in the modelling and numerical techniques are summarised below i Application of thick plate element for modelling the storage modules Normally, researchers used thin plate elements for modelling the VLFS In contrast, we shall adopt the modified NC-QS Mindlin plate element proposed by Choi (1986) to model the floating fuel storage modules The advantage of the NC-QS Mindlin plate element is that it allows a more accurate prediction of the stress resultants since the spurious modes and shear locking phenomena are eliminated The accurate stress distributions are significant in determining the suitable wall thicknesses of the floating storage modules It will be shown herein that hydroelastic analysis carried out using the NC-QS element is not only accurate in both deflections and stress resultants computed, but also fast in achieving convergence to the true solution, thereby greatly reducing the computational time ii Development of numerical model for hydroelastic analysis and hydrodynamic interactions of floating fuel storage modules For the first time, the hydroelasic interactions behaviour of the floating storage modules placed side-by-side will be investigated in detail The computed hydroelastic results enable us to design suitable spacings between the floating modules A suitable channel spacing is important because if the spacing is too small, the interactions of the floating modules increase 24 Introduction significantly and if the channel spacing is too large, the FFSF utilises precious sea space The number of mooring dolphins required when the floating storage modules are placed too far apart will also increase correspondingly, hence such a design is not cost effective The behaviour of the floating modules under different fuel loading combinations will also be studied in order to determine the suitable loading combinations so as to minimise the undesirable interaction between the floating modules iii Development of numerical model for wave propagation along channel formed by two floating storage modules The developed numerical model would enable us to investigate the effect of hydroelastic interaction towards the wave elevations along the channel formed by two floating storage modules The prediction of the wave runup due to wave being squeezed in the narrow channel is crucial for the design of suitable freeboard and draft of the floating storage modules so as to avoid green water on deck The wave field surrounding the floating storage modules could also be computed in order to assess the diffracted and radiated behavior of the waves as it interacts with the floating modules This information could contribute significantly for coastal engineers in understanding the reflections of waves by deformable floating structures and its impact towards the coastal erosion especially when the FFSF is located near shore 25 Introduction iv Development of numerical model for predicting steady drift forces The developed numerical model will be used to investigate the steady drift forces allowing for the interaction of floating storage modules These steady drift forces are important to the engineers when designing the mooring dolphin rubber fender system It is desirable to use the optimal size and number of mooring dolphin systems so as to save costs In the next section, a brief overview on the organisation of this thesis is given 1.4 Organisation of Thesis In this chapter, the background information, the applications and advantages of VLFS as a floating fuel storage facility in Singapore are presented Literature reviews are given on the recent advances in the hydroelastic analyses of VLFS The research gaps related to the studies on the FFSF design are identified The objectives and scope of this thesis are articulated and key developments on the numerical techniques are highlighted In Chapter 2, we first define the hydroelastic problem of FFSF The assumptions made to enable the formulation of the fluid-structure interaction problems are stated The governing equations and boundary conditions that describe the coupled fluid-structure motion are then presented The Mindlin plate theory is adopted to model the box-like floating structures as equivalent solid plates and the linear potential theory is used to model the water 26 Introduction The solution technique to solve the governing equations and the boundary conditions is given in Chapter A modified non-conforming quadratic-serendipity (NC-QS) Mindlin plate element (an 8-node Mindlin plate element with additional non-conforming modes) which ensures a better prediction to the hydroelastic responses and stress resultants is introduced in discretising the equivalent solid plate The hybrid finite element–boundary element (FE-BE) method technique is used for determining the hydroelastic response and the wave field surrounding the floating structure The steady drift forces are determined using the near-field method (pressure integration method) In Chapter 4, we verify the accuracy of the modified NC-QS Mindlin plate element introduced in modelling the floating structures by comparing the numerical results on plate deflections and stress resultants with various existing results The significant improvement in shear forces predicted using the 8-node NC-QS Mindlin plate element as compared with their counterparts modelled using the 4-node Mindlin plate element is highlighted After establishing the accuracy of the NC-QS element, the developed numerical model is then used to perform hydroelastic analysis on the specific example of FFSF in Chapter We first study the hydroelastic interactions behaviour of the floating storage modules when the modules are placed side-by-side Experimental tests are carried out in order to validate the hydroelastic interactions behaviour of the two adjacently placed floating storage modules After validating the numerical model, parametric studies are carried out to investigate the interaction behaviour of the 27 Introduction two floating storage modules under different floating breakwater sizes, channel spacings, drafts, water depths and wave angles In Chapter 6, we investigate the wave elevations along the channel formed by the two floating storage modules placed side-by-side Experimental tests are also conducted to validate the computed wave elevations along the channel Parametric studies are then carried out to investigate the effect of wave angle, channel spacing, parapet wall, floating breakwater and water depth have on the wave elevations along the channel The computed wave elevations are used to design the allowable freeboards and drafts of the floating storage modules A suitable channel spacing that could mitigate the hydroelastic response of the empty storage modules and maximise the loading capacities of the storage modules is proposed In Chapter 7, we investigate the steady drift forces acting on the storage modules by considering the effect of hydroelastic interactions between the modules placed side-by-side The steady drift forces are computed based on the near-field method (pressure integration method) The numerical results on a single VLFS are first verified with Watanabe et al.’s (2000) far-field method The hydroelastic interactions behaviour of the two adjacently placed storage modules towards the steady drift forces is then studied These drift forces are used for the design of the mooring fenders Conclusions and recommendations for future research studies on the floating fuel storage facility are presented in the final chapter 28 ... hydroelastic responses and interactions behaviour of the floating storage modules when they are placed side-by-side 1. 2.3 Hydroelastic Responses and Interactions of Adjacently Placed Floating Modules. .. hydroelastic theory of VLFS are Ertekin and Riggs (19 93), Suzuki (19 96, 2005), Yago and Endo (19 96), Kashiwagi (19 98, 2000), Utsunomiya et al (19 98) and Ohmatsu (19 98, 19 99) The development of. .. the hydroelastic responses and interactions of two box-like floating storage modules by using the frequency domain approach The hydroelastic interaction behaviors of the floating storage modules