numerical offshore tank - description

12
Santos Offshore Conference 2009 21 a 23 de Outubro de 2009 - Mendes Convention Center - Santos - São Paulo - Brasil Pág: 1 de 1 TPN - Tanque de Provas Numérico: Uma Infra-Estrutura Inovadora para Os Novos Desafios da Produção Brasileira Os atuais desafios impostos pela produção offshore no Brasil têm demandado o desenvolvimento de ferramentas de projeto e análise cada vez mais precisas e robustas no que tange à abordagem dos problemas inerentes às atividades desta natureza. São comuns pesquisas que contam com uma abordagem analítico-numérica, concomitante a uma abordagem experimental responsável pela geração de resultados para confrontação e calibração. O TPN, neste contexto, é uma iniciativa brasileira inovadora caracterizada por uma infra-estrutura aparelhada com dois elementos principais: um cluster para simulações numéricas com sala de projeção 3D e um tanque físico especificamente construído para calibração dos coeficientes hidrodinâmicos de uso no simulador. Em linhas gerais, o cluster para simulações numéricas é dotado de um conjunto de processadores trabalhando em paralelo, compondo uma capacidade de 50 teraflops. A visualização das simulações, por sua vez, conta com um ambiente de realidade virtual, no qual o expectador tem a possibilidade de interagir com os resultados e, até mesmo, experimentar parte dos comportamentos dinâmicos dos sistemas em estudo através de um hexapod. O tanque físico, denominado Calibrador Hidrodinâmico, é uma infra-estrutura experimental voltada ao estudo de modelos em escala reduzida, cuja característica principal é a geração de ondas multidirecionais e concomitante absorção das mesmas. Em resumo, com estas inovações o TPN se habilita como uma infra-estrutura alinhada às demandas atuais, servindo não só aos novos desenvolvimentos do cenário de produção nacional de petróleo offshore, como também à formação de recursos humanos especificamente voltados à atuação no segmento científico-tecnológico brasileiro. Palavras-chave: Tanque de provas numeric (TPN); cluster de alta performance; de provas com absorção ativa de ondas; multidisciplinaridade; novas pesquisas e desenvolvimento.

Upload: rodolfo-goncalves

Post on 03-Jul-2015

514 views

Category:

Documents


2 download

DESCRIPTION

The Numerical Offshore Tank - TPN was idealized to work through a cooperative approach. In its new infrastructure, TPN has a high performance cluster of 50 TeraFLOPS, which runs an integrated and multitask set of analytical models and numerical tools for a wide diversity of operational conditions of new offshore and naval architecture projects. In addition, TPN has an hydrodynamic basin, with active wave absorption, specifically dedicated to generate experimental results for comparison purpose and, in specific cases, for validation of design hypothesis and, eventually, new analytical models.

TRANSCRIPT

Page 1: Numerical Offshore Tank - Description

Santos Offshore Conference 2009 21 a 23 de Outubro de 2009 - Mendes Convention Center - Santos - São Paulo - Brasil

Pág: 1 de 1

TPN - Tanque de Provas Numérico: Uma Infra-Estrutura Inovadora

para Os Novos Desafios da Produção Brasileira

Os atuais desafios impostos pela produção offshore no Brasil têm demandado o

desenvolvimento de ferramentas de projeto e análise cada vez mais precisas e robustas no que

tange à abordagem dos problemas inerentes às atividades desta natureza.

São comuns pesquisas que contam com uma abordagem analítico-numérica,

concomitante a uma abordagem experimental responsável pela geração de resultados para

confrontação e calibração.

O TPN, neste contexto, é uma iniciativa brasileira inovadora caracterizada por uma

infra-estrutura aparelhada com dois elementos principais: um cluster para simulações

numéricas com sala de projeção 3D e um tanque físico especificamente construído para

calibração dos coeficientes hidrodinâmicos de uso no simulador.

Em linhas gerais, o cluster para simulações numéricas é dotado de um conjunto de

processadores trabalhando em paralelo, compondo uma capacidade de 50 teraflops. A

visualização das simulações, por sua vez, conta com um ambiente de realidade virtual, no qual

o expectador tem a possibilidade de interagir com os resultados e, até mesmo, experimentar

parte dos comportamentos dinâmicos dos sistemas em estudo através de um hexapod.

O tanque físico, denominado Calibrador Hidrodinâmico, é uma infra-estrutura

experimental voltada ao estudo de modelos em escala reduzida, cuja característica principal é

a geração de ondas multidirecionais e concomitante absorção das mesmas.

Em resumo, com estas inovações o TPN se habilita como uma infra-estrutura alinhada

às demandas atuais, servindo não só aos novos desenvolvimentos do cenário de produção

nacional de petróleo offshore, como também à formação de recursos humanos

especificamente voltados à atuação no segmento científico-tecnológico brasileiro.

Palavras-chave: Tanque de provas numeric (TPN); cluster de alta performance; de provas

com absorção ativa de ondas; multidisciplinaridade; novas pesquisas e desenvolvimento.

Page 2: Numerical Offshore Tank - Description

Santos Offshore Conference 2009 21 a 23 de Outubro de 2009 - Mendes Convention Center - Santos - São Paulo - Brasil

Pág: 2 de 2

TPN – Numerical Offshore tank: an Innovative Infrastructure to the

New Brazilian Production Challenges

Abstract

It is quite evident that the new researches and developments in offshore oil production

have became considerably more complex as a consequence of the recent growing in the

demand and, therefore, the necessity of exploration in ultra deep water. Higher number of

operational conditions has being analyzed, taking into account simultaneous phenomena,

many of them in high level of complexity. In order to provide solutions and answers for many

of the problems involved in such scenario, a multidisciplinary approach, combining analytical

models, numerical tools and experimental activities, has being quite convenient and,

sometimes, the only prospective alternative. According to this philosophy, the Numerical

Offshore Tank - TPN was idealized to work through a cooperative approach. In its new

infrastructure, TPN has a high performance cluster of 50 TeraFLOPS, which runs an

integrated and multitask set of analytical models and numerical tools for a wide diversity of

operational conditions of new offshore and naval architecture projects. In addition, TPN has

an hydrodynamic basin, with active wave absorption, specifically dedicated to generate

experimental results for comparison purpose and, in specific cases, for validation of design

hypothesis and, eventually, new analytical models. This paper presents the main

characteristics of the new TPN, emphasizing capacities and, at the same time, discussing its

limitations. Further researches and developments are prospected based on this new facility, as

well as on the experience accumulated during the last years.

Keywords: Numerical Offshore Tank; high performance cluster; hydrodynamic basin with

active wave absorption; multidisciplinary approach; new researches and developments.

Page 3: Numerical Offshore Tank - Description

Santos Offshore Conference 2009 21 a 23 de Outubro de 2009 - Mendes Convention Center - Santos - São Paulo - Brasil

Pág: 3 de 3

1. Introduction

Brazil is currently one of the world leaders in deep and ultra deep water oil and natural

gas exploration as a result of extensive technological research program and strong

investments in exploration technologies.

Among others, the main particularity of the Brazilian oil and gas resources is its

location, along the coast in water depths up to three thousand meters deep. This makes

exploration more difficult and requires the development of new technologies, demanding the

increase of initial investments.

The exploration is performed making use of different types of anchored floating

production units, typically FPSOs or semi-submersibles. The risers and mooring system are

essential elements to extract oil from reservoir and connecting the floating platform to the sea

bed. The risers are pipes allowing the oil outflow from the reservoir and, depending on the

prevailing conditions, are of the rigid or flexible types. Conversely, the mooring lines are

responsible for holding the floating structure in a specific position and can be made of chain,

polyester and other synthetic ropes or a combination of these and are connected to the sea bed

by using anchors.

According to this scenario, there is also the need for special care on validation of the

production units before any start of operation begins. In general, the design requires extensive

small-scale tests at the laboratory. Through wave makers, fans and other systems, the model

tests in basins are able to reproduce the main environmental conditions that the production

units will be subjected to, such as winds, waves and currents, as well as to reproduce the

dynamics of mooring lines and risers.

One of the main challenges in model tests is the selection of the scale. The correct

choice of the model scale is important to represent, in reduced dimensions, the real

phenomena in study, details for this procedure can be found for example in Chakrabarti, S.K.

(1994). The combination of the ultra deep water and the large dimensions of the production

units make strongly difficult to select the model scale in order to represent all the behavior of

these complex systems. For example, in the typical tests basins, it is difficult to represent

correctly the mooring lines and riser system together with the floating unit. Moreover, a large

range of operational conditions must be analyzed experimentally, which involves long time

and expressive amount of capital.

In order to solve these problems, the TPN was created. The Numerical Offshore Tank or

Page 4: Numerical Offshore Tank - Description

Santos Offshore Conference 2009 21 a 23 de Outubro de 2009 - Mendes Convention Center - Santos - São Paulo - Brasil

Pág: 4 de 4

TPN is a computational hydrodynamic laboratory for design and analysis on offshore systems,

ships and barges developed for the design and analysis of ships and floating structures

involving the joint efforts of a multidisciplinary expertise team and close partnership among

different universities, research institutes and Petrobras.

Due to the extreme complexity of representing the actual physical phenomena and the

requirement of being able to analyze a particular case in a reasonable and feasible time frame,

the simulator, with an exceptionally large computational power, was inaugurated in February

2002.

To meet the new challenges of high productivity, stringent standards and top quality

research, the TPN carried out a complete modernization of its physical and technological

infra-structure, including the long awaited construction of a dedicated facility, see Figure 1.

Located aside the Department of Naval Architecture and Oceanic Engineering of the Escola

Politécnica, at the University of São Paulo – USP, the new TPN’s lab facility considering:

• A time-domain multi-body dynamic analysis software and a 3D visualization

room for pos-processed analysis;

• A computer cluster composed by high performance processors, enabling parallel

computing to solve the numerical simulations;

• A hydrodynamic basin, the test facility with active wave generation/absorption.

Figure 1: The actual TPN counts with a new cluster and 3D visualization room, as well as a dedicated hydrodynamic basin for calibration of the numerical simulator.

Page 5: Numerical Offshore Tank - Description

Santos Offshore Conference 2009 21 a 23 de Outubro de 2009 - Mendes Convention Center - Santos - São Paulo - Brasil

Pág: 5 de 5

2. The Numerical Offshore Tank Activities

The Numerical Offshore Tank was developed to provide an innovative technological

testing facility and to revolutionize the floating structure research field. It was a unique

technological laboratory in the international scientific community.

By means of its researcher center, during the past few years TPN has been involved

with many important studies, among them:

• Various up and running PETROBRAS units have undergone TPN testing,

including P18 and P43, which were the first units to serve as simulator

calibrators;

• Platforms P51 and P52 have also been analyzed by the TPN. Other units such as

P19 still require evaluation in specific operation regimes;

• In 2002, the docking simulation of the Brazilian Navy’s Aircraft carrier Nae São

Paulo was carried out. Because of the small size of the dry dock, there were

serious lateral constraints for the docking operation which required a meticulous

modeling of every single detail of the dry dock, aircraft carrier and surroundings

before the actual full scale operation could take place. The undertaken study was

indispensable for the successful conclusion of the operation;

• Another case study was the Load-Out of the Brazilian Navy’s Timbira

submarine. Structural calculations were conducted for the ramp and the barge

that would transport the submarine. A specific software was created to simulate

the barge ballasting operation and a video, demonstrating the whole operation,

was produced;

• On top of Petrobras’ complete production units, various non-conventional

analyses were performed by TPN. One example was the movement of shuttle

tank near a new PLEM – Pipe Line End Manifold. The concern was that during

offloading operations the ship could crash into the PLEM. The simulation of the

operation was made in the numeric simulator and the result was viewed in

TPNView;

• Another simulation analyzed a sub surface buoy, joining two types of units: a

semi-submersible and a FPSO type vessel. The dynamic stability was verified,

as were tensions in moorings and risers. Damaged conditions were analyzed in

the buoy’s cables and the moorings of the floating unit;

Page 6: Numerical Offshore Tank - Description

Santos Offshore Conference 2009 21 a 23 de Outubro de 2009 - Mendes Convention Center - Santos - São Paulo - Brasil

Pág: 6 de 6

• The design of new offshore systems, including detailed seakeeping and stability

analyses:

o MonoGoM, see Costa, A.P. et al. (2005);

o FPSO-BR, see Cueva, D. et al. (2005);

o MonoBR with dry tree capability, see Gonçalves, R.T. et al.(2008) and

Matsumoto, F.T. et al. (2008);

o FPSO-TLWP, see Malta, E.B. et al. (2009) and Rampazzo, F.P. et al.

(2009);

• The design and analyses of mooring and risers system, see Rampazzo, F.P.,

Masetti, I.Q. & Nishimoto, K. (2008);

• Experimental and phenomenological results for fluid-structure interaction:

o Vortex-Induced Vibrations (VIV) in risers, see Rosetti, G.F., Nishimoto,

K. & Wilde, J. (2009);

o Vortex-Induced Motions (VIM) in monocolumn platforms, see

Gonçalves, R.T. et al. (2009) and Fujarra, A.L.C. et al. (2009);

• Moving particle semi-implicit method (MPS), see Maeda, H. et al. (2004) and

Tsukamoto, M.M., Cheng, L.Y. & Nishimoto, K. (2009).

Figure 2 presents some examples of the new design developed in TPN, particularly the

MonoBR and FPSO-BR.

Figure 2: Examples of new designs developed at TPN.

Page 7: Numerical Offshore Tank - Description

Santos Offshore Conference 2009 21 a 23 de Outubro de 2009 - Mendes Convention Center - Santos - São Paulo - Brasil

Pág: 7 de 7

3. The Computer Cluster

The modernization efforts included the implementation of a new cluster comprised of a

large number of parallel processing units reaching a 50 TeraFLOPS capacity and, therefore,

allowing high speed numerical simulations and integration with similar clusters available at

Petrobras research centers.

To complement this capacity, a viewing room equipped with leading edge virtual reality

equipment is available, enabling a clearer understanding of the analysis results and deeper

immersion on the research findings. It features a high definition projection system and a six

degree-of-freedom seating capability. Some pictures took before the operational condition are

presented in Figure 3.

Figure 3: Illustration of the new cluster and 3D visualization room.

The numerical simulator developed by TPN is a computer based program capable of

representing full scale conditions with the advantage of not being restricted by the geometric

and physical constraints restrictions model test basins. Its capabilities include the detailed

representation of the floating system motion dynamics, the evaluation of different mooring

and rises arrangements and large spectra of environmental conditions.

Its basic architecture consists of a pre-processor (scientific software), parallelized

processor (core) and post processor (visualization software).

In order to provide a compatible and systematic entry procedure for the extremely large

amount of geometric, physical and environmental data, the TPN team carried out the

development and implementation of the pre-processing program PREA3D which is capable of

guaranteeing the coherence among the data as well as in speeding up the input process.

The software’s core is based on mathematical models that represent the system

dynamics equations and, integrated along time steps, allows the actual motion of the floating

system to be simulated. To evaluate the various external loadings acting on the floating unit,

Page 8: Numerical Offshore Tank - Description

Santos Offshore Conference 2009 21 a 23 de Outubro de 2009 - Mendes Convention Center - Santos - São Paulo - Brasil

Pág: 8 de 8

the numerical software makes use of a group of auxiliary hydrodynamic and structural codes.

Among them, the software WAMIT obtains the hydrodynamic coefficients of the wave

dynamic response, ANFLEX and PREADYN are responsible for the line dynamics

calculation and SLOSHING estimates the effect of the liquid movement in ballast or oil tanks.

The simulator’s generated information includes such a large amount of data that it is

quite impossible to analyze them by conventional means. As a consequence, the software

TPNView was developed with resources not only for providing a fundamental tool for

integrated data analysis but also for creating a new scientific virtual reality environment.

The software combines a 3D visualization of the actual motions of the floating system,

of the risers and mooring lines and of the environment waves as well as dynamic analysis

tools such as graphs, histograms and statistics.

4. The Hydrodynamic Basin

As part of the new TPN’s lab facility, the hydrodynamic basin with active absorber has

the main objective of generating a large experimental data base, such as motions,

hydrodynamic forces and coefficients. This data base will be applied for checking and

improving the theoretical models, enabling the simulator to represent as accurate as possible

the full scale dynamic behavior of the analyzed systems. One example is the study of the

second-order motions for large structures; see Simos, A.L. et al. (2008).

The hydrodynamic basin consists of a 14m x 14m rectangular wave tank with depth of

4m with an all around multi-directional wave absorption and generation system based on 148

flap-type wave makers. A graphical illustration of the facility, a picture before commissioning

and the main dimensions are presented in Figure 4.

The system was designed to generate waves in frequency ranging from 0.25 to 3.00Hz

and maximum wave height of 0.40m (considering the limits of the mechanical system and the

theoretical wave breaking limit of 14% in steepness). Details about the control system of the

flaps and dimensions one can be found in de Mello, P.C. et al. (2007).

Wave generation limits can be visualized in Figure 5, by means of the intersection

between limit areas according to the wave steepness, tank height, flap stroke and screw

velocity. In the same figure it is possible to see the typical centenarian spectrum of some

offshore basins under exploration around the world, particularly: Golf of Mexico (USA),

Campos Basin (Brazil) and Tupi Basin (Brazil) for reference scale model equal to 1:100.

Page 9: Numerical Offshore Tank - Description

Santos Offshore Conference 2009 21 a 23 de Outubro de 2009 - Mendes Convention Center - Santos - São Paulo - Brasil

Pág: 9 de 9

Figure 5 shows that the new TPN’s hydrodynamic basin was appropriated design for

generating wave excitation of the most important scenarios of offshore oil production.

Figure 4: Graphical views and picture before commissioning of the new wave basin.

Figure 5: Wave height versus frequency limits forthe new hydrodynamic basin.

The instrumentation used in the hydrodynamic basin is the most modern in monitoring

technology. The motion can be registered through six degree-of-freedom video monitoring

and also by conventional methods using accelerometers, rate-gyros (for velocity) and degree

0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

freq (Hz)

H (m

)

Limite de CursoLimite de DeclividadeOnda máximaLimite de Velocidade do atuadorCentenária GoMCentenária BCCentenária Tupi

Page 10: Numerical Offshore Tank - Description

Santos Offshore Conference 2009 21 a 23 de Outubro de 2009 - Mendes Convention Center - Santos - São Paulo - Brasil

Pág: 10 de 10

sensors.

For free surface monitoring ultrasonic wave probe were specifically developed for the

TPN’s hydrodynamic basin; details about this can be found in de Mello, P.C. et al. (2007).

The advantage of this apparatus in comparison with the conventional capacitive probe is the

facility of calibration that implies a reduced time in the tests.

Due to its faster operation and lower cost compare to similar facilities, it is important to

emphasize that one of the complementary objectives of the TPN’s hydrodynamic basin will be

to develop human resources specifically trained to work in the experimental research for naval

and ocean developments.

5. Conclusion

This paper presented the new TPN’s lab facility composed by: a 50 TeraFLOPS cluster

and a 3D visualization room, which will increase enormously its simulation capacity, and a

hydrodynamic basin for small-scale tests aiming to achieve paradigms for theoretical models

calibration.

Compared to the similar facilities in Brazil, the new TPN’s hydrodynamic basin has a

unique characteristic which means the concomitant generation and absorption of waves. This

peculiar aspect gives to this new basin the capacity to perform long time experiments,

appropriated for studying non-linear phenomena.

The TPN is an innovative and integrated system that brings high technology to naval

and ocean engineering, and thus becomes a fundamental tool for the recent developments.

Together with the principal Brazilian research institutes and Petrobras, TPN works to

ensure that Brazil continues to be efficiently exploring oil in deeper waters, as well as

developing technologies in the state of art.

References

Chakrabarti, S.K. (1994). Offshore Structure Modeling. Advanced Series on Ocean

Engineering.

Costa, A.P., Masetti, I.Q., Cueva, M., Nishimoto, K., Machado, G. & Corte, A. (2005).

Development of a Mono-Column Type Unit for Harsh Environment. Proceedings of the

11th International Congress of the International Maritime Association of the Mediterranean

– IMAM, Lisbon, Portugal.

Page 11: Numerical Offshore Tank - Description

Santos Offshore Conference 2009 21 a 23 de Outubro de 2009 - Mendes Convention Center - Santos - São Paulo - Brasil

Pág: 11 de 11

Cueva, D., Campos, F., Donato, M., Ferrari, J.A., Torres, F. & Nishimoto, N. (2005).

Dimensional Study for Brazilian FPSO. Proceedings of the 24th International Conference

on Offshore Mechanics and Artic Engineering. OMAE2005-67333.

Fujarra, A. L., Gonçalves, R. T., Faria, F., Nishimoto, K., Cueva, M., & Siqueira, E. F.

(2009). Mitigation of Vortex-Induced Motions of a Monocolumn Platform. Proceedings of

the 28th International Conference on Ocean, Offshore and Arctic Engineering.

OMAE2009-79380 .

Gonçalves, R.T., Matsumoto, F.T., Medeiros, H.F., Brinati, H.L., Nishimoto, K. & Masetti,

I.Q. (2008). Conceptual Design of Floating Production and Storage with Dry Tree

Capability. Proceedings of the 27th International Conference on Offshore Mechanics and

Artic Engineering. OMAE2008-57440.

Gonçalves, R. T., Fujarra, A. L., Rosetti, G. F., Nishimoto, K., Cueva, M., & Siqueira, E. F.

(2009). Vortex-Induced Motion of a Monocolumn Platform: New Analysis and

Comparative Study. Proceedings of the 28th International Conference on Ocean, Offshore

and Artic Engineering. OMAE2009-79378.

Maeda, H., Nishimoto, K., Masuda, K., Asanuma, T., Tsukamoto, M.M. & Ikoma, T. (2004).

Numerical Analysis for Hydrodynamic Motions of Floating Structures Using MPS Method.

Proceedings of the 23th International Conference on Offshore Mechanics and Artic

Engineering. OMAE2004-51435.

Malta, E.B., Rampazzo, F.P., Cruz, R.E., Oliveira, A.L. & Nishimoto, K. (2009). FPSO and

TLWP Interacting at a Reduced Distance for Dry Tree Completion System. Proceedings of

the 28th International Conference on Ocean, Offshore and Artic Engineering. OMAE2009-

79098.

Matsumoto, F.T., Gonçalves, R.T., Malta, E.B., Medeiros, H.F., Nishimoto, K. & Masetti,

I.Q. (2008). The Influence at Vertical First Order Motions Using a Appendages in a

Monocolumn Platform. Proceedings of the 27th International Conference on Offshore

Mechanics and Artic Engineering. OMAE2008-57410.

de Mello, P.C., Carneiro, M.L., Casetta, L., Simos, A.N., Adamowski, J.C. & Nishimoto, K.

(2007). Development of a Wave Tank with Active Absorption. Proceedings of th 3rd

International Workshop on Aplplied Offshore Hydrodynamics. IWAOH-2007.

Nishimoto, K.; Ferreira, M.D.; Martins, M.R.; Masetti, I.Q.; Martins, C.A., Jacob, B.P.,

Russo, A.; Caldo, J. & Silveira, E.S.S. (2003). Numerical Offshore Tank: Development of

Page 12: Numerical Offshore Tank - Description

Santos Offshore Conference 2009 21 a 23 de Outubro de 2009 - Mendes Convention Center - Santos - São Paulo - Brasil

Pág: 12 de 12

Numerical Offshore Tank for Ultra Deep Water Oil Production Systems. Proceedings of

the 22nd International Conference on Offshore Mechanics and Arctic Engineering.

OMAE2003-37381.

Rampazzo, F.P., Masetti, I.Q. & Nishimoto, K. (2008). The Mooring System Design

MONOBR Platform for Harsh Environmental Conditions (GoM). 20th Ocean Engineering

Symposium, Tokio, Japan.

Rampazzo, F.P., Malta, E.B., Watai, R.A., Cruz, R.E. & Nishimoto, K. (2009). Design of an

Innovative FPSO-TLWP Coupled System Based on the Numerical Offshore Tank (TPN)

Methodology. Proceedings of the 10th International Marine Design Conference – IMDC,

Trondheim, Norway.

Rosetti, G. F., Nishimoto, K. & Jaap de Wilde. (2009). Vortex-Induced Vibrations on Flexible

Cylindrical Structures Coupled with Non-Linear Oscillators. Proceedings of the 28th

International Conference on Ocean, Offshore and Artic Engineering. OMAE2009-79022.

Simos, A.L., Sparano, J.V., Aranha, J.A.P. & Matos, V.L.F. (2008). 2nd Order

Hydrodynamic Effects on Resonant Heave, Pitch and Roll Motions of a Large-Volume

Semi-Submersible Platform. Proceedings of the 27th International Conference on Offshore

Mechanics and Artic Engineering. OMAE2008-57430.

Tsukamoto, M.M., Cheng, L.Y. & Nishimoto, K. (2009). Numerical Study of the Motions in

Shallow Water Waves of Floating Bodies Elastically Linked to Bottom. Proceedings of the

28th International Conference on Ocean, Offshore and Artic Engineering. OMAE2009-

80126.