30 3B 2010 5 315

30 3B2010 5

pp. 315 ~ 324

Development of a Design Chart for the Initial Design Stage of Very Large Floating Structures

**********

Zi, GoangseupKim, Jin GyunLee, Seung OhLee, Phill-Seung

Abstract

We developed a design chart for very large floating structures through intensive hydroelastic analysis. Using this chart, one can

predict the hydroelastic response of very large floating structures preliminarily at design stage without the cost-demanding

hydroelastic analysis. This paper presents two new design charts based on the theory of VLFS. The purpose of the first design chart

is to determine RAOs of the maximum longitudinal stress of VLFS considering properties of waves and structures. The design

chart I can be applied to any sizes of VLFS in same aspect ratios and dimensionless stiffness parameters. The second design chart is

developed to take into account the actual wave condition by using the Bretschneider spectrum with Beaufort sea state.

Keywords : VLFS, design chart, hydroelastic analysis, wave spectrum, spectrum analysis

.

.

I, II . I

. I

. I II , Beaufort

Bretschneider .

: , , , ,

1.

(Very Large Floating Structure;

VLFS)

, ,

, , LNG ,

. VLFS

MOB (ONR, 1997~2000),

MHP (NFESC, 1998~2004), (TRAM,

1995~2001)

.

1999 , KAIST

2009

(, 2008; KAIST, 2009).

VLFS , ,

. VLFS

VLFS .

.

VLFS 1980

(Ando , 1983; Bishop , 1983).

.

2

,

.

(Webster , 1994; , 2001).

* (E-mail : g-zi@korea.ac.kr)

** () (E-mail : simpleis@korea.ac.kr)

*** (E-mail : seungoh.lee@hongik.ac.kr)

**** (E-mail : phillseung@kaist.ac.kr)

316

VLFS

. VLFS

(Andrianov, 2005) ,

(2006, 2008)

.

, VLFS

VLFS

.

,

,

(characteristic length, c)

(Suzuki, Yoshida, 1996). 100

m (Lw)

100 m 8

. VLFS

50:1 VLFS

(ISSC,

2006; , 2008).

VLFS

,

, .

.

,

2~3 .

,

.

VLFS

,

.

VLFS

.

VLFS ,

.

2. VLFS

2.1

.

, , ,

(Newman, 1994).

I, S,

R .

(1)

,

,

.

.

(a) Laplace :

(b) (z=0):

(c) :

(d) : 0

(e) :

p (Reza , 2006).

(2)

z t , , g

. (2)

F M .

(3)

(4)

, n , r

. (3) (4)

.

(5)

mij, dij, kij , , , aij,

bij, cij (added mass), (damping),

I S R+ +=

2

0=

p gz t=

F pn Sds=

M p r n( ) Sds=

2

mpq apq+( ) i bpq dpq+( ) cpq kpq+( )+ +[ ]qp

j 1=

N

F pexct

=

1. VLFS

30 3B 2010 5 317

(hydrostatic) ,

. ,

, ,

.

(6)

, p . p=1

.

,

. (3) (4)

, .

2.2 VLFS RAO

VLFS 1

. VLFS

1

. 1

VLFS

.

(1) (6)

, (6)

p p

.

(7)

(x, y, z) (6) (7) .

(Response amplitude operators, RAO)

(6)

.

(8)

RAO .

4 RAOp

RAO . ,

RAO

RAO .

2.3 VLFS

( ) .

VLFS

, ,

(Riggs , 2007; , 2008;

, 2008; Kim , 2009). ,

.

,

.

3. VLFS

3.1

VLFS

1 . 1

qi

qi

ui up x y z, ,( )qp

p 1=

=

up x y z, ,( )

F iexct

qp up

qp qp0

cos t p+( ) isin t p+( )+[ ]=

RAO x y z, ,( ) up x y z, ,( )qp0cos

p( )

p 1=

2

up x y z, ,( )qp0sin

p( )

p 1=

2

+=

up x y z, ,( ) p x y z, ,( ) Mp x y z, ,( )

2. (RAO)

1.

Lw(T) (wave length)

S(f) (wave spectrum)

Ls, Ws, Ds , , a(f)

(wave amplitude)

T, f , xx

(longitudinal stress)

(wave induced angle)

Mu (ultimate bending capacity)

S (section modulus)

2.

(aspect ratio)Ss

(stiffness parameter)

(dimensionless wave length)

L

3.

318

,

. 2

.

(aspect ratio, )

( 3).

VLFS

. (9) Ls

Ws .

(9)

=5 10

.

Ls

Ws------=

4. I, ( =5)

30 3B 2010 5 319

VLFS

VLFS

. (10) .

(10)

, Lw (m), Ls VLFS (m)

. .

(11) (Wang

, 2008).

(11)

, T (sec) .

.

Lee Newman(2000)

L

L

LLw

Ls------=

Lw 1.56T2

=

5. I, ( =10)

320

(12) .

(12)

, Ss , E , I

, s VLFS , g

, L .

3.2 I:

I,

II . I VLFS

RAO

. I

(wave induced angle, ), (dimen-

sionless wave length, ),

(dimensionless stiffness parameter, Ss)

(aspect ratio, )(Lee, Newman, 2000).

,

. ,

RAO. 0.70106 4.90106

. 0o 90o

. I

RAO

.

4 5 5 10 I

7 . I

7 0o 90o

. I ,

1/4 .

I

RAO .

RAO ,

RAO

. RAO

5 10 RAO

5 .

3.3 II:

,

.

RAO

(ultimate bending capacity,

Mu) .

Bretschneider

. Bretschneider (9)

.

(13)

, H1/3 (m), T1 (average wave

period, sec), f (rad/sec) .

VLFS

.

(13) H1/3 T1

6a 1 12

SsEI

sgL5

--------------=

L

S f( ) 173H1 3

2T1

4f

5exp 692T

1

4f

4( )=

6. Beaufort

7.

30 3B 2010 5 321

Beaufort (Journee Massie,

2001).

fi ai (14)

.

(14)

6 VLFS

I RAO

,

Mu (15) .

(15)

, As , Larm

, , , (fi)s RAO

.

8 9 II .

S fi( )df1

2---ai

2=

Mu AsLarm fi( )a fi( )=

8. II : Mu ( =5, Ls=300 m)

322

7 II .

VLFS , ,

, VLFS

Beaufort . VLFS

II ,

, (Sreq) .

(Sdes)

VLFS .

.

.

9. II: Mu ( =10, Ls=100 m)

30 3B 2010 5 323

4.

. VLFS

5, 300 m, Ss

=2.80106 , VLFS

10 .

Sdes 5.7 m3.

12

.

II

1600103 kNm . 100

MPa Sreq 16 m3

. 400 MPa

4 m3

,

3.30106 ( 8).

1750103 kNm .

400 MPa 4.2 m3

.

II

5% .

VLFS

.

5.

,

. , ,

,

.

10. , 3D

11. II

324

,

.

.

. Beaufort Bretschneider

.

.

2010 ()

(2010-0015690)

(: 05B01)

.

, , (2008)

,

, , 18 3, pp. 356-360.

, , , (2006)

, ,

, 16 2, pp. 132-140.

(2008) .

(2001)

,

, , 38 4, pp. 39-47.

, , , , (2008,

, 2008

, , pp. 1123-1127.

(2008) Andrianov, A.I. (2005) Hydroelastic Analysis of Very Large Float-

ing Structures, Doctorate Thesis, Delft University of Technol-

ogy, ISBN 90-8559-081-7, p. 188.

Ando, S., Ohakawa, Y., and Ueno, I. (1983) Feasibility study of a

floating airport, Report of Ship Research Institute, Japan, Sup-

plement No. 4.

Bishop, R.E.D. and Price, W.G. (1983) An introduction to ship

hydroelasticity, Journal of Sound and Vibration, Vol. 87, No. 3,

pp. 391-407.

ISSC (2006) Report of Special Committee VI.2 Very Large Float-

ing Structures, Proceeding 16th International Ship and Off-

shore Structure Congress, Vol. 2, pp. 391-442.

Journee, J.M.J. and Massie, W.W. (2001) Offshore Hydromechan-

ics, Delf University of Technology.

KAIST (2009) Mobile Floating Harbor for Jump Increased Con-

tainer Handling Capacity.

Kim, Y.I., Kim, K.H., and Kim, Y.H. (2009) Springing analysis of a

seagoing vessel using fully coupled BEM-FEM in the time

domain, Ocean Engineering, Vol. 36, pp. 785-796.

Lee, C.-H. and Newman, J.N. (2000) An assessment of hydroelas-

ticity for very large hinged vessels, Journal of Fluids and

Structures, Vol. 14, pp. 957-970.

Newman, J.N. (1994) Wave effects on deformable bodies, Ocean

Research, Vol. 16, No 1, pp. 47-59.

Riggs, H.R., Hideyuki Suzuki, Ertekin, R.C., Kim, J.W., and Iijima,

K. (2008) Comparison of hydroelastic computer codes based

on the ISSC VLFS benchmark, Ocean Engineering, Vol. 35,

Issue 7, pp. 589-597.

Riggs, H.R., Niimi, K.M., and Huang, L.L. (2007) Two benchmark

problems for three-dimensional, linear hydroelasticity, Journal

of Offshore Mechanics and Arctic Engineering, Vol. 129, pp.

149-157.

Reza, T., Shixiao, F., and Torgeir, M. (2006) Validated two and

three dimensional linear hydroelastic analysis using standard

software, Proceeding of the Sixteenth (2006) International Off-

shore and Polar Engineering Conference, San Francisco, USA,

pp. 101-107.

Suzuki, H. and Yoshida, K. (1996) Design flow and strategy for

safety of very large floating structure, VLFS'96, pp. 21-27.

Wang, C.M., Watanabe, E., and Utsunomiya, T. (2008) Very Large

Floating Structures, Taylor & Francis.

(: 2009.11.30/: 2010.2.3/: 2010.3.11)