A time domain code based on strip theory is applied to calculate the probability distributions of relative motions and bending moments of a cruise ship in a set of extreme seas. The code includes two levels of complexity. The simpler one combines linear radiation and diffraction forces with nonlinear Froude–Krylov forces, hydrostatic forces, and shipping of green water on the bow. Cummins formulation is used to represent the radiation forces. The second approach is a generalization of the first one and, although the formulation is based on the linear assumption (of the radiation forces), the effects of body nonlinearity are considered by a simplified method: the memory functions, infinite frequency added masses, and the radiation restoring coefficients are assessed at each time instant as function of the instantaneous wetted surface. A similar procedure is used to calculate the diffraction forces. The code is used to analyze the responses of a cruise ship in a set of extreme sea conditions. The short-term nonlinear responses are represented by empirical probability distributions, obtained from the nonlinear time domain simulations, and the quality of the predictions is assessed by comparing with model tests experimental data. Finally, the long-term value of the bending moment is calculated from the short-term distribution of the nonlinear loads in a few extreme sea states selected based on coefficient of contribution method, and the results are compared with the International Association of Classification Societies (IACS) rule bending moment.

References

References
1.
Nakos
,
D.
, and
Scalavounos
,
P.
,
1991
, “
Ship Motions by a Three Dimensional Rankine Panel Method
,”
18th Symposium on Naval Hydrodynamics
, Ann Arbor, MI, Aug. 20–23, pp.
21
40
.https://www.nap.edu/read/1841/chapter/6
2.
Lin
,
W. M.
,
Bergquist
,
J. R.
,
Collette
,
M. D.
,
Liut
,
D.
,
Treakle
,
T. W.
,
Weems
,
K. M.
,
Weems
,
M. H.
, and
Zhang
,
S.
,
2008
, “Large Amplitude Motion Program (LAMP) for Ship Motions and Wave Loads Predictions, Version 3.2.1.,” Science Applications International Corporation, McLean, VA, Technical Report.
3.
Hirdaris
,
S. E.
,
Bai
,
W.
,
Dessi
,
D.
,
Ergin
,
A.
,
Gu
,
X.
,
Hermundstad
,
O. A.
,
Huijsmans
,
R.
,
Iijima
,
K.
,
Nielsen
,
U. D.
,
Parunov
,
J.
,
Fonseca
,
N.
,
Papanikolaou
,
A.
,
Argyriadis
,
K.
, and
Incecik
,
A.
,
2014
, “
Loads for Use in the Design of Ships and Offshore Structures
,”
Ocean Eng.
,
78
(
1
), pp.
131
174
.
4.
Fonseca
,
N.
, and
Guedes Soares
,
C.
,
1998
, “
Time Domain Analysis of Large Amplitude Vertical Motions and Wave Loads
,”
J. Ship Res.
,
42
(
2
), pp.
100
113
.
5.
Fonseca
,
N.
, and
Guedes Soares
,
C.
,
1998
, “
Nonlinear Wave Induced Responses of Ships in Irregular Seas
,”
ASME
Paper No. OMAE1998-0446.
6.
Mikami
,
T.
, and
Shimada
,
K.
,
2006
, “
Time-Domain Strip Method With Memory-Effect Function Considering the Body Nonlinearity of Ships in Large Waves
,”
J. Mar. Sci. Technol.
,
11
(
3
), pp.
139
149
.
7.
Mortola
,
G.
,
Incecik
,
A.
,
Turan
,
O.
, and
Hirdaris
,
S. E.
,
2011
, “
Nonlinear Analysis of Ship Motions and Loads in Large Amplitude Waves
,”
Trans. R. Inst. Naval Architects Part A: Int. J. Maritime Eng.
,
153
(
2
), pp.
81
87
.https://www.researchgate.net/publication/259609609_Non_linear_analysis_of_ship_motions_and_loads_in_large_amplitude_waves
9.
Fonseca
,
N.
, and
Guedes Soares
,
C.
,
2002
, “
Comparison of Numerical and Experimental Results of Nonlinear Wave-Induced Vertical Ship Motions and Loads
,”
J. Mar. Sci. Technol.
,
6
(
4
), pp.
193
204
.
10.
Fonseca
,
N.
, and
Guedes Soares
,
C.
,
2004
, “
Experimental Investigation of the Nonlinear Effects on the Vertical Motions and Loads of a Containership in Regular Waves
,”
J. Ship Res.
,
48
(
2
), pp.
118
147
.https://www.researchgate.net/publication/233522892_Experimental_Investigation_of_the_Nonlinear_Effects_on_the_Vertical_Motions_and_Loads_of_a_Containership_in_Regular_Waves
11.
Fonseca
,
N.
, and
Guedes Soares
,
C.
,
2004
, “
Experimental Investigation of the Nonlinear Effects on the Statistics of Vertical Motions and Loads of a Containership in Irregular Seas
,”
J. Ship Res.
,
48
(
2
), pp.
148
167
.https://www.researchgate.net/publication/233622085_Experimental_Investigation_of_the_Nonlinear_Effects_on_the_Statistics_of_Vertical_Motions_and_Loads_of_a_Containership_in_Irregular_Waves
12.
Guedes Soares
,
C.
,
Fonseca
,
N.
, and
Pascoal
,
R.
,
2008
, “
Abnormal Wave Induced Load Effects in Ship Structures
,”
J. Ship Res.
,
52
(
1
), pp.
30
44
.http://www.ingentaconnect.com/content/sname/jsr/2008/02160252/02160201/art00003?crawler=true
13.
Fonseca
,
N.
,
Pascoal
,
R.
,
Guedes Soares
,
C.
,
Clauss
,
G. F.
, and
Schmittner
,
C. E.
,
2010
, “
Numerical and Experimental Analysis of Extreme Wave Induced Vertical Bending Moments on a FPSO
,”
Appl. Ocean Res.
,
32
(
4
), pp.
374
390
.
14.
Rajendran
,
S.
,
Fonseca
,
N.
, and
Guedes Soares
,
C.
,
2011
, “
Time Domain Comparison With Experiments for Ship Motions and Structural Loads on a Container Ship in Abnormal Waves
,”
ASME
Paper No. OMAE2011-50316.
15.
Rajendran
,
S.
,
Fonseca
,
N.
, and
Guedes Soares
,
C.
,
2012
, “
Experiment and Time Domain Method Comparison for the Responses of a Container Ship Induced by the Three Sisters Abnormal Waves
,”
Marine Technology and Engineering
,
C.
Guedes Soares
,
Y.
Garbatov
,
S.
Sutulo
, and
T. A.
Santos
, eds.,
Taylor & Francis
,
London
, pp.
223
230
.
16.
Longuet-Higgins
,
M. S.
,
1952
, “
On the Statistical Distribution the Heights of Sea Waves
,”
J. Mar. Res.
,
11
(
3
), pp.
245
226
.
17.
Fukuda
,
J.
,
1967
, “
Theoretical Determination of Design Wave Bending Moments
,”
Jpn. Shipbuilding Mar. Eng.
,
2
(
3
), pp.
12
22
.
18.
Guedes Soares
,
C.
,
1993
, “
Long-Term Distribution of Non-Linear Wave Induced Vertical Bending Moments
,”
Mar. Struct.
,
6
(
5–6
), pp.
475
483
.
19.
Guedes Soares
,
C.
, and
Schellin
,
T. E.
,
1998
, “
Nonlinear Effect on Long-Term Distribution of Wave-Induced Loads for Tankers
,”
ASME J. Offshore Mech. Arct. Eng.
,
120
(
2
), pp.
65
70
.
20.
Fonseca
,
N.
,
Pascoal
,
R.
, and
Guedes Soares
,
C.
,
2004
, “
Long Term Prediction of Nonlinear Vertical Bending Moments on a Fast Monohull
,”
Appl. Ocean Res.
,
26
(6), pp.
288
297
.
21.
Larsen
,
C. M.
, and
Passano
,
E.
,
1990
, “
Extreme Response Estimation for Marine Risers
,”
Nineth International Conference on Offshore Mechanics and Arctic Engineering
, Houston, TX, Feb. 18–23, p.
361
.https://trid.trb.org/view.aspx?id=437464
22.
Baarholm
,
G. S.
, and
Moan
,
T.
,
2000
, “
Estimation of Nonlinear Long-Term Extremes of Hull Girder Loads in Ships
,”
Mar. Struct.
,
13
(
6
), pp.
495
516
.
23.
Drummen
,
I.
,
Wu
,
M.
, and
Moan
,
T.
,
2009
, “
Experimental and Numerical Study of Containership Response in Severe Head Seas
,”
Mar. Struct.
,
22
(
2
), pp.
1
22
.
24.
Guedes Soares
,
C.
,
Fonseca
,
N.
,
Pascoal
,
R.
,
Clauss
,
G. F.
,
Schmittner
,
C. E.
, and
Hennig
,
J.
,
2006
, “
Analysis of Design Wave Loads on a FPSO Accounting for Abnormal Waves
,”
ASME J. Offshore Mech. Arct. Eng.
,
128
(
3
), pp.
241
247
.
25.
Fonseca
,
N.
, and
Guedes Soares
,
C.
,
2010
, “
Global Structural Loads Induced by Extreme Waves on Ships
,”
Advanced Ship Design for Pollution Prevention
,
C.
Guedes Soares
and
J.
Parunov
, eds.,
Taylor & Francis Group, London
, pp.
3
15
.
26.
Denchfield
,
S. S.
,
Hudson
,
D. A.
,
Temarel
,
P.
,
Bateman
,
W.
, and
Hirdaris
,
S. E.
,
2009
, “
Evaluation of Rogue Wave Induced Loads Using 2D Hydroelasticity Analysis
,”
Fifth International Conference on Hydroelasticity in Marine Technology
, Southampton, UK, Sept. 8–10, pp.
347
360
.https://www.researchgate.net/publication/284713803_Evaluation_of_Rogue_Wave_Induced_Loads_Using_2D_Hydroelasticity_Analysis
27.
Cummins
,
W. E.
,
1962
, “
The Impulse Response Function and Ship Motions
,”
Schiffstechnik
,
47
(9), pp.
101
109
.http://www.marinecontrol.org/References/papers/Cummins%201962.pdf
28.
Ogilvie
,
T.
,
1964
, “
Recent Progress Towards the Understanding and Prediction of Ship Motions
,”
Fifth Symposium on Naval Hydrodynamics
, Bergen, Norway, Sept. 10–12, pp.
3
80
.https://www.scribd.com/document/355498937/1964-Ogilve-Recent-progress-toward-the-understanding-and-prediction-of-ship-motions-pdf
29.
Buchner
,
B.
,
1995
, “
The Impact of Green Water on FPSO Design
,”
Offshore Technology Conference
(
OTC
), Houston, TX, May 1–4, pp.
45
57
.
30.
Rajendran
,
S.
,
Fonseca
,
N.
, and
Guedes Soares
,
C.
,
2015
, “
Effect of Surge Motion on the Vertical Responses of Ships in Waves
,”
Ocean Eng.
,
96
, pp.
125
138
.
31.
Rajendran
,
S.
,
Fonseca
,
N.
, and
Guedes Soares
,
C.
,
2015
, “
Simplified Body Nonlinear Time Domain Calculation of Vertical Ship Motions and Wave Loads in Large Amplitude Waves
,”
Ocean Eng.
,
107
, pp.
157
177
.
32.
Rajendran
,
S.
,
Fonseca
,
N.
, and
Guedes Soares
,
C.
,
2016
, “
Body Nonlinear Time Domain Calculation of Vertical Ship Responses in Extreme Seas Accounting for 2nd Order Froude-Krylov Pressure
,”
Appl. Ocean Res.
,
54
, pp.
39
52
.
33.
Ramos
,
J.
, and
Guedes Soares
,
C.
,
1997
, “
On the Assessment of Hydrodynamic Coefficients of Cylinders in Heaving
,”
Ocean Eng.
,
24
(
8
), pp.
743
763
.
34.
Von Kerczek
,
C.
, and
Tuck
,
E. O.
,
1969
, “
The Representation of Ship Hulls by Conformal Mapping Functions
,”
J. Ship Res.
,
13
(4), pp.
284
298
.https://trid.trb.org/view.aspx?id=417848
35.
Bishop
,
R. E. D.
, and
Price
,
W. G.
,
1978
, “
Hydrodynamic Coefficients of Some Heaving Cylinders of Arbitrary Shape
,”
Int. J. Numer. Methods Eng.
,
13
(
1
), pp.
17
33
.
36.
Rajendran
,
S.
,
Fonseca
,
N.
, and
Guedes Soares
,
C.
,
2016
, “
Prediction of Vertical Responses of a Containership in Abnormal Waves
,”
Ocean Eng.
,
119
, pp.
165
180
.
37.
Chan
,
K. K.
,
Sclavonous
,
P. D.
,
Jonkman
,
J.
, and
Hayman
,
J.
,
2015
, “
Computation of Nonlinear Hydrodynamic Loads on Floating Wind Turbines Using Fluid-Impulse Theory
,”
ASME
Paper No. OMAE 2015-41053.https://www.nrel.gov/docs/fy15osti/63697.pdf
38.
IACS, 2001, “
Standard Wave Data—IACS Recommendation No.34, (Rec 34 Rev1 Corr1 CLN)
,” International Association of Classification Societies, London, accessed Nov. 22, 2017, http://www.iacs.org.uk/download/1978
39.
Guedes Soares
,
C.
,
1990
, “
Effect of Spectral Shape Uncertainty in the Short Term Wave-Induced Ship Responses
,”
Appl. Ocean Res.
,
34
(
2
), pp.
54
69
.
40.
Teixeira
,
A. P.
, and
Guedes Soares
,
C.
,
2009
, “
Reliability Analysis of a Tanker Subjected to Combined Sea States
,”
Probab. Eng. Mech.
,
24
(
4
), pp.
493
503
.
41.
Guedes Soares
,
C.
,
1998
, “
Representation of Double-Peaked Sea Wave Spectra
,”
Ocean Eng.
,
11
(
2
), pp.
185
207
.
42.
IACS,
2016
, “IACS Requirements Concerning Strength of Ships,” International Association of Classification Societies, London, accessed Nov. 22, 2017, http://www.iacs.org.uk/publications/unified-requirements/?page=10
43.
Clauss
,
G.
,
2002
, “
Dramas of the Sea: Episodic Waves and Their Impact on Offshore Structures
,”
Appl. Ocean Res.
,
24
(
3
), pp.
147
161
.
44.
Guedes Soares
,
C.
,
Cherneva
,
Z.
, and
Antão
,
E. M.
,
2003
, “
Characteristics of Abnormal Waves in North Sea Storm Sea States
,”
Appl. Ocean Res.
,
25
(
6
), pp.
337
344
.
45.
Guedes Soares
,
C.
,
Cherneva
,
Z.
, and
Antão
,
E.
,
2004
, “
Steepness and Asymmetry of the Largest Waves in Storm Sea States
,”
Ocean Eng.
,
31
(
8–9
), pp.
1147
–11
67
.
46.
Petrova
,
P. G.
,
Cherneva
,
Z.
, and
Guedes Soares
,
C.
,
2007
, “
On the Adequacy of Second Order Models to Predict Abnormal Waves
,”
Ocean Eng.
,
34
(
7
), pp.
956
961
.
47.
Clauss
,
G. F.
,
Klein
,
M.
, and
Dudek
,
M.
,
2010
, “
Influence of the Bow Shape on Loads in High and Steep Waves
,”
ASME
Paper No. OMAE2010-20142.
48.
Wu
,
M. K.
, and
Moan
,
T.
,
2006
, “
Statistical Analysis of Wave-Induced Extreme Nonlinear Load Effects Using Time-Domain Simulations
,”
Appl. Ocean Res.
,
28
(
6
), pp.
386
397
.
49.
Bennett
,
S. S.
,
Hudson
,
D. A.
, and
Temarel
,
P.
,
2014
, “
Global Wave-Induced Loads in Abnormal Waves: Comparison Between Experimental Results and Classification Society Rules
,”
J. Fluids Struct.
,
49
, pp.
498
515
.
50.
Lloyd's Register,
2012
, “
Rules and Regulations for the Classification Naval Ships
,” Lloyd's Register Group Services Limited, London, accessed Nov. 22, 2017, http://www.lr.org/en/RulesandRegulations/naval-ships.aspx
You do not currently have access to this content.