Research Papers: Ocean Engineering

A Two-Dimensional Hydroelastoplasticity Method of a Container Ship in Extreme Waves

[+] Author and Article Information
Weiqin Liu

Departments of Naval Architecture,
Ocean and Structural Engineering,
School of Transportation,
Wuhan University of Technology,
Wuhan, Hubei 430063, China
e-mail: liuweiqin_123@sina.com

Katsuyuki Suzuki

Department of Systems Innovation,
School of Engineering,
The University of Tokyo,
7-3-1 Hongo,
Tokyo 113-8656, Japan
e-mail: katsu@race.u-tokyo.ac.jp

Kazuki Shibanuma

Department of Systems Innovation,
School of Engineering,
The University of Tokyo,
7-3-1 Hongo,
Tokyo 113-8656, Japan
e-mail: shibanuma@struct.t.u-tokyo.ac.jp

1Corresponding author.

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received July 10, 2014; final manuscript received December 20, 2014; published online January 20, 2015. Assoc. Editor: Ron Riggs.

J. Offshore Mech. Arct. Eng 137(2), 021101 (Apr 01, 2015) (9 pages) Paper No: OMAE-14-1077; doi: 10.1115/1.4029484 History: Received July 10, 2014; Revised December 20, 2014; Online January 20, 2015

Extreme waves have led to many accidents and losses of ships at sea. In this paper, a two-dimensional (2D) hydroelastoplasticity method is proposed as a means of studying the nonlinear dynamic response of a container ship when traversing extreme waves, while considering the ultimate strength of the ship. On one hand, traditional ultimate strength evaluations are undertaken by making a quasi-static assumption and the dynamic wave effect is not considered. On the other hand, the dynamic response of a ship as induced by a wave is studied on the basis of the hydroelasticity theory so that the nonlinear structural response of the ship cannot be obtained for large waves. Therefore, a 2D hydroelastoplasticity method, which takes the coupling between time-domain waves and the nonlinear ship beam into account, is proposed. This method is based on an hydroelasticity method and a simplified progressive collapse method that combines the wave load and the structural nonlinearity. A simplified progressive collapse method, which considers the plastic nonlinearity and buckling effect of stiffened, is used to calculate the ultimate strength and nonlinear relationship between the bending moment and curvature, so that the nonlinear relationship between the rigidity and curvature is also obtained. A dynamic reduction in rigidity related to deformation could influence the strength and curvature of a ship's beam; therefore, it is input into a dynamic hydrodynamic formula rather than being regarded as a constant structural rigidity in a hydroelastic equation. A number of numerical extreme wave models are selected for computing the hydroelastoplasticity, such that large deformations occur and nonlinear dynamic vertical bending moment (VBM) is generated when the ship traverses these extreme waves. As the height and Froude number of these extreme waves are increased, a number of hydroelastoplasticity results including VBM and deformational curvature are computed and compared with results obtained with the hydroelasticity method, and then, some differences are observed and conclusions are drawn.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Kharif, C., and Peliniovsky, E., 2003, “Physical Mechanisms of the Rogue Wave Phenomenon,” Eur. J. Mech. B/Fluids, 22(6), pp. 603–634. [CrossRef]
Muller, P., Garrett, C., and Osborne, E., 2005, “Rogue Wave,” Oceanogr. Soc., 18(3), pp. 66–75. [CrossRef]
Haver, S., and Andersen, O. J., 1990, “Freak Waves: Rare Realizations of a Typical Population or a Typical Realization of a Rare Population,” Proceedings of the 10th International Society of Offshore and Polar Engineers, Seattle, WA, Vol. 3, pp. 123–130.
Waseda, T., Rheem, C. K., Sawamura, J., Yuhara, T., Kinoshita, T., Tanizawa, K., and Tomita, H., 2005, “Extreme Wave Generation in Laboratory Wave Tank,” Proceedings of the 15th ISOPE, pp. 1–9.
Minami, M., Sawada, H., and Tanizawa, K., 2006, “Study of Ship Responses and Wave Loads in Freak Wave,” Proceedings of the 16th International Offshore and Polar Engineering Conference, Vol. 3, pp. 272–279.
Yamamoto, Y., Fujino, M., and Fukasawa, T., 1977, “Motion and Longitudinal Strength of a Ship in Head Sea and the Effects of Non-Linearity,” Conference of the Society of Naval Architects of Japan in Spring, Vol. 3, pp. 214–218.
Senjanović, I., Tomašević, S., and Vladimir, N., 2009, “An Advanced Theory of Thin-Walled Girders With Application to Ship Vibrations,” Mar. Struct., 22(3), pp. 387–437. [CrossRef]
Huang, L. L., and Riggs, H. R., 2000, “The Hydrostatic Stiffness of Flexible Floating Structures for Linear Hydroelasticity,” Mar. Struct., 13(2), pp. 91–106. [CrossRef]
Senjanović, I., Vladimir, N., and Tomić, M., 2012, “Formulation of Consistent Restoring Stiffness in Ship Hydroelastic Analysis,” J. Eng. Math., 72(1), pp. 141–157. [CrossRef]
Senjanović, I., Vladimir, N., Tomić, M., Hadžić, N., and Malenica, Š.,2014, “Some Aspects of Structural Modeling and Restoring Stiffness in Hydroelastic Analysis of Large Container Ships,” Ships Offshore Struct., 9(2), pp. 199–217. [CrossRef]
Senjanović, I., and Vladimir, N., 2013, “Hydro Structural Issues in the Design of Ultra Large Container Ships,” Brodogradnja, 64(3), pp. 323–347.
Iijima, K., Kimura, K., Xu, W., and Fujikubo, M., 2011, “Hydroelasto-Plasticity Approach to Predicting the Post-Ultimate Strength Behavior of Ship's Hull Girder in Waves,” J. Mar. Sci. Technol., 16(4), pp. 379–389. [CrossRef]
Liu, W., Suzuki, K., and Shibanuma, K., 2014, “Nonlinear Dynamic Response and Strength Evaluation of a Containership Beam in Extreme Waves Based on Hydroelasticity–Plasticity Method,” Proceedings of the International Society of Offshore and Polar Engineers, Vol. 4, pp. 652–657.


Grahic Jump Location
Fig. 1

Coordinate system of the 2D hydroelastoplasticity method

Grahic Jump Location
Fig. 2

Body plan of the container ship

Grahic Jump Location
Fig. 3

Former ten flexuous modal shapes of ship

Grahic Jump Location
Fig. 4

Ship weight distribution

Grahic Jump Location
Fig. 5

Ship weight distribution

Grahic Jump Location
Fig. 6

Stress distribution of structural section

Grahic Jump Location
Fig. 7

Relationship between average strain and average stress of three stiffened elements

Grahic Jump Location
Fig. 8

Bending moment-curvature of 500TEU

Grahic Jump Location
Fig. 9

Rigidity-curvature of 500TEU container ship at midship point

Grahic Jump Location
Fig. 10

Numerical extreme wave by superposition between numerical regular wave and focusing wave. (a) Numerical regular wave, (b) numerical focusing wave, and (c) numerical extreme wave.

Grahic Jump Location
Fig. 11

Wave elevation profile of 500TEU container ship at S.S.5.0

Grahic Jump Location
Fig. 12

Midship curvature obtained with hydroelastoplasticity and hydroelasticity. (a) Curvature @ Hf/D = 0.7, Fr = 0.3, (b) curvature @ Hf/D = 1.33, Fr = 0.3, and (c) curvature @ Hf/D = 1.35, Fr = 0.3.

Grahic Jump Location
Fig. 13

VBM as obtained with hydroelastoplasticity and hydroelasticity methods at midship point. (a) VBM/Ms @ Hf/D = 0.7, Fr = 0.3, (b) VBM/Ms @ Hf/D = 1.33, Fr = 0.3, and (c) VBM/Ms @ Hf/D = 1.35, Fr = 0.3.

Grahic Jump Location
Fig. 14

Rigidity distribution of three extreme wave (t = 72 s)

Grahic Jump Location
Fig. 15

Models obtained with hydroelasticity and hydroelastoplasticity models. (a) hydroelastic model and (b) hydroelastic–plastic model.

Grahic Jump Location
Fig. 16

Time-domain hydroelastoplastic model in WH-1

Grahic Jump Location
Fig. 17

Max. VBM/Mu curves obtained with hydroelasticity and hydroelastoplasticity methods

Grahic Jump Location
Fig. 18

Curvature curves obtained at S.S.5.0 with hydroelasticity and hydroelastoplasticity methods

Grahic Jump Location
Fig. 19

Max. VBM/Mu curves obtained with hydroelasticity and hydroelastoplasticity methods, versus Froude number

Grahic Jump Location
Fig. 20

Max. curvature points between hydroelasticity and hydroelastoplasticity method regard to Froude number




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In