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.

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Fig. 1

Coordinate system of the 2D hydroelastoplasticity method

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Fig. 2

Body plan of the container ship

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Fig. 3

Former ten flexuous modal shapes of ship

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Fig. 4

Ship weight distribution

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Fig. 5

Ship weight distribution

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Fig. 6

Stress distribution of structural section

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Fig. 7

Relationship between average strain and average stress of three stiffened elements

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Fig. 8

Bending moment-curvature of 500TEU

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Fig. 9

Rigidity-curvature of 500TEU container ship at midship point

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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.

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Fig. 11

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

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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.

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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.

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Fig. 14

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

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Fig. 15

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

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Fig. 16

Time-domain hydroelastoplastic model in WH-1

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Fig. 17

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

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Fig. 18

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

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Fig. 19

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

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Fig. 20

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



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