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Research Papers: Structures and Safety Reliability

Nonlinear Dynamic Response and Structural Evaluation of Container Ship in Large Freak Waves

[+] Author and Article Information
Weiqin Liu

Department of Systems Innovation,
School of Engineering,
The University of Tokyo,
7-3-1 Hongo,
Tokyo 113-8656, Japan
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 October 25, 2013; final manuscript received August 27, 2014; published online October 3, 2014. Assoc. Editor: Thomas E. Schellin.

J. Offshore Mech. Arct. Eng 137(1), 011601 (Oct 03, 2014) (9 pages) Paper No: OMAE-13-1101; doi: 10.1115/1.4028506 History: Received October 25, 2013; Revised August 27, 2014

Many ship accidents and casualties are caused by large freak ocean waves. Traditionally, the strength of ships against freak waves is assessed by means of ultimate strength evaluation, assuming quasi-static conditions, but the nonlinear dynamic structural response of ships to freak waves should be considered as well. This paper describes how the strength of a ship can be evaluated in terms of its nonlinear vertical bending moment (VBM). Linear dynamic VBM of a ship, which is derived from hydrodynamics, is calculated using a time-domain strip theory code under freak wave conditions, and the nonlinear dynamic VBM, which is dependent on structural nonlinearity, is calculated using a combination of quasi-static and dynamic nonlinear analyses based on the finite element method (FEM). The nonlinear and linear VBMs are then compared to assess how they differ. Then, the influence of freak wave height and wave speed on the VBMs and deformation is studied.

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References

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Figures

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Fig. 1

Methodology of the study

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Fig. 2

Coordinate systems considered in strip theory analysis

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Fig. 3

Body plan of the container ship

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Fig. 4

Numerical freak wave by superposition of two waves

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Fig. 5

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

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Fig. 6

Heave motion of 500-TEU container ship

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Fig. 7

Pitch motion of 500-TEU container ship

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Fig. 8

Linear VBM of 500-TEU container ship

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Fig. 9

FEM model of the middle part of the 500-TEU container ship

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Fig. 10

Bending moments of the 500-TEU container ship

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Fig. 11

Stress contour map of midship

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Fig. 12

Boundary conditions of the dynamic FEM model

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Fig. 13

Loading distribution on the ship FEM model

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Fig. 14

Wave elevation for FEM computation

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Fig. 15

Combination of quasi-static FEM and nonlinear dynamic FEM

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Fig. 16

Middle section of the nonlinear dynamic model

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Fig. 17

Internal energy histories of the middle section for the three wave models

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Fig. 18

VBM history of wave case (Hf/D = 0.7 and Fr. = 0.3)

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Fig. 19

VBM history of wave case (Hf/D = 1.2 and Fr. = 0.3)

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Fig. 20

VBM history of wave case (Hf/D = 1.63 and Fr. = 0.3)

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Fig. 21

Maximum VBM/Mu curves as Hf/Hr is increasing

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Fig. 22

Maximum rotational angle versus Hf/D

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Fig. 23

Maximum VBM/Mu versus Fr. number (for Hf/D = 1.63)

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Fig. 24

Stress distribution for Hf/D = 0.7 (t = 22 s)

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Fig. 25

Stress distribution for Hf/D = 1.2 (t = 22 s)

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Fig. 26

Stress distribution for Hf/D = 1.6 (t = 22 s)

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Fig. 27

Stress distribution for Hf/D = 1.63 (t = 22 s)

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