THESIS FOR THE DEGREE OF LICENTIATE OF ENGINEERING

Random Fatigue Analysis of Container

Ship Structures

Wengang Mao

Department of Mathematical Sciences

Division of Mathematical Statistics

Chalmers University of Technology and University of Gothenburg

Gteborg, Sweden 2009

Random Fatigue Analysis of Container

Ship Structures Wengang Mao

Wengang Mao, 2009

ISSN 1652-9715 /NO 2009:22

Department of Mathematical Sciences

Division of Mathematical Statistics

Chalmers University of Technology and University of Gothenburg

SE-412 96 Gteborg, Sweden

Telephone: +46 (0) 31 772 1000

Author e-mail: wengang@chalmers.se

Printed in Gteborg, Sweden, 2009

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Random Fatigue Analysis of Container

Ship Structures

Wengang Mao

Department of Mathematical Sciences

Division of Mathematical Statistics

Chalmers University of Technology and University of Gothenburg

Abstract

The work presented in this thesis concerns the fatigue estimation model and the

corresponding uncertainties for container vessels based on both onboard

measurement and theoretical analysis. The fatigue model developed is based on the

generalized narrow band approximation, where the significant response height is

shown to have a linear relation with the corresponding significant wave height Hs,

and the zero up-crossing response frequency, fz, is represented by the encountered

wave frequency also in terms of Hs. It is then validated by the measurement from the

onboard hull monitoring system of a 2800 TEU container vessel operated in the

North Atlantic. Considering that the model is strongly dependent on the Hs, we also

calibrated the Hs measurement from onboard system using different types of satellite

measurement. It shows that there is about a 25% overestimation from the onboard

measurement system, which coincided well with the captains report. Based on such

calibration, the fatigue model is then improved with a less than 10% bias with regard

to the accurate rainflow estimation for all 14 voyages measured during 2008.

The uncertainty in using the proposed fatigue model, as well as the other general

uncertainty sources, i.e. S-N curve, failure criterion, etc, is investigated through the

so called safety index. In the computation of such an index, the variation coefficient

for the accumulated damage is required. Firstly, the expected fatigue damage and its

coefficient of variation are estimated from measured stresses referred to above.

Secondly, when suitable stress measurements are not available, these are computed

from models for damage accumulation and sea states variability. The space time

variability of significant wave height is modeled as a lognormal field with

parameters estimated from the satellite measurements. The proposed methods for

estimating uncertainties in the damage accumulation process are finally validated

using the onboard time series of stresses measurement of the same voyages during

2008, as described above.

Keywords: RAOs, rainflow counting, narrow band approximation, zero up-crossing

response frequency, significant wave height, ship structure response, S-N curve,

spatio-temporal model, safety index.

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Acknowledgements

When I sit here looking back the whole process of writing this thesis, there are a lot

people that immediately come into my mind. It is your nice guidance,

encouragement and company that makes the thesis look like what it is now.

First of all, I would like to express my utmost gratitude to my supervisor Igor

Rychlik for giving me this opportunity and helping me further continue this

interesting research topic. Your inspiring, experience and intelligence are extremely

beneficial to my research here. I have never felt so confident about my research,

since I know you are always walking with me and sharing your creative mind with

me. I am very proud of being one of your students. Beside the scientific guidance,

your encouragement and care about my life also makes my stay in Sweden full of

warmth. Also, many thanks for your positive company in the early morning flights

to many meetings. Thank you!

My next sincere appreciation goes to my associate advisor Jonas Ringsberg; you

should know I am very grateful for your beneficial discussions, being the co-author

of appended papers and working with all the contents in this thesis. Whenever I

encounter any problems, not only on the research but also in my daily life, you are

the person who can always encourage me and supply the most immediate help.

Thank you my dear friend! I also want to thank my co-advisor Gaute Storhaug, for

sharing the practical engineering ideas, and setting up this PhD project. Grateful

acknowledgement is also made to the EU SEAMOCS fund for supporting my PhD

studies in Sweden.

I would like to thank all my colleagues in the Department of Mathematical Sciences,

Thomas, Anastassia, Frank, Ottmar, Emilio, Oscar, Daniel, Fardin for nice chats

and communications with different kinds of topics, as well as my friends in the other

department: Zhiyuan, Per, Martin Also I thank all the administrators in the

department; your work makes my studying here more convenient.

Finally, I want to show my gratitude towards my family, specially my dear Tiantian,

for your enduring support and love, as well as your appropriate encouragement and

push that made me full of energy.

Gteborg, April, 2009

Wengang Mao

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List of Papers The licentiate thesis includes the following papers.

Paper I. Mao, W., Ringsberg, J.W., Rychlik, I. and Storhaug, G., (2009). Comparison between a Fatigue Model for Voyage Planning and

Measurements of a Container Vessel. 28th International

Conference on Ocean, Offshore and Arctic Engineering, in Hawaii

USA, 31st May to 5th June, 2009.

Paper II. Mao, W., Ringsberg, J.W., Rychlik, I. and Storhaug, G., (2009). Estimation of Fatigue Damage Accumulation in Ships during

Variable Sea State Conditions. Submitted.

Paper III. Mao, W., Rychlik, I. and Storhaug, G., (2009). Safety index of fatigue failure for ship structure details. Submitted.

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Contents

Abstract iii

Acknowledgements v

List of Papers vii

1 Introduction .................................................................................. 1

1.1 Fatigue problems of commercial vessels ................................................ 1

1.2 General fatigue estimation methods ....................................................... 3

1.2.1 Rainflow fatigue analysis................................................................ 3

1.2.2 Narrow Band Approximation .......................................................... 7

1.3 Ship fatigue design guidelines ............................................................ 9

1.3.1 Fatigue design based on empirical formula .................................... 9

1.3.2 Fatigue design based on direct calculation ..................................... 9

1.3.2.1 Sea states description .......................................................... 10

1.3.2.2 Response amplitude operators (RAOs) ................................ 10

1.3.2.3 Structure stress response analysis ........................................ 11

1.3.2.4 Fatigue estimation by Narrow Band Approximation ........... 12

1.4 Spatio-temporal wave model ................................................................ 12

1.5 Objectives of research project and thesis............................................. 13

2 Summary of appended papers .................................................. 15

2.1 Workflow ................................................................................................ 15

2.2 Fatigue model in terms of Hs (Paper I & II) ........................................ 16

2.3 Uncertainty of fatigue model (Paper III) ............................................. 18

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3 Future work ................................................................................ 21

3.1 Whipping contribution to fatigue ......................................................... 21

3.2 Torsion and Nonlinear effects ............................................................... 23

3.3 Fatigue model for other vessels ............................................................. 24

4 Bibliography ............................................................................... 25

Appended Papers

Paper I: Comparison between a fatigue model for voyage planning and

measurements of a container vessel29

Paper II: Estimation of Fatigue Damage Accumulation in Ships during

Variable Sea State Conditions.47

Paper III: Safety Index of Fatigue Failure for Ship Structure Details..77

1

1 Introduction In materials science, fatigue is the progressive and localized structural damage that

occurs when a material is subjected to cyclic loading. Fatigue failure can happen

when the maximum stress value is less than the ultimate tensile stress limit or

possibly even b