Longitudinal ultimate bending strength analysis of ship

Fengfeng Mao

Delft

Univ

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ity o

f Tech

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Longitudinal ultimate bending strength analysis of ship structure for emergency response

Delft University of Technology

Longitudinal ultimate bending strengthanalysis of ship structure for emergency

response

Author:

Fengfeng Mao

Thesis Committee:

Prof.dr.ir. M.L. Kaminski

Dr.ir. Xiaoli Jiang

Menno van der Horst

Panagiotis Antonakas

Guoqing Hong

Jeroen Jacobs

A thesis submitted in fulfilment of the requirements

for the degree of Master of Science

in

Offshore and Dredging Engineering

http://www.tudelft.nl/en/

mailto:[email protected]

http://www.3me.tudelft.nl/en/about-the-faculty/departments/maritime-and-transport-technology/organisation/staff/persoonlijke-paginas/kaminski/kaminski/

http://www.3me.tudelft.nl/en/about-the-faculty/departments/maritime-and-transport-technology/organisation/staff/persoonlijke-paginas/jiang/jiang/

http://www.3me.tudelft.nl/en/about-the-faculty/departments/maritime-and-transport-technology/organisation/staff/persoonlijke-paginas/jiang/jiang/

http://staff.tudelft.nl/M.P.vanderHorst/

Research Group Web Site URL Here (include http://)

i

Summary

Maritime emergency response requires time-saving in order to mitigate loss, thus a

fast numerical tool is very important for supporting decision making and related salvage

engineering work. Currently, most fast numerical modeling method is either by manually

laboriously building or requires 3D or 2D AUTO CAD drawing, which is very difficult

to obtain in emergency situation. Thus this thesis is aiming to propose a fast numerical

method based on limited information from emergency situation. Based on the fast

numerical model, structural analysis, weight estimation can be assessed, thus support

decision making and engineering work. In consistent with the emergency situation, the

fast numerical model is used for analyzing global longitudinal strength in the present

work.

Firstly, the whole process of emergency response is investigated to know the minimal

information available in a short time after the emergency. Secondly, a rapid numerical

modeling method for generic ship structure based on limited information from emergency

situation is developed in the present work. The point storing algorithm, point generating,

curve generating and surface generating algorithm are developed here. A corresponding

fast numerical tool based on container ship is produced here.

Thirdly, the fast numerical model generated for container ship is validated in structural

response of global FE model. The failure mechanism of container ship under sagging is

investigated in both numerical model and analytical model. Based on it, the ultimate

bending moment is obtained by the generated fast numerical model. Finally, the non-

linear finite element method is adopted for assessing ultimate strength for other type of

ship structures like OT, FPSO, BC etc. The failure mode of the structure under pure

bending is investigated by nonlinear finite element analysis. Based on the failure mode,

a simplified method for assessing ultimate bending moment by NLFEM is proposed and

validated with experiment result and ISSC benchmark study.

The validated fast numerical tool for container ship can be used for structural analysis

, structural weight estimation etc, and thus supporting emergency salvage engineering.

The generic fast numerical method can be further applied for other types of ship struc-

ture, like OT, BC, FPSO etc. A corresponding simplified NLFEM method can be used

for assessing maximum bending capacity and thus support lifting engineering work.

Acknowledgements

This thesis could not have been completed without the support of many people.

I would like to give my deepest gratitude to Prof. Kaminski. He has been an inspiring

and encouraging teacher. His broad, deep knowledge and enthusiasm in research has

motivated me to work. He also taught me how to analyze a problem and the correct

way of being a responsible engineer.

I am heartily thankful to my daily supervisor, Xiaoli jiang, who gave me a lot of advice

and ideas during my thesis. I would also give my great appreciation to my supervisors

from Boskalis, Panos and Guoqing, for their critical comments and guidances in various

stages of my thesis work.

I would like to thank my committee member Menno van der Horst for his ideas in my

thesis and Prof. Hopman for his time spent in this project. Also I would like to thank

my colleagues at Boskalis for supporting me. Thank Jeroen for initiating this project

and Waikit Tang for many help in FEM.

Finally, I want to thank my Yunan, my parents and my sister for supporting me in

entering the field of offshore engineering.

iii

Contents

Abstract ii

Acknowledgements iii

Contents iv

List of Figures vii

List of Tables x

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Emergency response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Problem description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Research objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.5 Scope of work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.6 Thesis structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Hull girder ultimate strength 8

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 Hull girder ultimate strength . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3.1 Simple beam theory . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3.2 Elastic buckling theory . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3.3 Cross section stress distribution . . . . . . . . . . . . . . . . . . . . 11

2.3.3.1 Full plastic bending . . . . . . . . . . . . . . . . . . . . . 11

2.3.3.2 Caldwell’s method . . . . . . . . . . . . . . . . . . . . . . 12

2.3.4 Smith’s method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3.5 ISUM method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3.6 Non-linear finite element method . . . . . . . . . . . . . . . . . . . 15

2.4 Method applied in this work . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3 Rapid geometric tool for numerical modeling 17

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2 Rapid numerical tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.2.1 Requirement of numerical tool . . . . . . . . . . . . . . . . . . . . 18

3.2.2 User interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

iv

Contents v

3.3 Ship structure characteristic . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.3.1 General ship characteristic . . . . . . . . . . . . . . . . . . . . . . . 20

3.3.2 Container ship characteristic . . . . . . . . . . . . . . . . . . . . . 21

3.3.2.1 General arrangement plan . . . . . . . . . . . . . . . . . . 21

3.3.2.2 Midship section . . . . . . . . . . . . . . . . . . . . . . . 22

3.3.2.3 Transverse bulkhead . . . . . . . . . . . . . . . . . . . . . 23

3.4 Rapid ship hull form generating . . . . . . . . . . . . . . . . . . . . . . . . 23

3.4.1 Characteristic of NURBS . . . . . . . . . . . . . . . . . . . . . . . 24

3.4.2 Control parameters selecting . . . . . . . . . . . . . . . . . . . . . 25

3.4.3 Ship hull form constructing . . . . . . . . . . . . . . . . . . . . . . 25

3.5 Rapid inside structural layout generating . . . . . . . . . . . . . . . . . . 26

3.5.1 Parametric seeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.5.1.1 Identification of critical parameters . . . . . . . . . . . . 27

3.5.1.2 Working principle of parametric seeds . . . . . . . . . . . 27

3.5.2 Points structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.5.2.1 Points storing algorithm . . . . . . . . . . . . . . . . . . . 29

3.5.3 Line generation by neighboring . . . . . . . . . . . . . . . . . . . . 31

3.5.3.1 “Finding neighbor” algorithm for line generating . . . . . 31

3.5.4 Plate generation by propagation . . . . . . . . . . . . . . . . . . . 32

3.5.4.1 “Hand in hand” algorithm for plate generating . . . . . . 33

3.5.5 Stiffeners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4 Longitudinal ultimate bending strength of container ship 36

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.2 Vessel particulars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.3 Elastic buckling strength of container ship . . . . . . . . . . . . . . . . . . 37

4.3.1 Material model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.3.2 Element type and size . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.3.3 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.3.4 Stress distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.3.5 Elastic buckling moment under sagging condition . . . . . . . . . . 41

4.4 Full plastic bending strength of container ship . . . . . . . . . . . . . . . . 43

4.4.1 Failure mechanism of container ship under sagging . . . . . . . . . 46

4.5 Ultimate bending strength of container ship . . . . . . . . . . . . . . . . . 48

4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5 Ultimate strength of ship box girder under pure bending 50

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5.2 Description of box girder for experiment . . . . . . . . . . . . . . . . . . . 51

5.2.1 Model parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.3 Shell element model for box girder . . . . . . . . . . . . . . . . . . . . . . 53

5.3.1 Element type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5.3.2 Material property . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5.3.3 Boundary condition . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.3.4 Initial imperfection . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.3.4.1 Description of initial imperfection . . . . . . . . . . . . . 55

Contents vi

5.3.4.1.1 Plate deflection . . . . . . . . . . . . . . . . . . 56

5.3.4.1.2 Stiffener deflection . . . . . . . . . . . . . . . . . 57

5.3.4.1.3 Column initial deflection . . . . . . . . . . . . . 58

5.3.5 Ultimate strength under pure bending moment for plate model byNLFEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

5.3.5.1 Convergence study . . . . . . . . . . . . . . . . . . . . . . 59

5.3.5.2 Validation with ISSC benchmark study and experiment . 60

5.3.5.3 Collapsing mode . . . . . . . . . . . . . . . . . . . . . . . 61

5.4 Simplified beam and shell element model for box girder . . . . . . . . . . 61

5.4.1 Element type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.4.2 Material property . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

5.4.3 Boundary condition . . . . . . . . . . . . . . . . . . . . . . . . . . 64

5.4.4 Initial imperfection . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

5.4.5 Ultimate strength under pure bending moment for simplified modelby NLFEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

6 Conclusion 68

6.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

6.1.1 Information obtained emergency response . . . . . . . . . . . . . . 68

6.1.2 Methods for assessing hull girder ultimate strength . . . . . . . . . 68

6.1.3 Rapid numerical modeling method . . . . . . . . . . . . . . . . . . 69

6.1.4 Longitudinal ultimate bending strength of container ship . . . . . 69

6.1.5 Simplified NLFEM method for assessing ultimate bending strengthfor other ship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

6.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

6.3 Recommendations for further work . . . . . . . . . . . . . . . . . . . . . . 70

A Full plastic bending moment 72

B Slenderness ratio of deck plate 76

C Material property of high strength steel 78

Bibliography 80

List of Figures

1.1 Costa Concordia accident . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Mol Comfort accident . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Loss rate W.R.T locations[1] . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.4 loss rate W.R.T causes[2] . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.5 loss rate W.R.T types[2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.6 Brief process of emergency response . . . . . . . . . . . . . . . . . . . . . 3

2.1 Buckling of simple column in pinned boundary condition[3] . . . . . . . . 11

2.2 Force equilibrium[3] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Fully plastic bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.4 Caldwell’s presumption of stress distribution over the cross section(Saggingas example) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.1 Drawing example from emergency project . . . . . . . . . . . . . . . . . . 18

3.2 User interface structure of rapid numeric tool . . . . . . . . . . . . . . . . 19

3.3 Interface of rapid numerical tool . . . . . . . . . . . . . . . . . . . . . . . 19

3.4 Frame system, girder system and stringer system[4] . . . . . . . . . . . . . 21

3.5 General arrangement plan . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.6 Midship cross section drawing . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.7 Non-watertight bulkhead . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.8 Watertight bulkhead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.9 Characteristic points and curves of ship hull form . . . . . . . . . . . . . 26

3.10 Ship hull form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.11 Process diagram of rapid numerical tool . . . . . . . . . . . . . . . . . . . 27

3.12 Working principle of parametric seeds . . . . . . . . . . . . . . . . . . . . 28

3.13 Parametric seeds for the rapid numerical tool . . . . . . . . . . . . . . . . 28

3.14 Midship section characteristic points . . . . . . . . . . . . . . . . . . . . . 29

3.15 Bulkhead characteristic points . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.16 Point storing structure for the rapid numerical tool . . . . . . . . . . . . . 30

3.17 Points generated based on the storing algorithm . . . . . . . . . . . . . . 30

3.18 Correct and wrong way of neighboring points . . . . . . . . . . . . . . . . 31

3.19 Pseudocode for “find neighbor” algorithm for generating curves in X . . . 32

3.20 Example of rapid curve generating . . . . . . . . . . . . . . . . . . . . . . 32

3.21 Rapid curve generating . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.22 Pseudocode for “hand in hand” algorithm for generating surfaces in X . . 33

3.23 Rapidly generating surface in X direction . . . . . . . . . . . . . . . . . . 34

4.1 Midship cross section drawing . . . . . . . . . . . . . . . . . . . . . . . . . 38

vii

List of Figures viii

4.2 Boundary condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.3 Frame cross section stress distribution of one cargo model . . . . . . . . . 40

4.4 Frame cross section stress distribution of one cargo model . . . . . . . . . 40

4.5 Stress distribution over the mid-cargo of the 2 cargo holds model . . . . . 41

4.6 Stress distribution over the mid-cargo of 2 cargo holds model . . . . . . . 41

4.7 Stress distribution over mid-cargo of the 3 cargo holds model . . . . . . . 42

4.8 Stress distribution over mid-cargo of the 3 cargo holds model . . . . . . . 42

4.9 Buckling shape of 1 cargo model . . . . . . . . . . . . . . . . . . . . . . . 43

4.10 Before buckling(1 cargo model) . . . . . . . . . . . . . . . . . . . . . . . . 43

4.11 After buckling(1 cargo model) . . . . . . . . . . . . . . . . . . . . . . . . . 43





4.16 Full plastic stress distribution over hull cross section . . . . . . . . . . . . 44

4.17 Aiσyi distribution over the height . . . . . . . . . . . . . . . . . . . . . . . 45

4.18 Stress distribution under buckling bending moment(linear FEM) . . . . . 46

4.19 Critical stress variation for columns of different slenderness ratio[5] . . . . 47

4.20 Ultimate bending moment of container ship . . . . . . . . . . . . . . . . . 48

5.1 Experimental test setting on box girder[6] . . . . . . . . . . . . . . . . . . 52

5.2 Sketch of box girder[6] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5.3 Cross section of box girder[6] . . . . . . . . . . . . . . . . . . . . . . . . . 52

5.4 Boundary condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.5 Example of fabrication induced initial imperfection of steel structure[7] . . 55

5.6 plate initial deflection shape[8] . . . . . . . . . . . . . . . . . . . . . . . . 56

5.7 Plate initial deflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5.8 Stiffener side deflection(coupled with plate)[8] . . . . . . . . . . . . . . . . 57

5.9 Stiffener side deflection(coupled with column)[8] . . . . . . . . . . . . . . 57

5.10 Stiffener side way initial deflection(coupled with plate deflection) . . . . . 58

5.11 Stiffener web initial deflection[8] . . . . . . . . . . . . . . . . . . . . . . . 58

5.12 column initial deflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

5.13 Mesh size convergence study . . . . . . . . . . . . . . . . . . . . . . . . . . 60

5.14 ISSC mean numerical result(H200) . . . . . . . . . . . . . . . . . . . . . . 61

5.15 Numerical result of full plate model(H200) . . . . . . . . . . . . . . . . . . 61





5.20 Overall collapse mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.21 Simplification: initial deflection in the full box girder . . . . . . . . . . . . 64


5.23 Numerical result of simplification case(H200) . . . . . . . . . . . . . . . . 66





List of Figures ix

A.1 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

A.2 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

A.3 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

B.1 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

C.1 Steel supplied by Dillinger Hutten Worke[6] . . . . . . . . . . . . . . . . . 79

List of Tables

3.1 Control parameters from GA plan and midship section drawing . . . . . . 25

4.1 Main particulars of the container ship(m) . . . . . . . . . . . . . . . . . . 37

4.2 Material property in container ship . . . . . . . . . . . . . . . . . . . . . . 38

4.3 elastic buckling moment of container ship(GN.m) . . . . . . . . . . . . . . 43

4.4 Elastic buckling and full plastic bending moment of container ship(GN.m) 46

4.5 Plate Slenderness ratio of deck part of container ship . . . . . . . . . . . . 47

4.6 Ultimate bending moment of container ship under sagging(GN.m) . . . . 48

5.1 Geometric dimensions of the box girder[6] . . . . . . . . . . . . . . . . . . 51

5.2 Geometric parameters of the box girder[6] . . . . . . . . . . . . . . . . . . 53

5.3 Comparison of present work with ISSC mean value of ultimate bendingmoment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.4 Comparison of simplification case with ISSC2015 in ultimate bending mo-ment(KN.m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

x

Chapter 1

Introduction

1.1 Background

In the real world, despite the great advances in technology of offshore/marine engineering

and the design safety margin from classification societies, it is almost unavoidable for ship

accidents to occur due to the human intervention and severe environmental conditions.

Once these accidents happens, they will always attract concerns from both industry and

the public, as it will lead to serious consequences such as heavy environmental pollution,

loss of human life, asset and the corresponding huge economic loss.

There have been many tragedies created by maritime accidents in the last 3 years. In

January 2012, one young cruise ship “Costa Concordia”(figure 1.1) grounded in Italy,

causing 32 deaths, which make it the biggest maritime loss in 2012. In August 2013,

“MV Smart” broke into two pieces after grounding. In February, the bulk carrier “Harita

Bauxite” sank in south China sea, 14 out of 24 crews on board were killed.

In 2013, “Mol Comfort”(figure 1.2) suffered a crack in the bottom of vessel, the crack

started to grow rapidly in bad weather and finally the vessel went into two pieces. It

rapidly sank in deep water of 200 nautical miles off the coast. This event attracted

public concern for the marine safety issue, especially for the container vessel. As in

recently years, the size of the container vessel in use is growing bigger. These “mega

container vessels” might also be involved with safety issues, increased risks, emergency

response difficulties and salvage difficulties.

Marine or offshore accidents are characterized by its random property and time urgent

property. Based on the data of Lloyd’s List[2] from 2012 to 2014, the loss rate of

ships with regarding to location(figure 1.3), cause(figure 1.4) and types(figure 1.5). The

accident might happen to any type of ships at any locations due to multiple causes based

1

Chapter 1. Introduction 2

Figure 1.1: Costa Concordia accident Figure 1.2: Mol Comfort accident

on “Safety and Shipping Review 2015” from AGCS[1]. Once these accidents happen,

emergency response needs to be taken in order to mitigate the loss. So a method to

rapidly generate a numerical model of ship structure with reasonable accuracy is very

important in facilitating decision making in these emergency cases.

Besides supporting ship salvage cases, for other time urgent projects like tender project,

the rapid numerical tool will also significantly increase the efficiency and support en-

gineering business. In the phase of concept design for ship structure, it will be very

profitable to have a global finite element model to evaluate the ship structure. So be-

cause of the rapid property of this method, this tool can also support the design phase.

Figure 1.3: Loss rate W.R.T locations[1]

1.2 Emergency response

After the ship accident happens, the first 48 hours are of crucial importance with re-

garding to saving life and assets loss.

Based on the information gathered from salvage company, the normal process of emer-

gency response is shown in figure 1.6. Usually, after the maritime accident happens,


Figure 1.4: loss rate W.R.T causes[2] Figure 1.5: loss rate W.R.T types[2]

emergency contact will be conducted from an insurance company to salvage company.

From this emergency contact, the salvage company can get the information about ship

accident location, ship name, ship principal dimension. 2-3 hours after the emergency

contact, GA plan (general arrangement plan) and midship section drawing can be sent

from the ship owner to the salvage company if the salvage company makes a request. In

1-2 weeks after the emergency call, more detailed information about this ship like the

construction drawing can be accessed from other stakeholders like shipyard, ship society.

So, due to the fact that ship information documents are held by multiple stakehold-

ers(ship owner, insurance company, shipyard, Salvage Company), within 24 hours after

the accident happens, the minimal information can be accessed by the salvage company

are GA plan and midship drawing. By using these initial input information within 4

hours after the maritime accident, a method for rapidly generating a numerical model

within a short time is needed to be developed in order to facilitate rapid while wise

decision making.

Figure 1.6: Brief process of emergency response


1.3 Problem description

With this limited information at hand, a rapid and wise decision must be made by

the salvage company in response to this accident. So a rapid numerical model is of

crucial importance to facilitate decision making, with this model, by small modifications

corresponding to the specific accident, structural assessment can be made, thus can

support decision making.

Currently, FE method is widely used in industry, a finite element model is needed for

analyzing the structural behavior. However, it requires detailed structural drawing from

the ship to build the model for the accidental ship, which is often not accessible after

the ship accident happens. The building procedure for the FE model is often tedious

and time-consuming. Usually, it takes 2-3 month for a person to build the FE model for

the full ship depending on different experience level, which is far from the requirement

of emergency response or time-urgent projects.

Although it is possible for now to automatically generate a numerical model of ship

structure based on 3D/2D AUTO CAD digital drawings. A lot of researchers have

investigated on this problem, like Jang[9]. Unfortunately this method is not possible to

be applied in this problem, since in most cases of emergency response there is rarely any

3D drawings available and mostly these available drawings can be very old and scanned

version of the original drawings.

Thus in situation required for rapid emergency response, it is of critical importance to

have a fast numerical tool for aiding engineering work. With limited information avail-

able after the ship accident, the fast numerical can be used for automatically generating

a ship model.

Since ship emergency situation is usually related with its ultimate strength capacity.

Together with the ship’s trend of becoming larger and larger in recent years, the struc-

tural safety problem related with ultimate limit state arises. Thus it is very important

to have a better understanding of the ultimate strength of the ship structure, especially

for these super-sized ships.

Currently, in ultimate strength analysis for normal ships like oil tanker, bulk carrier etc,

nonlinear finite element method is adopted to analyze the ultimate strength. Usually

the finite element modeling of structure for ultimate strengths requires use of plate

element, which is very laborious and inflexible for the case of global ship model. Thus,

a new method of simplifying this modeling is very important for the purpose of possible

application for global ship model.


1.4 Research objective

The main objective of this thesis work is to rapidly generate a numerical model for as-

sessing longitudinal ultimate bending strength of ship structure for emergency response.

The corresponding objectives are addressed as:

. Develop a geometrical tool of a numerical modeling for container ship based on limited

information.

. Propose a method for fast numerical modeling based on limited information in emer-

gency situation, which is applicable for other types of ships.

. Verify the developed geometrical tool.

. Assess longitudinal ultimate bending strength of container ship based on rapid numer-

ical model.

. Assess the longitudinal ultimate bending strength for other types of ship structure.

1.5 Scope of work

So this thesis tries to find a solution to solve this problem based on limited information

obtained from the ship in emergency situation. Since it is the nature of ship emergency

situation that closely relates with its ultimate limit state[7], the rapid numerical model

will be verified and used in assessing ultimate bending strength.

Based on the objective, the corresponding main scope of work is as follows:

. Investigate on process of emergency response and find out the minimal information

the salvage company can get within a short time after the accident happens;

Identify the parameters from the minimal information available. Create a rapid numer-

ical tool for container vessel based on the identified parameters.

. Identify the characteristic of ship structure, propose a data structure to store the ship

geometric information based on the ship structure characteristic;

Create a ship hull form parametrically for numerical modeling purpose;

Propose a method for rapidly generating inside structural layout incorporating ship hull

form in numerical environment, which includes topological structure design, point storing

and connecting algorithm, line generating algorithm and surface generating algorithm.


. Verify the rapid numerical tool in stress distribution under pure bending moment.

. Based on the numerical model for container ship created by rapid numerical tool,

analyze the global buckling behavior of container vessel under bending moment;

Based on the global buckling moment and full plastic bending moment, find out the

failure mechanism of container ship under bending and assess the ultimate bending

moment of container ship. The sagging condition of the container ship is investigated,

since the failure mechanism is different from other ships.

. For other type of ship structure, investigate the collapse mode of ship box girder under

pure bending on full-plate element model by NLFEM;

Based on the result from full-plate model, propose a simplified method for assessing

ultimate bending moment of ship box girder under pure bending.

1.6 Thesis structure

This thesis is structured in the way to provide a natural flow for understanding the prob-

lem of longitudinal ultimate strength analysis of ship structure for emergency response.

In the first chapter, main motivation, background information and input information

for this thesis project are described. In order to find the minimal input information

available after the emergency situation, a brief description of emergency response process

is described in this part. The rapid numerical modeling is based on the minimal input

information defined in this part.

In the second chapter, based on literature review, the advantages and disadvantages

between different method for analyzing ultimate bending moment are described here.

Thus, methods for assessing longitudinal ultimate bending strength for this thesis work

are selected.

In the third chapter, a method of rapidly generating mesh-able geometric model for

emergency response is presented. This method is described in the case of container ship,

it can be applied to other ship structures like oil tanker, bulk carrier, FPSO etc.

In the fourth chapter, the rapidly generated numerical model for container ship is vali-

dated in stress distribution and used for assessing longitudinal ultimate strength. Con-

tainer ship’s extrally strengthened deck structure make it more buckling resistant under

sagging condition, its failure mechanism in sagging can be found by using the elastic


buckling theory and comparison with full plastic bending moment. Based on the found-

ing, the ultimate strength in sagging for container ship is assessed by the validated fast

numerical model.

In the fifth chapter, a simplified non-linear finite element method for analyzing ultimate

bending strength is described and validated with the normal NLFEM as well as the

experimental test. For other types of ship structures like Oil tanker, Bulk carrier and

FPSO, unlike container ship, they are not designed with extrally strengthened structure.

The deck structure of these ship will buckle first before yielding under sagging condition.

In these cases, it is very important to properly assess its post-buckling behavior in

order to give a correct estimation of longitudinal ultimate strength. Nonlinear finite

element method is thus adopted for assessing the post-buckling behavior properly. The

traditional non-linear finite element method is further simplified so to be possibly applied

for global ship model.

In the sixth chapter, a conclusion based on this thesis work is made and possible future

work after the present work is discussed in this chapter.

Chapter 2

Hull girder ultimate strength

2.1 Introduction

In maritime or offshore structural design, there are limit states involved: ultimate limit

states (ULS), fatigue limit states (FLS), accidental limit states (ALS) and serviceabil-

ity limit state(SLS)[7]. When a structure or structural element becomes unfit for its

intended use, that is, fails to perform the designated function, it is said to have reached

a limit state[10]. The ultimate limit state represents the fail of its most fundamental

function, which is related with the collapse of the whole structure.

Most ships can fulfill their tasks in their designed service life. However, due to the

random nature of the ocean environment, a ship can get trapped in a severe environment

and may fail. This kind of emergency situation is often related with the ship’s ultimate

capacity, in which the maximum capacity of ship structure is exceeded. Because of the

natural relation between ultimate strength and emergency situation, properly assessing

the ultimate capacity of ship structure is of great importance to emergency response

project.

In this chapter, a literature review has been carried out in order to choose the proper

way to assess the ultimate bending strength in the present work.

2.2 Hull girder ultimate strength

Hull girder strength, or longitudinal strength, is the most important and fundamental

strength for structural safety of marine structures. The loss of hull girder strength is

related to ship collapse with catastrophic disasters as indicated in the first chapter.

8

Chapter 2. ultimate strength analysis 9

As hull girder loads increase, the components of ship structure will exceed their yielding

limit and the corresponding stress redistribution will happen in order to withstand the

load as a system. Until one moment, the ship as a system can not resist the load anymore,

even after the stress redistribution, that is the state when the ship structure reaches its

ultimate limit state and the ship collapses. One of the most typical ship collapses is the

whole ship breaking into two parts under extreme vertical bending moment[7].

So assessing the hull ultimate strength properly is very important in order to support

ship design and evaluate the emergence response project properly. Currently, many

researchers have worked on this topic, a brief literature review with regarding to the

methodologies for assessing the ultimate hull girder strength is conducted in this work.

2.3 Literature review

The existing method for assessing ultimate hull girder strength can be summarized

into six categories based on calculation effort: simple beam theory, cross section stress

distribution, Smith method, ISUM method, Non-linear finite element method.

2.3.1 Simple beam theory

The simple-beam theory is the simplest way of giving an estimation of hull girder

strength, which is very easy to apply. It simplifies the whole ship as a beam with

equivalent bending stiffness and area, thus it is not possible to account for the local

failures of the structural component.

σ =Mz

I(2.1)

In which, M is the bending moment applied in the ship, I is the equivalent moment of

inertia of one ship section, z is the vertical distance of the calculation location to the

neutral axis. So, the maximum stress will be at the deck or at the bottom of the ship.

2.3.2 Elastic buckling theory

When axial compressive load is applied in a column structure, instead of yielding failure

under compressive load, the structure will become unstable and deflect sideways when

the axial compressive load reaches a certain critical value. This buckling behavior will

appear in the deck structure of ship structure in sagging condition.


For a simple column with both ends in pinned boundary condition(figure 2.1), no shear

force is involved in the axial loading in this case. When cutting the column at an

arbitrary location X with regards to one pinned end, the following force equilibrium can

be obtained:

M + Pω = 0 (2.2)

and thus,

EId2ω

dx2+ Pω = 0 (2.3)

The solution to this basic differential equation is in the form as:

ω = Acos(αx) +Bsin(αx) (2.4)

In which,

α2 =P

EI(2.5)

As pinned boundary condition in both ends, which means: when x=0, ω=0; when x=l,

ω = 0. Substitute x=0, ω=0 into 2.4, so that A=0; Substitute x=l, ω = 0 into 2.4, so

that

Bsin(αl) = 0 (2.6)

B=0 is not true, otherwise the column will not have side deflection. So this boundary

condition can be satisfied by:

sin(αl) = 0 (2.7)

which means:

αl = 0, π, 2π, ... (2.8)

From 2.5, it can be known that αl = 0 is not possible, so αl = π is the first solution to

fulfill this boundary condition. Thus,

Pe = π2EI

l2(2.9)


The corresponding deflection form over this column is:

ω = Bsin(πx

l) (2.10)

While for boundaries with both ends fixed, the same method can be applied. Because

of the fixed ends, an unknown bending moment is induced by the fixed ends. Thus, the

corresponding equilibrium is

EId2ω

dx2+ Pω = Mx (2.11)

With the additional boundary condition as dωdx = 0 at both ends, 2.11 can be solved, the

corresponding buckling load at the lowest reasonable mode is:

Pe = 4π2EI

l2(2.12)

Figure 2.1: Buckling of simple column in pinned boundary condition[3]

Figure 2.2: Force equilibrium[3]

2.3.3 Cross section stress distribution

2.3.3.1 Full plastic bending

For full plastic bending, a simple stress distribution over the cross section of ship struc-

ture is also assumed. Instead of considering the buckling induced stress reducing in the

compression part, all of the material in the cross section is yielded, with the compression

part and the tension part divided by neutral axis(figure 2.3 ). For the ship under sagging

condition, the upper part is in compression while the lower part is in tension.

Generally, to calculate the full plastic bending moment of a ship cross section, take

sagging for example, the following steps are needed:


Figure 2.3: Fully plastic bending

1. Find the location of neutral axis of the cross section, divide the ship cross section

into 2 parts based on the neutral axis founded, the above part is in compression, while

the lower part is in tension.

2. For the compression part, find the distance of every structural component from

neutral axis in the cross section, multiply it with the corresponding yielding stress and

area of that component. Thus get the bending moment contribution by that component.

3. Integrate the moment contributions by all structural components in compression part,

Thus the overall moment contribution by the compression part is obtained.

4. For the tension part, same method can be applied to get the overall moment contri-

bution by the tension part.

5. Add the moment contribution from the compression part and tension part together

to get the fully plastic bending moment.

2.3.3.2 Caldwell’s method

Caldwell[11] is the pioneer in calculating the ultimate strength by stress distribution

over the ship cross section. In this method, the stiffened panels of the cross section

are idealized into panels with equivalent thickness. Also, the buckling induced strength

reduction is taken into account in this method. The bending stress distribution(figure

2.4 ) is presumed over the simplified cross section, with the compressed part reaching

ultimate limit with buckling while the tension part reaches its yielding limit, where f

and f1 are the strength capacity reduction factors due to buckling for deck and side shell


separately. The ultimate longitudinal bending moment is calculated by integrating the

stress over the whole simplified cross section.

Figure 2.4: Caldwell’s presumption of stress distribution over the cross sec-tion(Sagging as example)

Caldwell’e method is the first to include buckling induced strength reduction in the

estimation of longitudinal ultimate capacity. Since in real ship structure, it is never

possible to for the whole cross section to reach its limit stress, especially for the part

near the neutral axis, far from the yielding limit stress or bulking stress. Thus caldwell’s

method overestimated the ultimate strength of the ship box girder. Caldwell’s method

also does not take the progressive collapse behavior into account. Later, more researchers

developed further based on Caldwell method, like Nishihara [12] and Paik [13]. These

improved methods are simple and show good comparison with the experiment/non-linear

FEM result in many cases. But the main disadvantage of this method is that in the

analysis, the progressive collapse behavior has not been taken into account.

2.3.4 Smith’s method

It is Smith method[14] which for the first time takes the progressive collapsing behav-

ior into account when estimating the ultimate longitudinal strength of ship structure.

The Smith’s method initiated from the Caldwell’s method, but it takes the strength

reduction of the structural component into consideration during the collapsing of ship

structure. Currently Smith’s method is widely used among marine or offshore industry

for estimating longitudinal hull girder ultimate strength under bending for its simplicity

and relatively good accuracy.


In this method, the ship cross section is decomposed into small assemblies made of

stiffener and corresponding attached plating. The average stress-strain relation of these

individual structural components has already been known or analyzed before performing

Smith’s method. During the process when bending moment is applied incrementally,

the axial stress induced by bending moment will cause failures of part of the structural

components. These structural component will be removed from the analysis, thus the

neutral axis will be shifted to new location. So the next interactive step is based on the

new neutral axis while the failed structural component has been removed. In this way

the progressive collapse behavior is considered. Smith’s method is a simple method for

assessing ultimate strength while taking the progressive collapse into account. It can

give good estimation of collapsing behavior until the structure reaches its ultimate limit

state if proper average stress-strain relation is assumed for the structural component.

In smith method, the transverse stress from the stress redistribution during the process

of collapsing of ship structure has not been taken into account. Thus, smith method

does not perform well in estimating the post-buckling behavior of ship structure. Also,

the interaction between different structural components can not be accounted. Smith

method is based on one ship section, so the possible effect from transverse structural

members like webframe, bulkhead can not be taken into account.

2.3.5 ISUM method

Another simplified method to perform progressive collapse analysis for ultimate strength

is Idealized Structural Unit Method(ISUM), which is proposed by Ueda[15] almost in

the same era of Smith method. ISUM method is actually similar to the finite element

method. But instead of using the normal finite element, it use the structural component

as basic element for his method. Structural components are idealized as one unit, such as

stiffened plate unit, stiffened panel unit etc. New elements representing idealized units

are developed to perform progressive collapse analysis. In this way, the number of degrees

of freedoms are significantly decreased and thus the calculation effort is significantly

reduced in the K matrix. It is believed that if the proper element type is defined, the

ISUM can achieve a relatively good result in assessing ultimate strength.

The ISUM has been accepted as an efficient while accurate method for ultimate strength

analysis of ship structure. Lots of significant effort of further development of this method

has been done by many researchers. However the number of users of this method is still

limited in offshore and marine industry according to Paik[16]. Possible reasons could

be the use of ISUM need to be based on the understanding of structural behavior of

structural unit, which requires significant education effort. Also, further effort needs


to be done on the property of large structural unit in order to make ISUM mature for

application.

2.3.6 Non-linear finite element method

Finite element method has been widely used in marine or offshore industry for analyzing

the linear structural response. While based on the non-linear numerical experiment done

by a lot of researchers, the non-linear finite element method is a powerful method for

estimating the ultimate strength of ship structure.

The earliest application of non-linear finite element method for estimating longitudinal

strength of ship structure is done by ABS[17]. Since then, with the development of

computer technology, many FEM software has been developed to perform non-linear

structural analysis for ultimate strength, such as ANSYS, ABAQUS etc. Usually, the

non-linear finite element analysis utilize a static solver for quasi-static analysis as well as

a convergence iterator which is usually arc-length method or Newton Raphson method[8].

If modeled and analyzed properly, the non-linear finite element method is believed to

be the most accurate way of assessing ultimate strength. Since most factors affecting

ultimate strength can be utilized and considered in non-linear finite element method, like

the progressive behavior, interaction between structural component, 3D effects, initial

imperfection, residual stress etc.

The main disadvantage of non-linear finite element analysis is its large computational

effort. But the advantage accompanied by the large effort is the high accuracy and the

good performance in assessing post buckling behavior. This problem could be solved

gradually with the development of the computer capacity. The numerical modeling

for non-linear finite element analysis performed for hull girder analysis often requires

a full-plate model, which is a time-consuming and laborious task. The reason for this

requirement is based on the consideration of including possible side deflection of stiffeners

for local buckling failure mode.

2.4 Method applied in this work

The present work aims to assess the longitudinal ultimate bending strength of ship

structure. Based on the 3D property of fast numerical model, 2 methods are selected

for assessing the longitudinal ultimate bending moment of the ship structure.

For ship structure like OT, FPSO, BC etc, the strength of deck structure is less than the

strength of bottom part. So under sagging condition, the deck structure buckles much


earlier than when the bottom structure reaches its yielding limit in tension. After that,

the deck structure enters its post buckling state until it can not resist anymore, which is

also the time when the ultimate strength of hull girder is reached. In this case, proper

assessing of post buckling behavior is very important in assessing the ultimate strength

of ship structure.

For container ship which is the example chosen for the application of this rapid numerical

method, it is characterized by its extrally strengthened deck structure, which is usually

strengthened with plates of large thickness. Because of this property, the deck structure

of container ship is more resistant against buckling. Correspondingly, the failure mecha-

nism of container ship under sagging could be different from the other ship types like Oil

tanker, Bulk carrier, FPSO, etc. It could be yielded to failure under sagging condition.

Thus, the elastic buckling theory and full plastic bending theory are adopted to find out

the failure mechanism of the container ship under sagging. Then the ultimate strength

of the container ship will be assessed by the fast numerical model by linear FEM.

While for the other ship structure mentioned above which do not have a strengthened

deck, the method of non-linear finite element analysis is adopted for assessing the post

buckling behavior of the deck structure of these ships. Because the fast numerical model

of the present work is a plate-beam element combination model, the non-linear finite

element analysis is also investigated in a plate-beam element combination model. This

method is validated with the full plate model as well as the result from ISSC2015 [8].

Chapter 3

Rapid geometric tool for

numerical modeling

3.1 Introduction

Although many researchers have been working on the topic of rapidly generating nu-

merical model for ship structure[18],[19]. However, most methods for rapid numerical

modeling currently are trying to work out a solution to utilize the AUTO CAD systems

for fast generating a numerical model. Thus 2D or 3D CAD drawings are required to

generate a numerical model for ship structure. However, in real situations of the emer-

gency response projects, the 2D drawings can often be old and can only be identified by

an engineer manually. There is rarely any 3D drawings available in emergency response

situations. An example of drawing from emergency response project is in figure 3.1 to

give an idea of how unclear the drawing can be.

Thus in order to make the present work more applicable to real emergency situations,

the drawing information obtained is assumed to fulfill the minimal needs: the drawings

can be scanned versions of 2D drawing and only identifiable for engineers manually.

Based on limited number of parameters identified by an engineer from the minimal

drawings information mentioned above from emergency response project, a mesh-able

ship structure can be generated quickly with the method from this present work.

In this chapter, firstly, the requirement of the numerical tool and the corresponding user

interface of this tool will be presented. Secondly, after analyzing the ship characteristic,

a method of rapidly generating ship structure will be presented.

17

Chapter 3. Rapid numerical ship geometry 18

Figure 3.1: Drawing example from emergency project

3.2 Rapid numerical tool

3.2.1 Requirement of numerical tool

Since the main purpose of this numerical tool is to serve emergency response, this tool

focuses on analyzing structural strength and the user-friendly property. The main con-

siderations are listed as follows:

Easy to use:

. The input file for parameters should be very easy to use, and the number of parameters

should be small enough to reduce the inputting time for an engineer in emergency

situation.

. The numerical software package based for this numerical tool should have wide users

in industry and it should be relatively cheap.

Based on the above consideration, the numerical package as Femap is selected for the

application of this numerical tool. Correspondingly, one possible user interface struc-

ture(figure 3.2) is proposed in the present work.

Ship geometry definition:


Figure 3.2: User interface structure of rapid numeric tool

. Ship hull form defined by users and variation with regarding to principle dimensions

from general arrangement plan.

. Ship internal structural arrangement defined by users and variation with regarding to

main dimensions from middle ship section.

. easy to be visualized by users.

. Modifiable for users after being generated.

3.2.2 User interface

A brief introduction of the user interface of this tool(see figure 3.3) will be included here.

Figure 3.3: Interface of rapid numerical tool


First, key parameters identified from GA plan and midship section drawing are put into

an EXCEL sheet. In this excel sheet, all the main parameters for generating ship hull

form as well as for internal layout are put in, which is a basic input for any following

operation. Second, a ship hull form needs to be generated parametrically in Rhino with

the help of grasshopper and then stored as step file. Third, the ship hull form file need

to be imported in femap. Finally, a fast numerical model can be generated in Femap.

This tool is created to rapidly generate a numerical model for container ship. The

method of fast numerical modeling of ship structure used in the tool can be further

extended to other types of ship structure. In the following part of this chapter, this

generic method will be presented based on ship structure’s characteristic.

To give the readers of how the tool works, a video has been recorded for the full process

of rapid numerical modeling with the tool. It was originally generated in 3 hours and

it has been cut into 3 minutes for presenting. The link to this video is listed in this

website: https://www.youtube.com/watch?v=BqmZfbSX7E4

3.3 Ship structure characteristic

In this present work, the ship type as container ship is selected to describe the method

of rapid numerical modeling. In the current time, there is a tendency for ship structure

of becoming large, especially for the container ship. Thus, the unpredictable structural

problem may arise together with the growth in ship size, like the famous case of “Mol

comfort” mentioned in the first paragraph. So, there is a growing demand for global

finite element analysis of ship structures to investigate the safety problem of these mega

marine structure. Based on this consideration, the present work selected container ship

for exploring the method of fast numerical modeling. The same method presented here

can be extended to other ship structures, like Oil tanker, Bulk carrier, FPSO etc.

3.3.1 General ship characteristic

A ship structure is characterized by its structural arrangement system, which is the

longitudinal frame system, transverse girder system and vertical stringer system(see

figure 3.4), which corresponds the three axises of a ship, X axis(longitudinal direction),

Y axis(transverse direction) and Z axis(vertical direction).

The longitudinal direction from aft to bow in ship offer a natural axis as X in Cartesian

coordinate. The longitudinal frame system in ship structure corresponds to locations of

the transverse bulkheads or web frames which locate along the longitudinal direction of

https://www.youtube.com/watch?v=BqmZfbSX7E4


the ship. Similarly, the girder system locates in the transverse direction(Y direction) of

ship while the stringer system locates in the vertical direction(Z direction).

In the present work, taking advantage of this natural characteristic of ship structural

arrangement system, a special data structure is designed to efficiently store the ship

geometrical information from available drawings in order to achieve the goal of fast

numerical modeling. The date structure will be described in the later part of this

chapter.

Figure 3.4: Frame system, girder system and stringer system[4]

3.3.2 Container ship characteristic

Container ship is designed for transporting containers, which have standardized dimen-

sions. A lot of structural components and their arrangement should be adjusted to

facilitate the containers stowage plan, like the girder spacing, the large hatch opening

and the corresponding strengthened deck structure.

3.3.2.1 General arrangement plan

The general arrangement of a post-panamax size container ship is included in figure 3.5.

Main particulars required for fast numerical modeling obtained from the GA plan are

listed as follows:

Length over all(LOA)

Length between perpendiculars(LPP)

Breadth

Depth


Draught

Service speed

Bulkhead spacing

Frame spacing

Figure 3.5: General arrangement plan

3.3.2.2 Midship section

One midship section drawing for a post-panamax container ship is included in figure 3.6.

A container ship midship section is characterized by its large opening, which reduces it

torsional rigidity. The locations of longitudinal stringers are defined by arrangement of

below deck containers as well as hatch opening size. The side walls are normally 2 to

2.5 m width[20]. The location of longitudinal girders are defined based on the above

containers spacing. So, the main structural components locations required as pre-input

obtained from the midship section drawing are listed as follows:

Stinger locations

Girder locations

Double bottom height

Side wall width

Deck height

Hatch coming size

Stiffeners spacing

The corresponding scantling information to the above listed items can also be obtained

from the midship section drawing.


Figure 3.6: Midship cross section drawing

3.3.2.3 Transverse bulkhead

Transverse bulkhead in container ships are used to support double bottoms as well as

the side structure. Not every bulkhead structure in container ships is required to be

watertight. A usual plan for the watertight bulkhead structure is by making every other

bulkhead a watertight one. Both watertight and non-watertight bulkhead are designed

as grillage structure to fit the arrangement of containers below deck. For watertight

bulkhead, one transverse side of the bulkhead structure is water tightened with plating.

For non-watertight bulkhead, the lower part of the non watertight is required to be

strengthened by plating.

3.4 Rapid ship hull form generating

Ship hull form is characterized by its curvy surface due to the consideration of hydro-

mechanic performance. Thus in FE modeling for ship structure, one laborious and

time-consuming part is from the ship hull form surface. In the present work, instead

of traditional, laborious ways of modeling ship hull form surface by inputting a lot of

points, NURBS(Non-uniform rational B-spline)[21] are incorporated to construct the

ship hull form surface for the purpose of “rapid” as well as parametric-able with the

main particulars from midship drawing and GA plan.


Figure 3.7: Non-watertight bulkhead Figure 3.8: Watertight bulkhead

3.4.1 Characteristic of NURBS

A spline curve is a linear combination of B-spline basis functions with control points as

the coefficients[21].

C(u) = [X(u), Y (u)] =n∑i=0

ViNki (u) (3.1)

where:

Nki (u) = B-spline function of degree of k

Vi = (Xi, Yi),i = 1, 2, 3...n

While the rational spline is weighted spline curve:

C(u) =

∑ni=0 ωiViN

ki (u)∑n

i=0 ωiNki (u)

(3.2)

where:

ωi = the ith weight

So the corresponding spline surface is:

S(u,w) =

n∑i=0

m∑j=0

Vi,jNpi (u)N q

i (w) (3.3)


Table 3.1: Control parameters from GA plan and midship section drawing

Name Value

Length overall(m) 300Beam on deck(m) 40

Depth(m) 24.2Bilge radius(m) 5

where:

Npi (u), N q

i (w) = B-spline function

Vi,j = (Xij , Yij , Zij),i = 1, 2, 3...n

Like the rational curve, the rational spline surface is the weighted spline surface.

3.4.2 Control parameters selecting

Based on the available information from GA plan and midship section drawing, some

main parameters(see 3.1) are chosen to construct the ship hull form.

3.4.3 Ship hull form constructing

The construction of ship hull form is based on the software of Rhino, which is both

economical and widely used in marine and offshore industry. In order to make the whole

process parametric, the programming interface(Grasshopper) in Rhino is selected to

achieve the goal. Based on the open work from “rhinocenter”[22], the ship hull form is

divided into 3 parts during the construction process: the fore part, the middle part and

the aft part. Because the longitudinal ultimate strength is closely related to the middle

part of the ship structure, more parameters are adopted to define the middle ship part

in order to be relatively more accurate.

Based on the main parameters(see table 3.1) obtained, first characteristic points are con-

structed, which are directly controlled by main input parameters. After the generating

of characteristic points(see figure 3.9), the characteristic curves(see figure 3.9) are gen-

erated from the characteristic points based on B-spline method. From the characteristic

curves, the ship hull form(see figure 3.10) can be constructed by NURBS method.


Figure 3.9: Characteristic points and curves of ship hull form

Figure 3.10: Ship hull form

3.5 Rapid inside structural layout generating

Based on the parameters identified from drawings, a rapid numerical model will be

generated in FE environment. The whole process is seen in figure 3.11: Firstly, after the

rapid ship hull form based on NURBS is generated, it will be further incorporated into

FE environment as boundary surface for structural component generating automatically.

Secondly, the very topological parameters directly related with information obtained

form emergency drawing will be implanted as “seeds” in FE environment. Thirdly,

characteristic points will be grown from the “seeds” automatically, in which the points

storing algorithm is developed in this present work for rapid interactive use. This process

is called “growing”. Fourthly, based on the characteristic points, geometric lines will be

generated in FE environment, in which the “finding neighbor algorithm” is developed

in this present work for rapid generating lines in FE environment. Finally, based on

the lines generated, the surfaces will be generated automatically with “hand in hand”


algorithm developed in the present work, thus a numerical model for ships structure

is completed. In the present work, FEMAP[23] is selected as the FE environment for

implementation of this method based on its economic advantage over other similar FE

packages.

Figure 3.11: Process diagram of rapid numerical tool

3.5.1 Parametric seeds

The so called parametric seeds are a representation of the critical structural parameters

identified from the drawings available from rapid emergency response. The identification

of critical parameters from the drawings is a balance between accuracy and time saving.

Generally speaking, more parameters means more accurate while more time-consuming

for an engineer during the identification of the drawing, which is very precious in rapid

emergency project.

3.5.1.1 Identification of critical parameters

Based on the drawings, the critical parameters selected in this present work are bulkhead

location, bulkhead width, frame spacing, double bottom height, the side shell width,

girder location, the stringer location, deck height, the hatch coaming height.

3.5.1.2 Working principle of parametric seeds

The parametric seeds are the very topological parameters for the rapid numerical model,

which are also directly controlled by the user through the interface as EXCEL. In figure


3.12, the working principle of parametric seeds is indicated. Once the user updates

the information through the interface, the parametric seeds will directly feel it and

send an event change information to the points for updating and all following objects

to update correspondingly. In this way, the generating procedure of points and lines

are independent of directly parameter inputting by users, instead they are generated

automatically in a rapid way.

Figure 3.12: Working principle of parametric seeds

This design of parametric seeds as topological parameters gives an obvious advantage

to this rapid numerical tool in the present work. As can be seen from figure 3.13, each

parametric seed locates a distance from the origin (the aft bottom end of the ship) in

the central plane of the ship structure. Each seed controls a certain section across the

ship structure. For example, each bulkhead seed along the X axis represent a bulkhead

section of the ship. From these parametric seeds, the sections are constructed. In this

way, the whole construction of a numerical model is parametric-able. One update in

the parametric seed will lead to associative updates of the all the corresponding sections

and thus the whole structure.

Figure 3.13: Parametric seeds for the rapid numerical tool


Figure 3.14: Midship section charac-teristic points

Figure 3.15: Bulkhead characteristicpoints

3.5.2 Points structure

It is a ship’s characteristic that along its longitudinal direction from aft to fore part, the

inside structural layout does not vary a lot. Midship section and bulkhead propagates

through the ship hull form with the hull as boundary limit. This inherent characteristic of

ship structure simplifies the whole process of rapid numerical modeling of ship structure.

In the present work, the midship section and the corresponding bulkhead are selected to

propagate through the ship hull form. The corresponding characteristic points directly

linked with main parameters identified from the drawing are in figure 3.14, 3.15. The

inside structural characteristic points will be adjusted regarding to the change in ship

hull form.

Based on parametric “seeds” embedded in the ships, the characteristic points will be

“grown” automatically from them. Since in the later part of the automatic line generat-

ing and surface generating are based on the foundation as points, information from these

points are very important and needed to be frequently exchanged in the whole process

of rapid numerical modeling. Thus building a proper algorithm to store the point infor-

mation for exchanging is very critical for the purpose of “rapid”. In the present work, a

point storing algorithm is developed and suggested here.

3.5.2.1 Points storing algorithm

A point in ship is a 3D object carrying information in X, Y, Z coordinates with regarding

to the origin. Normally when creating the point in FE environment, it is often stored

as a 1D array [x,y,z], which is very low-efficient to exchange the information from them


because only the location information can be used to identify them. Instead of this, in

the present work the points are categorized into 3 planes: the longitudinal plane, the

transverse plane and the vertical plane. A 4 dimension array(figure 3.16) for storing the

points in the rapid numerical tool is created for rapid exchanging purpose. As can be

seen from figure 3.16, all the information stored in this 4-dimension array are directly

linked with the parametric seeds.

Figure 3.16: Point storing structure for the rapid numerical tool

This point storing algorithm gives a great benefit to the rapid numerical method. In this

way, each point “knows” where it is located in the whole ship based on the ID in 2nd,

3nd, 4th array carrying in itself. Points are generated directly based on their frame ID,

girder ID and stringer ID instead of by inputting coordinates directly. This structure

also makes it possible for the implementation of “finding neighbor” algorithm and “hand

in hand” algorithm for the lines generating and surface generating based on their IDs in

3 directions. If any change event information is sent from parametric seeds, the points

will respond rapidly and transfer the change event information downward to lines and

surfaces(figure 3.17).

Figure 3.17: Points generated based on the storing algorithm


3.5.3 Line generation by neighboring

Now, the characteristic points for all structural components are inside the ship hull

form. What is needed is to connect the lines in an automatic while wise way, which

means the lines can be only created in between two neighboring points. Any connecting

points in a diagonal way(unless in specifically defined part like in the hopper part of a

ship) or directly connecting the third point is not allowed. A correct and a wrong way

of connecting in between neighbor points is shown in the left and right part of figure

3.18. Based on this idea, an algorithm of “finding neighboring algorithm” for generating

curves in a systematic way is developed and suggested in the present work.

Figure 3.18: Correct and wrong way of neighboring points

3.5.3.1 “Finding neighbor” algorithm for line generating

After the “point storing” algorithm has been defined previously, in the 3D space of a

ship, each point has neighbor points in three directions(X,Y and Z), except the points in

the boundary. So based on this characteristic of points, first the points are categorized

in 3 directions: longitudinal direction, transverse direction and vertical direction. With

the predefined points storing structure(figure 3.16), the categorizing of the points can be

easily done by ID information carried by themselves. The “finding neighbor” algorithm

along X direction in between frames is explained in figure 3.19, similar algorithm can be

used for generating curves in Y direction and Z direction, which will not be described

here.

The idea for this proposed curve generating algorithm is to make lines until the y, z

location information are matched(ensuring no diagonal connection) for 2 points in the

neighbor frames. The working principle for this algorithm is: A point Pt(N) in Frame K

is firstly selected, then sequential searching through all the points in Frame K+1 is

carried out until matched and the corresponding curve is created; then Pt(N+1) in

Frame K is selected...until all the points in Frame K have been done this process, which

means the curves from Frame K have been created and thus a new “finding neighbor”

process in between Frame K+1 and Frame K+2 is continued...


Figure 3.19: Pseudocode for “find neighbor” algorithm for generating curves in X

This way of creating curves turns out to be robust, simple and rapid, it ensures no

duplicate curves are generated. An example of automatically generating curve in FE

environment by using this algorithm is in figure 3.20, during this state, the rapid curve

generating has finished in the X direction(longitudinal direction) while the curve gener-

ating process is propagating in Y direction(transverse direction).

Figure 3.20: Example of rapid curve generating

3.5.4 Plate generation by propagation

With all the lines for the internal structural component generated(figure 3.21), the goal

now is to create the surface out of these curves in a systematical and organized way.

The surface to be created should be non-singular, mesh-able while stable in a fast way

of being generated. Based on this idea, “hand in hand algorithm” for rapid generating

surface is developed and suggested in the present work.


Figure 3.21: Rapid curve generating

3.5.4.1 “Hand in hand” algorithm for plate generating

The propagation for surface generating is also performed in 3 directions: the longitudi-

nal direction, the transverse direction and the vertical direction. Different from curves,

a panel in a ship structure is made of four curves in 2 directions. Take the horizon-

tal surface for example, a horizontal panel is normally made up out of 2 curves in x

direction while the other 2 curves are in y direction. Thus, before generating the sur-

face, a categorization of curves need to be made based on the ID carried by their end

points. For horizontal plate generating, all the curves on horizontal plane are categorized

into 2 groups. The first group is in Y direction along the frames: Curve Y frame N,

Curve Y frame N+1,Curve Y frame N+2 ... the other group is in x direction in between

every 2 frames and categorized by its starting frame: Curve X frame N, Curve X frame N+1,

Curve X frame N+2 ... The “hand in hand” algorithm(figure 3.22) will be explained in

X direction, the same method can be applied for transverse vertical plate and longitu-

dinal vertical plate generating, which will not be described here.

Figure 3.22: Pseudocode for “hand in hand” algorithm for generating surfaces in X


The idea of this surface generating algorithm is to make a sequential search among lines

in 2 neighboring frames and lines in between these 2 two neighbor frames until matching

information(3 points in 3 lines or 4 points in 4 lines) is reached. The working princi-

ple is this, first, select Curve Y N from Frame K, second, sequential searching Curves

Curve X N’, Curve X N’+i from Curves in between the two frames until matched infor-

mation found(Only 3 points in 3 lines), third, sequential searching Curves Curve Y N”

from Frame K+1 until matched information found(Only 4 points in 4 lines), last gener-

ate a new surface... go to the next frame Frame K+1 and Frame K+2 and in between.

This way of generating curves turns out to be rapid, robust and no duplicate lines. An

example of the process of generating surface is in figure 3.23, when the surface generating

is being performed in X direction by propagation.

Figure 3.23: Rapidly generating surface in X direction

3.5.5 Stiffeners

The generating of stiffener is very simple, stiffeners are just lines in the surface, which

can be incorporated in the process of line generating. But the stiffener spacing is rec-

ommended by incorporating ship design rules instead of directly identifying from the

drawing, which is very unhandy and time-consuming when in rapid emergency project.

The stiffener spacing can be calculated based on the plate thickness, while the plate

thickness can be calculated based on the lateral pressure and global section modulus re-

quirement from the rules. By using these values directly linked from the rules and then

incorporate them into this rapid tool, the rapid numerical tool will serve the emergency

response projects better. But in the present work, it was not performed for the consid-

eration of the author’s company’s interest, to make the tool more open for other types


of projects. So here in the present work, the stiffener generating is done by projecting

lines onto the surface, which takes less than 1 hour.

3.6 Conclusion

In this section, based on the ship structure’s characteristic, a method of rapid numerical

modeling for ship structures is presented here. This method is applied in the case of

container ship. With the limited information available from emergency situation, a fast

numerical model for global structural analysis can be parametrically generated within 3

hours. Compared with the manually generating FE model, this method will save a lot

of time, and thus it can support emergency engineering work.

A global data structure by incorporating design of “parametric seeds” for parametrically

generating rapid numerical model is developed in this method. A point storing algo-

rithm for efficiently storing the geometric information from available drawings. This

point storing algorithm is also the foundation of the “finding neighbor” curve generat-

ing algorithm and “hand in hand” surface generating algorithm, which are developed

in this thesis. These algorithms are developed based on the general ship characteristic.

Thus it can be further extended to be applied in other ship structures.

Chapter 4

Longitudinal ultimate bending

strength of container ship

4.1 Introduction

Before using the rapid numerical model for structural analysis, the rapid numerical

model will be verified first. After verification, this rapid numerical model will be used

for assessing longitudinal ultimate bending strength of container ship.

For container ship, it is characterized by its large opening and corresponding extrally

strengthened deck structure, which makes it different from the other ship structure

whose double bottom structure is much stronger than deck structure. This characteristic

of deck structure make the container ship is more buckling resistant under sagging

condition. And if the deck plate of the container ship is so stocky because of large

thickness, the container ship could not buckle in sagging condition. In this case, the

container ship will yield into its ultimate state under sagging, thus the ultimate strength

of the container ship can be estimated by linear FEM instead of the complex Non-linear

FEM.

Out of this consideration, before assessing the ultimate strength of container ship under

sagging, the failure mechanism of the container ship under sagging will be investigated.

The elastic buckling bending moment and the full plastic bending moment of the con-

tainer ship will be compared first. Because the full plastic bending moment is already

an overestimation of the ultimate bending strength, if the elastic buckling bending mo-

ment of container ship is even bigger than the full plastic bending moment. This means

the elastic buckling bending moment is just an “virtual” bending moment for container

ships with very stocky deck panels. In this case, the container ship will not buckle before

36

Chapter 4. Longitudinal ultimate bending strength of container ship 37

Table 4.1: Main particulars of the container ship(m)

LOA LPP Breadth(MLD) Depth(MLD) Draft(Design) Draft(Scant)

300 286.56 40 24.2 12 14.5

yielding in sagging condition, instead it will in-elastically yield into failure. Thus the

ultimate bending strength can be assessed by linear FEM. if not, more investigation is

needed to find out the failure mechanism.

So, this failure mechanism of container ship in sagging condition will be investigated

by comparing global buckling bending strength and full plastic bending moment. If the

container ship yields into ultimate state in sagging condition, the longitudinal ultimate

strength of container ship in sagging will be assessed by the validated fast numerical

model by linear FEM.

4.2 Vessel particulars

As described in the last chapter, the tool is applied in the case of container ship. The

main particulars of this container vessel are given in table 4.1. The cross section of

this container ship is shown in figure 4.1. The typical bulkhead structures are given

in figure 3.8, 3.7. Both bottom and side shell structures are double skin. The ship

is longitudinally stiffened with angle-bar stiffeners as well as flat-bar stiffeners. As a

container ship, the hatch coaming as well as the deck structure are strengthened with

very thick plates of about 60mm. The transverse web frame spacing is 3150mm, while

3 web frames are fitted in between every 2 bulkheads.

4.3 Elastic buckling strength of container ship

4.3.1 Material model

The ship is built mainly by using the high tensile strength steel of grade AH32 and

mild steel of grade A, while for the hatch coaming and deck structure, the extra tensile

strengthened steel of AH36 is used. The distribution of the steel over the cross section

can be seen in figure 4.1 For stress distribution checking and elastic buckling, a linear

material model is used for the steel in this model, which is normally used during the

elastic analysis in offshore and maritime industry. The Young’s modulus selected for

steel used in this ship model is 210Mpa, while the Possion ratio selected for the steel is

0.3.


Figure 4.1: Midship cross section drawing

Table 4.2: Material property in container ship

Steel grade Yielding limit(Mpa) Young’s modulus(Mpa) Poisson ratio

A 235 210000 0.3AH32 315 210000 0.3AH36 355 210000 0.3

4.3.2 Element type and size

Since this numerical model is directly generated by fast numerical tool, so plate ele-

ment(CQUAD4) is used for modeling the ship hull form, deck, side shell, double bot-

tom... CQUAD4 is a four-node element which is suited to model moderately-thick

structures like marine structures. This element has 6 degrees of freedom at each node:

X,Y,Z translations and rotations regarding to X,Y,Z axis. The beam element(CBEAM)

is used to model the longitudinal stiffeners, stiffeners on web frames and stiffeners on

bulkhead, with the purpose to reduce the calculation effort in the global model. For the


global finite element analysis of finite element model, the beam element for modeling

stiffeners is easier to apply and the accuracy is acceptable.

4.3.3 Boundary conditions

For global structural analysis of container ship, at least 2 cargo holds model is required

because of its large opening. In the present work, models for 1 cargo hold, 2 cargo

holds(1+1/2+1/2) and 3 cargo holds are compared for elastic buckling analysis to find

the effect of boundary conditions.

In order to take the advantage of symmetrical characteristic of load, boundary condition

and geometry, symmetry boundary condition is applied in the center plane(XZ plane).

The most critical part for boundary condition setting is in the aft and fore end where

bending load is applied. In order to simulate the constant moment loading over the

ship structure in the longitudinal direction, both ends are coupled with reference nodes

by a rigid element in all 6 degrees of freedom. The reference nodes are located at the

intersection of center-line and neutral axis. One pair of bending moments in the opposite

direction regarding to Y axis is applied on the reference nodes. Both ends are simply

supported, with translations in the Y and Z directions constrained. For the reason of

the symmetry boundary condition in the center plane, rotation of the reference node in

the end plane is not allowed to rotate around the Z axis.

Figure 4.2: Boundary condition


Figure 4.3: Frame cross section stressdistribution of one cargo model

Figure 4.4: Frame cross section stressdistribution of one cargo model

4.3.4 Stress distribution

Before going to the buckling analysis, the numerical model must be checked and verified.

Firstly, the nodes should be connected which can be checked by free edge, secondly,

there should be no coincident nodes in the numerical model, thirdly, there should be no

coincident elements in the numerical model.

After these checking procedure, the numerical model must be checked and verified with

the normal stress distribution first. So x axis normal stress distribution over the cross

section under a linear load is checked first. To simulate the sagging condition, a pair

of bending moment of 1GN.m about the Y axis is applied through the reference points

at both ends of this model. The stress distribution for the 3 models are compared with

each other in the midship cargo part.

As indicated in figure 4.3, under sagging condition, the deck is under compression while

the bottom is in tension. From the deck structure to bottom structure, the stress is

changing from compression to tension linearly, with a neutral axis in between these two

parts. This stress distribution has long been accepted as the normal way for the stress

distribution over the ship section under sagging condition.

The same load is applied to the 2 cargo holds model as well as the 3 cargo holds model

with the same boundary condition. The corresponding stress distribution over the mid-

cargo of these 2 models can be seen in figure 4.5 and figure 4.7. Similar to the 1 cargo

model, the normal linear stress distribution over the cross section can also be found in

the both of these 2 models.


Figure 4.5: Stress distribution over themid-cargo of the 2 cargo holds model

Figure 4.6: Stress distribution over themid-cargo of 2 cargo holds model

By comparison among these three models(figure 4.3, 4.5, 4.7), stress level in 2 cargo

hold model is similar to the stress level in 3 cargo model, while the stress level in 1 cargo

hold model is higher than the other 2 models. This is because of the boundary effect.

For 2 cargo hold model and 3 cargo hold model, the boundary condition is applied in

the neighbor cargoes, which will has little effect on the middle cargo. While for the one

cargo model, the boundary condition is added directly in the middle cargo, thus it will

have a big influence on the stress level of the middle cargo.

By linear stress distribution check, all three models are proven to have the correct linear

stress distribution under sagging condition. The stress level of the one cargo model will

get affected by the boundary significantly. While 2 cargo hold model and three cargo

hold model agrees well with each other. Thus further buckling analysis and ultimate

strength assessment can be performed based on the 2 cargo model.

4.3.5 Elastic buckling moment under sagging condition

The euler buckling analysis in NX-Nastran is based on the Euler buckling theory.

(K +KG)δ = F (4.1)

where:

KG = Geometrical stiffness matrix caused by loading


Figure 4.7: Stress distribution over mid-cargo of the 3 cargo holds model

Figure 4.8: Stress distribution over mid-cargo of the 3 cargo holds model

The critical condition will be achieved when deflection increases while load does not,

which is the condition the critical load vector can be accessed:

(K + λKG0)δi = 0 (4.2)

where:

λ = critical parameter

δi = the ith deflection increment

KG0 = Geometrical stiffness matrix caused by initial arbitrary load

Thus:

KG = λKG0, F = λF0 (4.3)

where:

F0 = initial arbitrary load

So based on this, corresponding bifurcation buckling shape are calculated for these three

models(figure 4.10,4.12, 4.14). The elastic buckling moments under sagging condition

are listed in table 4.3. Based on table 4.3, there is not much difference between the 2

cargo holds model and the 3 cargo holds model, while there is significant increase in

elastic buckling moment in one cargo hold model. The main reason is probably because

of the boundary. If only 1 cargo hold is modeled, the boundary effect will affect the

result significantly. This phenomenon can also be explained by the general decreasing


Table 4.3: elastic buckling moment of container ship(GN.m)

Model One cargo hold 2 cargo holds 3 cargo holds

bending moment 15.37 13.83 13.73

trend of elastic bending moment as more cargo holds are modeled. Thus for global

analysis, it is not recommended to use one cargo hold model for analyzing.

Figure 4.9: Buckling shape of 1 cargo model

4.4 Full plastic bending strength of container ship

In the present work, the full plastic bending moment is calculated to give a rough

estimation of the capacity of the ship hull cross section. The full plastic bending moment

Figure 4.10: Before buckling(1 cargomodel)

Figure 4.11: After buckling(1 cargomodel)






will give an overestimation of the ultimate bending moment, since it assumes the overall

cross section reaches yielding limit. The x axis stress distribution over the hull cross

section in full plastic state can be seen in figure 4.16.

Figure 4.16: Full plastic stress distribution over hull cross section

In pure bending under sagging condition, the following stress distribution rule should

be fulfilled based on the force balance:∫σxidAi = 0 (4.4)


where:

σxi = x axis stress of the ith structural component of the hull section

Ai = Area of the ith structural component of the hull section

Based on 4.4, the neutral axis for the full plastic section is calculated based on the

following formula:

Gp =

∑Aiσyizi∑Aiσyi

(4.5)

where:

σyi = yielding stress of the ith structural component of the hull section

The distribution of Aiσyi for the structural components over the height can be seen in

figure 4.17

Figure 4.17: Aiσyi distribution over the height

The corresponding neutral axis: Gp = 12.702 m.


Table 4.4: Elastic buckling and full plastic bending moment of container ship(GN.m)

name 2 cargo holds 3 cargo holds full plastic


Thus, the full plastic bending moment of the ship hull cross-section is calculated as

follows:

Mp =∑

Aiσyi |zi −Gp| (4.6)

Based on this, the full plastic bending moment of the ship hull cross-section is calculated

and presented in table 4.4

4.4.1 Failure mechanism of container ship under sagging

Based on the comparison between the elastic buckling bending moment and full plastic

bending moment(see table 4.4), it can be seen that the elastic bending moment is much

larger than the full plastic bending moment. Also, as can be seen from the figure 4.18,

when global buckling bending moment(13.8 GN.m) applied to the container structure,

the stress level of container ship deck plate has far surpassed the yielding limit.

Figure 4.18: Stress distribution under buckling bending moment(linear FEM)

This can be explained based on the critical stress variation for columns with different

slenderness ratio(figure 4.19). When column’s slenderness ratio is relatively small, the


Table 4.5: Plate Slenderness ratio of deck part of container ship

b/t Deck plate Top side plate Class 1 limit

value 16.36 25.45 26.73

material failure will occur inelastically after passing the yielding limit. In this case, the

critical buckling stress will be bigger than the yielding stress, and this buckling will

never happen since the structure yields into failure.

For container ship which is designed with extrally strengthened deck structure, the

slenderness ratio of its deck structure is very small. The deck structure is very buckling

resistant because the deck panels of the container ship are very stocky with big plate

thickness. Thus the very large elastic buckling bending moment calculated for container

ship is a “virtual” bending moment in sagging condition. Since the container ship will

yield into failure and it will never buckle in sagging.

As can be seen from table 4.5, the slenderness ratio(SR) of deck plate(s/t) of container

ship is smaller than the limit SR for class 1 from Eurocode 3[24]. Class 1 limit SR is the

lowest SR limit classified by Eurocode 3. Plate with SR below class 1 SR will yield into

failure. So the deck plate of the container ship is very stocky and will yield into failure

instead of buckle first.

Figure 4.19: Critical stress variation for columns of different slenderness ratio[5]

So, because of the property of container ship which are design with stocky deck plate,

the deck structure of container is buckling resistant and will yield into failure under

compression. Thus under sagging condition, the container ship yielded to failure. When

the deck structure reaches its yielding limit, the container ship reaches its ultimate state

under sagging condition. Based on this finding, ultimate bending moment can be found


Table 4.6: Ultimate bending moment of container ship under sagging(GN.m)

name elastic buckling full plastic ultimate


by applying load to the numerical model gradually until the the deck structure reaches

its yielding limit by using linear FEM.

4.5 Ultimate bending strength of container ship

Since the ultimate state under sagging condition has been found, by using the linear FE

model, bending moments are applied to the reference points of both ends gradually to

find the ultimate bending moment when the deck structure yields. The ultimate state

of the container ship can be found in figure 4.20, when the hatch coming reaches its

yielding limit(355Mpa). So the corresponding ultimate bending moment applied can be

seen in table 4.6 , which is 6.6 GN.m. This is the ultimate bending moment captured

by linear FEM.

Figure 4.20: Ultimate bending moment of container ship


4.6 Conclusion

In this chapter, the container ship generated by fast numerical tool is verified in stress

distribution. Based on the verified model, the elastic buckling moment is calculated

and is found to be bigger than the full plastic bending moment. It is because that the

container ship is designed with extrally strengthened deck structure, thus the container

ship equipped with stocky deck panels will yielding into failure in sagging instead of

buckling first. When reaching its ultimate state in sagging, the deck structure is close

to its yielding limit. Based on this failure mechanism of container ship, the ultimate

strength of container ship structure can be assessed in the validated rapid numerical

model by linear FEM by capturing the yielding bending moment.

Chapter 5

Ultimate strength of ship box

girder under pure bending

5.1 Introduction

Because of extrally strengthened deck structure, the deck part of container ship is more

buckling resistant. When reaching its ultimate state, the deck structure of the container

ship is very close to its yielding limit. Thus the ultimate bending moment of container

ship can be assessed as elastic yielding moment and calculated by linear FEM.

While for the other types of ship structure like OT, BC, FPSO etc, they are not designed

with extrally strengthened deck structure. So before entering its ultimate state under

sagging, the deck prat of these ship structure will buckle first. Thus it is very important

to analyze its post-buckling behavior in order to assess its ultimate bending strength

properly. So non-linear finite element method is adopted for assessing its post buckling

behavior.

The analysis of post-buckling behavior by NLFEM of is a complex process and remains

many unknowns, so it is important to have an experiment result to validate the NLFEM.

However, currently not many collapse tests have been carried out for hull girder collapse

analysis , probably because of high expense and time involved in these kind of exper-

iments. Especially for an actual ship, there is rarely any experiment carried out for

collapse analysis. The one full ship collapse test could be found is one experiment test

carried out by British navy, but that test was on a 1/3 of a frigate.

However, there were some box girder tests for collapse analysis carried out. Although

these tests were not scaled from the actual ship, the size of these box girders were mostly

dependent on the test machine capacity and slenderness ratio. These tests had provided

50

Chapter 5. Ultimate strength of ship box girder under pure bending 51

Table 5.1: Geometric dimensions of the box girder[6]

Model L(mm) b(mm) t(mm) h(mm) th(mm) Section area(mm2)

H200 1000 150 4 20 4 680H300 1100 150 4 20 4 680H400 1400 150 4 20 4 680

useful data for ultimate hull girder strength analysis. Reckling, Ostapenko, Nishihara,

and Mansour had carried out different tests on box girders for different purposes. In

2009, Gordo[6] performed a series of tests on box girders under pure bending. In ISSC

2015[8], benchmark study on ultimate strength of this box girder was carried out by

participants from 9 parties in order to demonstrate the degree of uncertainty in ultimate

strength analysis by NLFEM.

Based on this consideration, for other types of ship structures which have less strong deck

structure, assessing the ultimate bending strength by nonlinear finite element method

is performed on a box girder, which is the same as the one in Gordo’s experiment test.

Firstly, a full-plate element model is analyzed by NLFEM to find out the main failure

mode. Secondly, based on the collapse mode and also in coherence with the characteristic

of fast numerical model, a simplified NLFEM is investigated in plate-beam combination

model and compared.

5.2 Description of box girder for experiment

5.2.1 Model parameters

Three box girders made of high strength steel with different frame spacing is tested

in Gordo’s experiment. To reflect the collapse behavior under pure bending, the box

girders are tested by 4-point bending rig. The experiment setting up and corresponding

geometry sketch is shown in figure 5.1, figure 5.2 and figure 5.3.

The geometric size of this box girder is mainly designed based on the test machine

capacity. The geometric dimension of cross section for each model is the same, with the

size of 800 X 600mm. All box girders are stiffened with bar stiffeners with the same size

of 20 X 4mm. The transverse frames for all three box girders are “L” shape stiffeners

with the size of 50 X 28 X 6mm. The frame spacing of three box girders varies from

200mm to 400mm. The main geometric dimension of this box girder are presented in

table 5.1 while the related geometrical parameters is in table 5.2.


Figure 5.1: Experimental test setting on box girder[6]

Figure 5.2: Sketch of box girder[6]

Figure 5.3: Cross section of box girder[6]


Table 5.2: Geometric parameters of the box girder[6]

Model b/t β(plate slenderness ratio) λ(column slenderness ratio)

H200 37.5 2.2 0.97H300 37.5 2.2 1.45H400 37.5 2.2 1.93

5.3 Shell element model for box girder

Before a simplified NLFEM is adopted, a detailed numerical model of box girder made

up with shell181 in ansys is built for the purpose of finding out the main collapse mode

as well as comparison with simplified NLFEM. In this model, all plates, columns and

stiffeners are modeled by shell elements.

5.3.1 Element type

In analyzing the post-buckling strength of box girder, large deflection behavior of box

girder are often involved. So shell181, a four-node element with six degrees of freedom

at each node: translations in x, y, z axis and rotations about x,y,z axis, is suitable for

analyzing thin to moderately-thick shell structure like marine structure. Shell181 fits

linear, large rotation, and/or large strain nonlinear applications. In the element domain,

both full and reduced integration schemes are supported.

5.3.2 Material property

In the project of box girder by Gordo, high tensile steel HTS690 is used in the exper-

iment test. The detailed material data is attached in the appendix of this report. In

this non-linear finite element analysis, a bilinear material model is used: E=210GPA,

σ0 = 732MPa, Eh = 0.01 ∗ E.

ε =

σE : σ≤σ0σ0E + σ−σ0

Eh: σ>σ0

(5.1)

where:


ε = strain

σ = stress

σ0 = yield strength

E = Young’s modulus

Eh = strain harding ratio

5.3.3 Boundary condition

To simulate the pure bending longitudinal bending, the boundary condition is setting

as: one end is fixed in translations and rotation in x, y, z axis, while the other end

is constrained to a reference node, incremental load is applied through the reference

node(figure5.4). In this work, instead of load control, displacement control is applied

for the consideration of better convergence capability. Incremental rotation is applied

on the reference node, the relevant curvature and rotation is also obtained directly from

the reference node for ultimate bending moment.

Figure 5.4: Boundary condition

5.3.4 Initial imperfection

Welding is widely used during the fabrication process of ship structure, the corresponding

welding induced initial imperfection in ship structure will have a negative influence on

the stiffness and strength of the plates, and thus reduce the ultimate strength of ship

structure. So the initial imperfection of the ship structure should be taken into account

in this work. To give an idea of what is like of welding induced initial imperfection, one

example of the initial imperfection in steel structure is shown in figure 5.5.


Figure 5.5: Example of fabrication induced initial imperfection of steel structure[7]

Various researchers have investigated the welding-induced initial imperfection by exper-

iment measurement and proposed several empirical formulas based on the experiment

data. For practical application purpose, the initial deflection is assumed to be similar to

the buckling shape, which can be approximately expressed in the following mathematical

form:

ω = ωa·sin(πx

L) (5.2)

where:

ω = initial deflection

ωa = initial deflection amplitude

x = location with regarding to one end

L = length between supports

5.3.4.1 Description of initial imperfection

The welding induced initial deflection is considered to be the combination of three dif-

ferent initial deflection: plate initial deflection, stiffener initial deflection and column

initial deflection. In this work, the initial imperfection shape has been chosen to be

relatively conservative as well as to keep it consistent with the ISSC2015 [8] to validate

the model in this work. This amplitude and shape of initial deflection has been agreed

in ISSC2015 benchmark study[8] in order to be in the “average” deflection level[25] for

typical marine or offshore structures.


5.3.4.1.1 Plate deflection

The plate initial deflection shape long the longitudinal centreplane of the box girder is

shown in figure 5.6. And the amplitude direction of the plate initial deflection alternates

between neighbor plates(see figure 5.7).

Figure 5.6: plate initial deflection shape[8]

The initial plate deflection in the x direction has been chosen as: a double mode as a

combination of one and three half-waves, with the one half-wave as the main contributing

mode for the consideration of conservativeness. While the initial plate deflection in the y

direction has been chosen as one half-wave (figure 5.7). The mathematical representation

of the plate initial deflection is:

ωplate = ωaplate ·(0.8 sin(πx

a) + 0.2 sin(

πmx

a)) sin(

πy

b) (5.3)

where:

ωplate = plate deflection at a given coordinate position from a plate corner

ωaplate = 0.4mm, maximum initial deflection of plate

m = 3, half-wave numbers in the x direction

a = plate length

b = plate width


Figure 5.7: Plate initial deflection

Figure 5.8: Stiffener side deflec-tion(coupled with plate)[8]

Figure 5.9: Stiffener side deflec-tion(coupled with column)[8]

5.3.4.1.2 Stiffener deflection

Based on previous research work[26], there are mainly two kinds of initial deflection(figure

5.8, 5.9) related to stiffeners. The first one is the side way deflection, which describes the

“tilting” behavior of stiffeners from the idealized vertical direction. It may be coupled

with plate initial deflection(figure 5.8) or global column initial deflection(figure 5.9).

However, not much difference in ultimate strength will be between these two different

considerations of side way stiffener initial deflection. In this project, the stiffener side way

deflection will be coupled with plate initial deflection(figure 5.10). The corresponding

mathematical representation will be:

ωstiffener =ωplatehweb

·sin(πx

a)ωasti (5.4)

where:

ωstiffener = stiffener side deflection at a given position from a stiffener frame intersection

hweb = stiffener web height

ωasti = 0.015xhweb mm, maximum initial side way deflection of stiffener


Figure 5.10: Stiffener side way initial deflection(coupled with plate deflection)

The second initial stiffener deflection is stiffener web imperfection, which is used to

model the out of flatness behavior of the stiffener web plate(figure 5.11). In this work,

the stiffener web imperfection is not considered since all stiffeners in the box girder are

flat bars.

Figure 5.11: Stiffener web initial deflection[8]

5.3.4.1.3 Column initial deflection

The column initial deflection(figure 5.12) describes the welding-induced behavior that

every span(except the two ends) of box girder deviates from the idealized flat position.

Both plate and stiffener nodes will be shifted off the idealized flat position together in

column initial deflection. The single sine half-wave in both directions is assumed as

column deflection shape:

ωcolumn = 0.8ωacolumnsin(

πx

A)sin(

πy

B) (5.5)

where:


ωcolumn = column deflection at a given coordinate position from one frame corner intersecting with plate and stiffener

hweb = stiffener web height

ωacolumn= 1.5 mm, maximum column initial deflection

A = length between frames

B = width of box girder

In the side bays, a scaling factor of 0.25 will be applied to the maximum column imper-

fection amplitude(figure 5.12).

Figure 5.12: column initial deflection

5.3.5 Ultimate strength under pure bending moment for plate model

by NLFEM

A series of nonlinear finite element tests over the full plate element model have been

made and validated with the ISSC2015 Benchmark study, in order to prove the method

of NLFEM adopted in this project as well as to show the complexity involved in the

NLFEM.

5.3.5.1 Convergence study

Before comparing the ultimate strength with the experiment, a sensitivity analysis re-

garding to mesh size is made to obtain the proper mesh size(figure 5.13). Based on the

sensitivity test in mesh size, the size of 20mm is chosen for analyzing ultimate strength

under pure bending moment considering the balance between time and accuracy.


Figure 5.13: Mesh size convergence study

5.3.5.2 Validation with ISSC benchmark study and experiment

Based on the mean value of ultimate bending moment of ISSC participants(table 5.3),

it can be seen that the accuracy of the present work is good. For H200 and H300, the

accuracy with regarding to ISSC2015 Benchmark study is within 2%, while for H400,

the accuracy is within 4%. Thus the NLFEM used in the plate model is proper and can

be adopted for further simplification investigation.

While compared with the experimental test, just like the results from ISSC2015 partici-

pants, there is a significant difference between the experimental test result and numerical

test in the present work. The numerical test result is lower than the experimental test

result. Currently, there still remains a lot of unknowns in the field of ultimate strength.

Some possible explanations for the difference between the numerical result and experi-

mental result could be:

The initial imperfection shape in this study is selected in a conservative way, which may

reduce the ultimate strength. Other possible less conservative initial imperfection shape

like “hungry horse” shape for plate can be further tried and investigated.

The material property parameters, like yielding limit, plate thickness, etc, are provided

by the steel factory in a conservative way. The actual plate thickness is actually higher

than the one used for numerical investigation, and so is yielding limit and other param-

eters. Thus possible sensitivity analysis can further be performed for investigation.


Table 5.3: Comparison of present work with ISSC mean value of ultimate bendingmoment

Model Present(KN.m) ISSC mean value(KN.m) Accuracy W.R.T ISSC(%)

H200 1154 1132 1.94H300 969 955 1.46H400 844 817 3.3

Figure 5.14: ISSC mean numericalresult(H200) Figure 5.15: Numerical result of full

plate model(H200)

The accuracy achieved by the full plate model is good, but the process is very laborious

and time consuming, especially for the stiffener modeling as well as the imperfection

adding. For global ship structure model, the stiffeners are normally modeled by using

beam element to save the engineering time. Thus a simplified method incorporating

beam element for non-linear finite element analysis is of interest to this industry. So it

is investigated in this thesis.

5.3.5.3 Collapsing mode

From figure5.20, it can be seen that the box girder collapses with an overall failure mode

over the compressive part.

5.4 Simplified beam and shell element model for box girder

Normally in marine or offshore structures, stiffeners of different cross sections are used,

such as T-shape, I-shape, L-shape etc. If the stiffeners in numerical model are modeled

by plate element, more laborious work has to be done in order to obtain a node-connected


Figure 5.16: ISSC mean numericalresult(H300)

Figure 5.17: Numerical result of fullplate model(H300)


Figure 5.19: Numerical result of fullplate model(H400)

FE model for marine structures. The other problem brought by the plate-element stiff-

eners is that it will be not so adjustable to stiffeners with different cross sections, which

is a big problem for the parametric rapid model this project is aiming to create. It

is known that as the ship dimensions change, the stiffener size and cross section also

change in order to fit the new ship in different dimension. So in this case, beam element

is adopted to model the stiffener for the purpose of “rapid” as well as “parametric”. Nor-

mally, beam element for marine structure is widely used in the linear structure analysis.

In this project, beam element will be investigated for nonlinear structural analysis.

In the above full plate model, the initial deflection of the box girder is added by shifting


Figure 5.20: Overall collapse mode

nodes directly, which is very laborious and time-consuming. Based on the overall col-

lapse mode found from full-plate element model, the plate-beam combination model will

be investigated in analyzing ultimate bending strength by NLFEM. During this simpli-

fication investigation, the stiffener side deflection will be tried to be neglected, since it

is mainly related to stiffener tripping induced local failure mode.

5.4.1 Element type

A combination of beam element and plate element is used in the present work to simplify

the modeling of box girder. Beam188 is adopted for modeling the stiffeners, while

Shell181 is adopted for other structures as plate and transverse frames.

Beam188 is suitable for large rotation or large strain nonlinear problem involved in

post-buckling analysis for the present work. Beam188 is a 2-node beam element with six

degrees of freedom at each node: translations in x,y and z directions and rotations about

x,y and z axis. Beam188 includes stress stiffness terms for analyzing flexural, lateral and

torsional stability problems. Beam188 is suitable for analyzing slender to moderately

stubby/thick beam structures, so it is very suitable for modeling the stiffeners involved

in marine structures for ultimate strength analysis.

The property of Shell181 has been described in the full plate model, so it will not be

discussed here.


5.4.2 Material property

To be consistent with the full plate model, a bilinear material model for HTS690 with

an extra 1% post yield hardening is adopted for the new simplified numerical model.

5.4.3 Boundary condition

The same boundary condition as the full plate model is applied to the new simplified

model in this project. With one end fixed, the other end is constrained to a reference

point. Displacement load is applied through the reference node.

5.4.4 Initial imperfection

In the full plate model, all initial deflections including plate initial deflection, column

deflection and stiffener deflection are applied in the whole box girder.

While in the simplified model, there is a simplification in initial deflection applying for

the box girder. The stiffener side deflection is neglected in the simplified beam-plate

combination model(figure 5.21) based on its overall collapse mode.

Results of ultimate bending moment for both cases are compared with the full-plate

model as well as ISSC benchmark study.

Figure 5.21: Simplification: initial deflection in the full box girder


Table 5.4: Comparison of simplification case with ISSC2015 in ultimate bendingmoment(KN.m)

Model full plate ISSC2015 Simplification) Accuracy W.R.T ISSC(%)

H200 1154 1132 1119 1.15H300 969 955 952 0.31H400 844 817 819 0.24

5.4.5 Ultimate strength under pure bending moment for simplified

model by NLFEM

A convergence study for mesh size is also carried out before the validation, the mesh

size of 20mm is selected for the consideration of balance between time and accuracy.

The simplified model is compared with the full plate model, the ISSC Benchmark result

and the experimental test result. The simplification case(figure 5.23, 5.25, 5.27) is

plate-beam element combination model including plate and column initial deflection

but neglecting stiffener side deflection for full box girder.

As can be seen from the simplification case(table 5.4) when comparing with the ISSC

result, the accuracy of ultimate bending moment is good when beam element is adopted

to model the stiffeners. For all three models, the accuracy with respect to ISSC2015

benchmark study is within 2%. After this simplification in which the beam element

is adopted and side stiffener imperfection is neglected, a relatively simpler method is

achieved while maintaining a good level of “accuracy”. In this simplification, significant

effort is reduced from the modeling of stiffener by plate element as well as the corre-

sponding effort of nodes matching problem especially where stiffeners joined with other

structural components.

5.5 Conclusion

Both full plate element model and plate-beam element combination model for ultimate

strength analyzing by NLFEM are tested and validated with ISSC Benchmark study

as well as the experimental test. Based on the result comparison: first, using beam

element for modeling the stiffeners suits global ship structural model, which is consistent

with the numerical model produced by fast numerical tool; second, the accuracy loss

accompanied by the neglecting side stiffener initial imperfection is not significant. This

is mainly because the main failure mode of box girder under bending is overall collapse

and not so associated with the tripping of stiffener.


Figure 5.22: ISSC mean numericalresult(H200) Figure 5.23: Numerical result of sim-

plification case(H200)


Figure 5.25: Numerical result of sim-plification case(H300)

As can be seen from the above nonlinear finite element analysis, the whole process of

NLFEM is complex and the calculation time is time consuming. But as the improvement

of computer power, there will be significant reduction of nonlinear analysis calculation

time of FEM tool. Thus the simplified process this work presented will be important

in case of the emergency response case for marine industry, since it is more stable,

adjustable and less manual work required. This simplified method can be used for

ultimate strength analysis of oil tanker, bulk carrier, FPSO and other typical marine

structures.

In the present work, the plate-beam element model in analyzing ultimate bending

strength shows good comparison with ISSC benchmark study when the main failure



Figure 5.27: Numerical result of sim-plification case(H400)

mode is overall collapse. For other types of failure which are related to the local failure

of stiffener like tripping, possible way of applying initial stiffener side deflection to the

beam-element stiffeners could be shifting the degree of freedom of the beam element

nodes.

Chapter 6

Conclusion

6.1 Conclusion

In the present work, a method of rapid numerical modeling of ship structure based on

limit information from emergency situation is proposed and validated in global structural

response under bending on container ship. The fast numerical model of container ship

generated is further used in assessing the ultimate strength. For other ship structure

like oil tanker, bulk carrier, FPSO, etc, a possible method of using beam-plate element

combination model for assessing ultimate strength by non-linear finite element method

is proposed and validated with experimental test as well as ISSC benchmark study.

6.1.1 Information obtained emergency response

The whole process of emergency response is investigated. The corresponding ship infor-

mation available within 3 hours after the emergency is identified in the present work,

which are midship drawing, general arrangement plan and capacity plan as the minimal

information available. The present fast numerical modeling method requires CAD draw-

ings as input. However, the CAD drawings are not always available for different vessels.

Hence a fast numerical modeling method independent of CAD drawings is desired and

proposed in this thesis work.

6.1.2 Methods for assessing hull girder ultimate strength

Based on the literature review, current methods for assessing ultimate strength are

compared with each other. Advantages and disadvantages for different methods are

summarized in the present work. Based on it, the elastic buckling theory and full plastic

68

Chapter 7. Ultimate strength of ship hull 69

bending theory are selected for analyzing the failure mechanism of container ship in

sagging. While for other types of ship structure, the nonlinear finite element method is

selected for assessing the post-buckling behavior.

6.1.3 Rapid numerical modeling method

Based on the limited information available for emergency response, a method for rapid

numerical modeling for ship structure is proposed. The nurbs method is incorporated

for generating a parametric ship hull form in numerical environment rapidly. Based on

the investigation in characteristic of ship structure, critical control parameters for fast

numerical modeling is selected and a corresponding global data structure for storing

control parameters in “point” is proposed. And also “Finding neighbor” algorithm

for automatically generating lines , then, “Hand in hand” algorithm for automatically

generating surfaces for rapid numerical modeling are proposed. Accompanied with the

development of generic fast numerical method, a tool for rapid numerical modeling for

container ship structure is presented.

6.1.4 Longitudinal ultimate bending strength of container ship

The fast numerical model generated is further validated in stress distribution and used

for assessing ultimate bending moment of container ship. Proper boundary condition is

investigated for analyzing the bending behavior of container ship under sagging. The

global x-axis stress distribution of fast numerical model of container ship under sagging

condition is linear in vertical direction. Thus the fast numerical model is validated. The

failure mechanism of container ship under sagging is found based on the comparison of

elastic buckling bending moment and full plastic bending moment. Under sagging, the

container ship is yielding to failure because of the strengthened deck structure. Thus,

when reaching the ultimate state under sagging condition the deck structure of container

ship is close to its yielding limit, the ultimate bending strength of container ship can be

assessed by linear structural analysis.

6.1.5 Simplified NLFEM method for assessing ultimate bending strength

for other ship

For other types of ship structure, a simplified nonlinear finite element method for assess-

ing ultimate bending strength is proposed and validated with experimental result. The

post-buckling behavior of a box girder is investigated in a detailed model by NLFEM.

The main collapse mode of the box girder under bending is overall failure mode. Thus,


the stiffener side deflection is neglected and a simpler way for assessing ultimate strength

by using plate-beam element combination model by NLFEM is investigated and vali-

dated with the experimental test as well as full-plate element model.

6.2 Discussion

Although currently many researches focus on the problem of fast numerical modeling,

most of them relied on the AUTO CAD drawings as input, which is not always available

in emergency situation. While the generic numerical method developed in this thesis is

based on the limited input parameters identified from the available drawings. So in this

way the method applied in this thesis supports the emergency engineering better.

Normally when assessing longitudinal ultimate strength by FEM, nonlinear finite ele-

ment method is adopted, which is very complex and difficult. For container ship with

stocky deck panels as investigated in this thesis, it is found to yield into failure instead

of buckle first. Thus simple linear FEM is sufficiently for assessing the ultimate bending

moment by capturing its yielding bending moment.

For other ship structure which are not designed with extrally strengthened deck struc-

ture, like oil tanker, bulk carrier, FPSO, etc, non-linear finite element method is used in

this thesis for assessing the ultimate strength properly. In order to validate the method,

a box girder is selected for comparison. This is mainly because there is almost no col-

lapse test done for the full ship in recent years. A full ship collapse test will be beneficial

for further research verification.

6.3 Recommendations for further work

For the emergency response project, it is always a problem of how to balance the time

and accuracy. In the present work, the minimal input for support rapid numerical

modeling is selected to base on the available information within 3-4 hours(figure 1.6)

after the ship accident happens, from which the midship section drawing and GA plan

can be accessed. These input parameters need to be identified manually by engineer.

Thus to save more time, one recommendation is to incorporate the automatic drawing

recognizing technology to automatically read related parameters into the input excel.

Because of lack of time, the rapid scantling generating part is not included in the rapid

numerical model. So extra effort and time need to be spent in order to add the structural

scantling manually. Thus another further recommendation is to incorporate the scantling


generating into the rapid numerical model. Since the frame spacing, girder location and

stringer location can be accessed from the midship drawing, which can be an initial

starting point for generating scantling. In this way, more accurate model can be achieved

compared with the blandly new design from the principle dimension.

Since emergency response is also related with the stability problem and flooding prob-

lem, which sometimes can be the main cause of a tragedy. Based on this, one further

recommendation is to include volume definition in the rapid numerical model. In this

case, an algorithm to check the distance between the corner points of the compartment

can be developed and the corresponding pressure on the compartment can be developed

based on rule.

For analyzing the post-buckling behavior of other ship type, when the collapse mode

of the structure is not overall failure mode, it is important to consider the side initial

deflection of side stiffeners. It is recommended to make investigation on this problem.

One possible way could be to shift the degrees of freedom in nodes of beam element of

plate-beam combination model to take the side deflection of stiffeners into consideration.

During the lifting engineering work for salvage in Boskalis, it was found the fatigue

damage will have a significant negative influence on the ultimate bending capacity of

the ship structure. It is probably because most ships in salvage situation are old. But

currently there are rarely any researches focusing on the influence of the fatigue damage

to the ultimate capacity. Thus it is recommended to investigate more on this problem.

Appendix A

Full plastic bending moment

72

Appendix A. Full plastic bending moment 73

ys Name s_h s_w area(a) z(h) 1st moment(ah) σ*a σ*z*a distance moment

355 hatch deck 60 650 39050 26000 1015300000 1.4E+07 3.6E+11 13297.8 1.84E+17

355 300 70 21000 25850 542850000 7455000 1.93E+11 13147.8 9.8E+16

355 hatch side plate1800 55 99000 25100 2484900000 3.5E+07 8.82E+11 12397.8 4.36E+17

355 hatch side stringer70 400 28000 25200 705600000 9940000 2.5E+11 12497.8 1.24E+17

355 deck plating 55 2050 112750 24200 2728550000 4E+07 9.69E+11 11497.8 4.6E+17

355 deck stiffener 1400 70 28000 24100 674800000 9940000 2.4E+11 11397.8 1.13E+17

355 deck stiffener 2650 70 45500 23775 1081762500 1.6E+07 3.84E+11 11072.8 1.79E+17

355 BG upper out side plating60 2050 123000 24200 2976600000 4.4E+07 1.06E+12 11497.8 5.02E+17

355 BG upper girder 1400 70 28000 24000 672000000 9940000 2.39E+11 11297.8 1.12E+17

355 BG upper girder 2650 70 45500 23875 1086312500 1.6E+07 3.86E+11 11172.8 1.8E+17

355 BG left side 11600 55 88000 23600 2076800000 3.1E+07 7.37E+11 10897.8 3.4E+17

355 BG left side 21065 55 58575 22267.5 1304318813 2.1E+07 4.63E+11 9565.25 1.99E+17

315 BG left side 3865 30 25950 21102.5 547609875 8174250 1.72E+11 8400.25 6.87E+16

315 BG left side 41465 30 43950 19637.5 863068125 1.4E+07 2.72E+11 6935.25 9.6E+16

355 BG right side 11400 55 77000 23500 1809500000 2.7E+07 6.42E+11 10797.8 2.95E+17

355 BG right side 21065 55 58575 22267.5 1304318813 2.1E+07 4.63E+11 9565.25 1.99E+17

315 BG right side 3865 30 25950 21502.5 557989875 8174250 1.76E+11 8800.25 7.19E+16

315 BG right side 41465 30 43950 19637.5 863068125 1.4E+07 2.72E+11 6935.25 9.6E+16

315 BG left stiff 1 65 375 24375 22800 555750000 7678125 1.75E+11 10097.8 7.75E+16

315 BG left stiff 2 65 375 24375 21935 534665625 7678125 1.68E+11 9232.75 7.09E+16

315 BG left stiff 3 65 375 24375 21070 513581250 7678125 1.62E+11 8367.75 6.42E+16

315 BG right stiff 165 400 26000 22800 592800000 8190000 1.87E+11 10097.8 8.27E+16

315 BG right stiff 265 400 26000 21935 570310000 8190000 1.8E+11 9232.75 7.56E+16

315 BG right stiff 365 400 26000 21070 547820000 8190000 1.73E+11 8367.75 6.85E+16

315 2nd Deck 15 2050 30750 20205 621303750 9686250 1.96E+11 7502.75 7.27E+16

315 Deck stiff 4440 20036.9 88963680 1398600 2.8E+10 7334.62 1.03E+16

315 2nd comp left side 1265 11 2915 19472.5 56762337.5 918225 1.79E+10 6770.25 6.22E+15









315 2nd comp right side 1865 15 12975 19472.5 252655687.5 4087125 7.96E+10 6770.25 2.77E+16









315 2nd comp left side stiff 1 3060 19319.6 59118030 963900 1.86E+10 6617.37 6.38E+15





Figure A.1: 1





315 2nd comp right side stiff 1 3060 19019.6 58200030 963900 1.83E+10 6317.37 6.09E+15








315 Stringer 4 10 2050 20500 12420 254610000 6457500 8.02E+10 -282.25 1.82E+15

315 stringer 4 stiff150 10 1500 12415 18622500 472500 5.87E+09 -287.25 1.36E+14

315 3nd comp left side 1870 11 9570 11985 114696450 3014550 3.61E+10 -717.25 2.16E+15






315 3nd comp right side 1870 15 13050 11985 156404250 4110750 4.93E+10 -717.25 2.95E+15






315 3nd comp left side stiff 1 3850 11532.5 44400000 1212750 1.4E+10 -1169.8 1.42E+15





315 3nd comp right side stiff 1 3850 11532.5 44400000 1212750 1.4E+10 -1169.8 1.42E+15





315 Stringer 6 11 2050 22550 7200 162360000 7103250 5.11E+10 -5502.2 3.91E+16

315 stringer 6 stiff 5430 7005.34 38038995 1710450 1.2E+10 -5696.9 9.74E+15

315 4th comp left side 1870 15 13050 6765 88283250 4110750 2.78E+10 -5937.2 2.44E+16



315 4th comp right side 1870 15 13050 6765 88283250 4110750 2.78E+10 -5937.2 2.44E+16



315 4th comp left side stiff 1 4740 6314.66 29931480 1493100 9.43E+09 -6387.6 9.54E+15

315 4th comp left side stiff 2 4740 5444.66 25807680 1493100 8.13E+09 -7257.6 1.08E+16

315 4th comp right side stiff 1 4740 6314.66 29931480 1493100 9.43E+09 -6387.6 9.54E+15

315 4th comp right side stiff 2 4740 5444.66 25807680 1493100 8.13E+09 -7257.6 1.08E+16

315 Stringer 7 15 4675 70125 4590 321873750 2.2E+07 1.01E+11 -8112.2 1.79E+17

315 stringer stiff left 2 9480 4392 41636160 2986200 1.31E+10 -8310.2 2.48E+16

315 stringer stiff left 2 5430 4395.34 23866695 1710450 7.52E+09 -8306.9 1.42E+16

Figure A.2: 1


315 Cornor vertical 12590 15 38850 4590 178321500 1.2E+07 5.62E+10 -8112.2 9.93E+16

315 cornor vertical 1 stiff 1 4740 3709.66 17583780 1493100 5.54E+09 -8992.6 1.34E+16

315 cornor vertical 1 stiff 2 4740 2844.66 13483680 1493100 4.25E+09 -9857.6 1.47E+16

315 inner bottom 116.5 3565 58822.5 2000 117645000 1.9E+07 3.71E+10 -10702 1.98E+17

315 inner bottom 215 11760 176400 2000 352800000 5.6E+07 1.11E+11 -10702 5.95E+17

315 double bottom 121 3565 74865 0 0 2.4E+07 0 -12702 3E+17

315 double bottom 220.5 11760 241080 0 0 7.6E+07 0 -12702 9.65E+17

315 inner bottom stiff all12 56880 1802 102497760 1.8E+07 3.23E+10 -10900 1.95E+17

315 double bottom stiff all12 70800 227.873 16133400 2.2E+07 5.08E+09 -12474 2.78E+17

315 girder 0 2000 15.5 31000 1000 31000000 9765000 9.77E+09 -11702 1.14E+17

315 girder 1 2000 14 28000 1000 28000000 8820000 8.82E+09 -11702 1.03E+17

315 girder 2 2000 14 28000 1000 28000000 8820000 8.82E+09 -11702 1.03E+17

315 girder 3 2000 14 28000 1000 28000000 8820000 8.82E+09 -11702 1.03E+17

315 girder 4 2000 16 32000 1000 32000000 1E+07 1.01E+10 -11702 1.18E+17

315 girder 5 2000 14 28000 1000 28000000 8820000 8.82E+09 -11702 1.03E+17

315 girder 6 2000 15 30000 1000 30000000 9450000 9.45E+09 -11702 1.11E+17

315 girder 0 stiff 194.6602 985.489 191835.4968 61318 60428182 -11717 7.18E+14

315 girder 1,2,3,5,6 stiff1 10800 1271.44 13731525 3402000 4.33E+09 -11431 3.89E+16

315 girder 1,2,3 ,5,6 stiff2 10800 561.438 6063525 3402000 1.91E+09 -12141 4.13E+16

315 girder 4 stiff 5900 933.864 5509800 1858500 1.74E+09 -11768 2.19E+16

315 hopper cornor 73434.73 1400 102808619.6 2.3E+07 3.24E+10 -11302 2.61E+17

315 hopper stiff all 6 35400 1400 49560000 1.1E+07 1.56E+10 -11302 1.26E+17

sum 2904877 35674098580 9.5E+08 1.21E+13 9.09E+18

neutral axis 12702.24943 12702.2 9.09E+09

ultimate bending moment 9.094625

Figure A.3: 1

Appendix B

Slenderness ratio of deck plate

76

Appendix B. Slenderness ratio of deck plate 77

b h A Z A*Z Iyy Iyy2 Iyy R L SR

Unit mm mm mm^2 mm mm^3 mm^4 mm^4 mm^4 mm mm

Deck Plate 2050 55 1.13E+05 0 0 2.84E+07 1.63E+09 1.66E+09

Deck stiff1 70 400 2.80E+04 227.5 6.37E+06 3.73E+08 3.22E+08 6.95E+08

Deck stiff2 70 650 4.55E+04 352.5 1.60E+07 1.60E+09 2.45E+09 4.05E+09

sum 1.86E+05 2.24E+07 120.3154 6.41E+09 185.522 3150 16.98

E Ys SRc

Unit Mpa Mpa

Value 210000 355 76.40915

Figure B.1: 1

Appendix C

Material property of high

strength steel

78

Appendix C. Material property of high strength steel 79

Figure C.1: Steel supplied by Dillinger Hutten Worke[6]

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Longitudinal ultimate bending strength analysis of ship