numerical and analytical simulations of in-shore ship collisions … · 2018-03-28 · numerical...

Numerical and analytical simulations of in-shore ship collisions within the scope of A.D.N.

Regulations

Ye Pyae Sone Oo

Master Thesis

presented in partial fulfillment of the requirements for the double degree:

“Advanced Master in Naval Architecture” conferred by University of Liege "Master of Sciences in Applied Mechanics, specialization in Hydrodynamics,

Energetics and Propulsion” conferred by Ecole Centrale de Nantes

developed at L'Institut Catholique d'Arts et Métiers, Carquefou in the framework of the

“EMSHIP” Erasmus Mundus Master Course

in “Integrated Advanced Ship Design”

Ref. 159652-1-2009-1-BE-ERA MUNDUS-EMMC

Supervisor: Prof. Hervé Le Sourne, L’Institut Catholique d’Arts et Métiers, France.

Ing. Stéphane Paboeuf, Bureau Veritas, Nantes.

Reviewer: Prof. Philippe Rigo, University of Liège.

Nantes, February 2017

Numerical and analytical simulations of in-shore ship collisions within the scope of

A.D.N. Regulations

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“EMSHIP” Erasmus Mundus Master Course, period of study September 2015 – February 2017

ABSTRACT

Nowadays, due to the continuous increase in the inland waterway navigation, there has been a

higher risk of collisions, groundings, and of other undesired events. Especially for inland ships

carrying dangerous goods, the consequences of ship collision may lead to serious economic

losses as well as environmental pollution. Therefore, such accidents must be prevented at all

cost, and even if they were to occur, the ship designer has to make sure that the risk of cargo

tank damage or the oil spillage is the minimum. For the inland vessel construction, the rules are

governed by A.D.N. Regulations that consist in determining the probability of cargo tank

rupture using Finite Element Analysis (FEA). However, such numerical approach is often time

consuming and very expensive, and thus, is usually prohibited in the preliminary design phases.

In this context, ICAM and Bureau Veritas have been involved in the development of a

simplified damage assessment tool called SHARP based on the super-element method. Some

validation tests have already been performed on ocean-going tanker and FPSO application

cases. Nevertheless, the validity of the tool still needs to be verified for in-shore ship

applications. Thus, the main purpose of this thesis is to compare and validate the results of

SHARP with Non-linear Finite Element Explicit Code, LS-DYNA, within the scope of A.D.N.

Regulations. Some of the early results, however, show that although SHARP can be applicable

in the place of LS-DYNA, the tool still requires some more developments. Therefore, another

purpose of this thesis is to investigate the discrepancies in more details and at the same time, to

make suggestions for the future development of the tool.

P 4 Ye Pyae Sone Oo

Master Thesis developed at l'Institut Catholique d'Arts et Métiers, Carquefou

This page was left intentionally blank.


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CONTENTS

ABSTRACT 3

LIST OF FIGURES 9

LIST OF TABLES 12

ABBREVIATIONS 15

1. INTRODUCTION 16

1.1 Background and Motivation 16

1.2 Objectives 17

1.3 Scope of the Thesis 18

2. A.D.N. REGULATIONS 19

2.1 General 19

2.2 Carriage of Dangerous Goods by Inland Waterways 19

2.3 Alternative Design Procedure and its Approaches 20

2.4 Determination of the Collision Energy Absorbing Capacity 24

2.4.1 General 24

2.4.2 Creating the Finite Element Models 24

2.4.3 Material Properties 25

2.4.4 Rupture Criteria 25

2.4.5 Friction Energy 26

3. LITERATURE REVIEW 27

3.1 Inland Navigation Accident Study 27

3.2 Existing Simplified Ship Collision Models and Associated Software 29

3.2.1 Internal Sub-models of Structural Mechanics 29

P 6 Ye Pyae Sone Oo


3.2.2 External Ship Dynamics Sub-models 31

3.2.3 Coupled Approach of Internal and External Sub-models 33

4. SHIP COLLISION THEORY 34

4.1 General 34

4.2 Finite Element Theory 34

4.2.1 General Equation (Le Sourne, 2015) 34

4.2.2 The Newmark Method (Le Sourne, 2015) 35

4.2.3 Explicit Scheme (Le Sourne, 2015) 36

4.2.4 Implicit Scheme (Le Sourne, 2015) 37

4.2.5 LS-DYNA and MCOL 37

4.2.6 Advantages and Disadvantages of using LS-DYNA/MCOL 39

4.3 Super Element Theory 40

4.3.1 General Equations 40

4.3.2 SHARP Tool 44

5. LS-DYNA AND SHARP SIMULATIONS 48

5.1 LS-DYNA/MCOL Simulation Procedures 48

5.1.1 General 48

5.1.2 Modelling and Meshing 49

5.1.3 Elements, Materials and Parts 51

5.1.4 Boundary Conditions 55

5.1.5 Collision Scenarios 57

5.1.6 Contact Type and Friction 61

5.2 SHARP/MCOL Simulation Procedures 62

5.2.1 General 62

5.2.2 Modelling and Meshing 62


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5.2.3 Materials and Rupture Strain 67

5.2.4 Collision Scenarios 68

6. COMPARISON AND ANALYSIS 70

6.1 Simulations without Rupture Strain 70

6.1.1 Case 1 (V-shape bow : 90 deg : At web : Under deck of struck ship) 70

6.1.2 Case 2 (V-shape bow : 90 deg : Between webs : Mid-depth of struck ship) 74

6.1.3 Case 3 (Push barge bow : 55 deg : At web : Mid-depth of struck ship) 78

6.1.4 Case 4 (Push barge bow : 55 deg : At bulkhead : Above deck of struck ship) 83

6.1.5 Case 5 (V-shape bow : 90 deg : At web : Above deck of struck ship) 87

6.1.6 Overall Analysis 90

6.2 Simulations considering Rupture (A.D.N. Regulations) 91







6.3 Additional Simulations with Modified Rupture Strains 102







7. CONCLUSIONS AND RECOMMENDATIONS 116

P 8 Ye Pyae Sone Oo


ACKNOWLEDGEMENTS 118

REFERENCES 119

APPENDIX 123

A. CONVERGENCE TESTS FOR MCOL SUB-CYCLING 124

B. CASE SENSITIVITY OF RUPTURE STRAIN 127

B.1 Case 1 (V-shape bow : 90 deg : At web : Under deck of struck ship) 127

B.2 Case 2 (V-shape bow : 90 deg : Between webs : Mid-depth of struck ship) 128

B.3 Case 3 (Push barge : 55 deg : At web : Mid-depth of struck ship) 129

B.4 Case 4 (Push barge : 55 deg : At bulkhead : Above deck of struck ship) 130

B.5 Case 5 (V-shape bow : 90 deg : At web : Above deck of struck ship) 131


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LIST OF FIGURES

Figure 1 Definition of vertical striking positions (A.D.N. Regulations, 2015) ........................ 21

Figure 2 Number of accidents in inland water transportation in 8 EU countries, 2013 (Eurostat,

2015) ......................................................................................................................................... 27

Figure 3 Inland navigation accidents for 8 EU member states (Eurostat, 2015) ..................... 28

Figure 4 Distribution of vessel types involved in ship collisions (Youssef, Kim and Paik, 2014)

.................................................................................................................................................. 28

Figure 5 Minorsky’s Correlation (Minorsky, 1959) ................................................................. 30

Figure 6 Full-scale collision experiment in Netherlands. Figure available from: (Zhang, 1999)

.................................................................................................................................................. 31

Figure 7 LS-DYNA/MCOL collision simulation system (Le Sourne et al., 2003) ................. 39

Figure 8 Comparison of LS-DYNA/MCOL simulation with reality (Le Sourne et al., 2003) 39

Figure 9 Illustrations of super-elements for perpendicular collisions (Le Sourne et al., 2012)42

Figure 10 Descriptions of super-elements for oblique collisions (Le Sourne et al., 2012) ...... 45

Figure 11 Graphical user interface of SHARP ......................................................................... 46

Figure 12 Workflow diagram of SHARP (Le Sourne et al., 2012) .......................................... 47

Figure 13 Flow-chart of LS-DYNA simulation process .......................................................... 48

Figure 14 Finite Element model of struck ship (Type C inland double hull tanker) ............... 49

Figure 15 Finite Element models of striking ship bows ........................................................... 50

Figure 16 Arbitrary stress-strain curve for elasto-plastic material ........................................... 52

Figure 17 Organization of keywords to define structural parts in LS-DYNA ......................... 54

Figure 18 Typical collision simulation in LS-DYNA (Case 1) ............................................... 58

Figure 19 Undesirable effect (Conceptual diagram) ................................................................ 59

Figure 20 Definitions of the vertical impact locations (A.D.N. Regulations, 2015) ............... 59

Figure 21 Scheldt estuary – Zeebrugge (available from: Google Map) ................................... 60

Figure 22 Simulation procedures for SHARP/MCOL ............................................................. 62

Figure 23 Complete SHARP model of struck ship .................................................................. 63

Figure 24 Side shell becoming two super-elements due to virtual deck (Body plan view) ..... 64

Figure 25 Comparison of side shell super-element with and without virtual deck (profile view)

.................................................................................................................................................. 64

Figure 26 Model of the striking ship bow in SHARP (Besnard, 2014) ................................... 65

Figure 27 Models of striking ships in SHARP ......................................................................... 66

Figure 28 Adjustments in the push barge bow position in SHARP (Top view) ...................... 66

P 10 Ye Pyae Sone Oo


Figure 29 Comparison of the push barge bow models between LS-DYNA and SHARP ....... 67

Figure 30 Stress-strain curves considered for LS-DYNA and SHARP simulations ................ 68

Figure 31 Impact locations on side shell in SHARP ................................................................ 69

Figure 32 Typical collision scenario modelled in SHARP (case 1) ......................................... 69

Figure 33 Extent of damage in LS-DYNA – Case 1 (without rupture strain) ......................... 71

Figure 34 Extent of damage in SHARP – Case 1 (without rupture strain) .............................. 72

Figure 35 Comparison of the results – Case 1 (without rupture strain) ................................... 72













Figure 48 Comparison of damage extent in LS-DYNA and SHARP – Case 1 (With rupture

strain) ........................................................................................................................................ 92

Figure 49 Comparison of the results – Case 1 (With rupture strain) ....................................... 93


strain) ........................................................................................................................................ 94


Figure 52 Comparison of the crushing force in LS-DYNA and SHARP (Case 2) .................. 95


strain) ........................................................................................................................................ 96



strain) ........................................................................................................................................ 98



strain) ...................................................................................................................................... 100


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Figure 58 Comparison of the results – Case 5 (With rupture strain) ..................................... 100

Figure 59 Comparison of the results– case 1 (with modified rupture strain) ......................... 103

Figure 60 View of the deformation of weather deck and bottom in LS-DYNA .................... 104

Figure 61 View of the activated elements in SHARP (weather deck has not been impacted at

all) ........................................................................................................................................... 104


Figure 63 View of the bending of weather deck due to deformation of the side shell .......... 107

Figure 64 View of the activated super-elements in SHARP (The weather deck has not been

collided) .................................................................................................................................. 107


Figure 66 View of the side shell which has ruptured being still there and resisting the collision

– case 3 ................................................................................................................................... 110

Figure 67 Comparison of the crushing resistance of the side shell between LS-DYNA and

SHARP ................................................................................................................................... 110

Figure 68 Comparison of the results – case 4 (with modified rupture strain) ........................ 112

Figure 69 Comparison of the results – case 5 (with modified rupture strain) ........................ 113

Figure A - 1 MCOL convergence test for deformation energy (case 2 - without rupture strain)

................................................................................................................................................ 124

Figure A - 2 MCOL convergence test for penetration (case 2 - without rupture strain) ........ 124


................................................................................................................................................ 125

Figure A - 4 MCOL convergence test for penetration (case 3 - without rupture strain) ........ 125

Figure A - 5 MCOL convergence test for deformation energy (case 4 - with rupture strain) 126

Figure A - 6 MCOL convergence test for deformation energy (case 4 - with rupture strain) 126



LIST OF TABLES

Table 1 Values for uniform strain and necking for shipbuilding steel (𝑅𝑒𝐻 ≤ 355 N/mm2) 26

Table 2 Main characteristics of the striking ships .................................................................... 50

Table 3 Material failure strain calculation ............................................................................... 53

Table 4 Convergence tests for MCOL sub-cycling steps ......................................................... 56

Table 5 Results of convergence tests for MCOL ..................................................................... 56

Table 6 Collision scenarios ...................................................................................................... 57

Table 7 Location of the impact points in LS-DYNA ............................................................... 57

Table 8 Draft combinations of struck and striking ships ......................................................... 59

Table 9 Definitions of the parameters used in the SHARP bow model (Besnard, 2014) ........ 65

Table 10 Results calculated by LS-DYNA – Case 1 (without rupture strain) ......................... 70

Table 11 Results calculated by SHARP – Case 1 (without rupture strain) .............................. 71

Table 12 Comparison of the results – Case 1 (without rupture strain) .................................... 72

Table 13 Comparison of energy absorption – Case 1 (without rupture strain) ........................ 73

















Table 30 Summary of result discrepancy (cases without rupture strain) ................................. 91

Table 31 Comparison of the results – Case 1 (With rupture strain) ......................................... 92



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Table 35 Comparison of the results – Case 5 (With rupture strain) ....................................... 100

Table 36 Summary of result discrepancy (cases with rupture strain) .................................... 102

Table 37 Different rupture strain values considered in SHARP ............................................ 102

Table 38 Comparison of the results – case 1 (with modified rupture strain) ......................... 103

Table 39 Comparison of the energy dissipation – case 1 (with modified rupture strain) ...... 105






Table 45 Comparison of the energy dissipation – case 4 (with rupture strain) ...................... 112



Table 48 Result discrepancy of the simulations (cases with modified rupture strain) ........... 115

Table B - 1 Evaluation of energy distribution using different rupture strains – Case 1 ......... 127







DECLARATION OF AUTHORSHIP

I declare that this thesis and the work presented in it are my own and have been generated by

me as the result of my own original research.

Where I have consulted the published work of others, this is always clearly attributed.

Where I have quoted from the work of others, the source is always given. With the exception

of such quotations, this thesis is entirely my own work.

I have acknowledged all main sources of help.

Where the thesis is based on work done by myself jointly with others, I have made clear exactly

what was done by others and what I have contributed myself.

This thesis contains no material that has been submitted previously, in whole or in part, for the

award of any other academic degree or diploma.

I cede copyright of the thesis in favour of l'Institut Catholique d'Arts et Métiers (ICAM).

Date: Signature


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ABBREVIATIONS

3D : 3 Dimensions

A.D.N. : European Agreement concerning the International Carriage of

Dangerous Goods by Inland Waterways

BV : Bureau Veritas

CCNR : Central Commission for the Navigation of the Rhine

DOF : Degree of Freedom

DTU : Technical University of Denmark

EMSHIP : Erasmus Mundus Master Course in Advanced Ship Design

EU : European Unions

FE : Finite Element

FEA : Finite Element Analysis

FEM : Finite Element Method

FEMB : Finite Element Model Builder

GUI : Graphical User Interface

ICAM : l'Institut Catholique d'Arts et Métiers

IMO : International Maritime Organization

ITOPF : International Tanker Owner’s Pollution Federation

MARPOL : International Convention for the Prevention of Pollution from Ships

MCOL : Mitsubishi Collision

MIT : Massachusetts Institute of Technology

OPA : Oil Pollution Act

SE : Super-Element

SEM : Super-Element Method

SHARP : Ship Hazardous Aggression Research Program

SIMCOL : Simplified Collision Model

SNAME : Society of Naval Architects and Marine Engineers

SSC : Ship Structure Committee

UNECE : United Nations Economic Commission for Europe



1. INTRODUCTION

1.1 Background and Motivation

Recently, transportation of hazardous substances by sea has increased considerably, resulting

the risks of accidents such as collision and grounding to increase. Collision of ships, especially

the ones carrying dangerous goods, can not only pollute the environments but also lead to

serious economic losses as well as casualties. In the past, there had been a lot of catastrophes,

human life losses and tragic accidents due to ship collisions. Examples of such tragic accidents

include RMS Titanic (1912) which sank in North Atlantic Ocean owing to the collision with an

iceberg. This incident resulted in the deaths of more than 1500 people. In 1979, a Greek Oil

Tanker, SS Atlantic Express collided with another Oil Tanker, Aegean Captain and eventually

sank, having spilled 287,000 tons of crude oil into the Caribbean Sea. Moreover, the collision

accident of Philippine-registered passenger ferry, MV Doña Paz (1987), with the oil tanker, MT

Vector, was also known as one of the worst disasters in the history of maritime, amounting to

an estimated death of over 4300 people.

In addition, according to the oil spill statistics of International Tanker Owner’s Pollution

Federation (ITOPF, 2016), from 1970 to 2015, a large amount of oil spill (> 700 tons) is due to

collision and grounding, accounting for 30 % and 33 % respectively. Therefore, it is obvious

that collision can cause serious environmental pollution as well as human life losses. Reducing

the risks of such accidents as much as possible is one of the top priorities of any maritime

organizations, classification societies and ship designers.

International Maritime Organization (IMO) introduced a series of measures such as SOLAS

(Safety of Life at Sea), MARPOL (International Convention for the Prevention of Pollution from

Ships), OPA 90 (Oil Pollution Act, 1990), etc. to improve the safety at sea as well as to prevent

oil pollution due to tanker accidents. Additionally, A.D.N. Regulation which is the European

Agreement concerning the International Carriage of Dangerous Goods by Inland Waterways

also entered into force on 29th February 2008 for promoting the safety level for the carriage of

dangerous goods and for preventing any pollution resulting from any such accidents.

Many scientists and researchers have also conducted a series of experiments and published a

lot of research papers concerning with methods to assess ship impact damage. In this context,

one of the important questions is how to evaluate the crashworthiness of the vessels during the

pre-design stage. Although non-linear finite element methods can be applied, such approaches


A.D.N. Regulations

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are not very well suited for the early design stages as the modelling and simulation time are

unusually too high. Recently, a method known as Super-Element Method (SEM) has been

developed by (Lützen, Simonsen and Pedersen, 2000) to rapidly assess the collision damage of

a vessel. Such methods are very useful for optimization in the preliminary ship design phase as

the time and computational requirement is significantly lower than that of Finite Element

Analysis.

1.2 Objectives

There are two main objectives for this thesis.

The first objective is to validate the software SHARP by comparing the results with

non-linear finite element code, LS-DYNA for the application of inland vessels within

the scope of A.D.N. Regulations. According to the A.D.N. Regulations, the energy

absorption capacity of the colliding vessels needs to be calculated in order to determine

the probability of cargo tank rupture. Conventionally, Finite Element Analysis has been

applied for this step. However, it will require an immense amount of work and time in

order to make a complete collision analysis with FEM. And hence, the purpose of this

thesis is to see whether SHARP can replace conventional Finite Element (FE) software

since the simulation time of SHARP is significantly lower than that of an FE Software.

Unfortunately, some of the early comparison results show that the tool still needs some

additional improvement for inland vessel structures and thus, the second objective of

this thesis is to investigate the discrepancies presented between the two methodologies

and to make suggestions for the future improvement of the software.

To achieve both objectives mentioned above, various simulations of LS-DYNA and SHARP

will be made using the same collision scenarios and the obtained results will be compared. The

struck ship is a typical Type C inland tanker. Two striking ship bows, push barge bow and V-

shape bow, will be defined according to the geometries given by the A.D.N. Regulations.

Associated collision scenarios will also be defined in accordance with the A.D.N. Regulations.



1.3 Scope of the Thesis

This thesis will be comprised of the following main Sections.

Section 2 will present a brief review on A.D.N. Regulations. Important points within the

regulations will be highlighted and the alternative design approach will be described.

In Section 3, literature review on inland navigation accidents around European waterway will

be discussed along with the descriptions of the existing simplified models for ship collision

analysis.

The basic theories concerning with ship collision mechanisms will be studied in Section 4. The

Numerical approach (Finite Element) and the analytical approach (Super-element) which are

implemented in LS-DYNA and SHARP respectively will be elaborated in details.

In Section 5, applications of LS-DYNA and SHARP in ship collision analysis will be presented.

All simulation processes, modelling, assumptions, and different collision scenarios will be

defined in that section.

Section 6 will emphasize the validation of SHARP results with LS-DYNA/MCOL code. MCOL

is an external dynamic tool used to calculate the external dynamics of the colliding vessels

during impact, taking into account the hydrodynamic forces which apply to both ships. The

results will be compared in the form of deformation energy as well as the penetration damage.

Any discrepancies between the two methodologies will be investigated and analysed in details.

Moreover, possible development for improving SHARP tool will be suggested.

Section 7 will be about the conclusions and recommendations, exposing not only the advantages

but also the limitations of SHARP in comparison with LS-DYNA. Moreover, recommendations

regarding the future improvement of the SHARP tool will be particularised.


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2. A.D.N. REGULATIONS

2.1 General

A.D.N. is the European Agreement concerning the International Carriage of Dangerous Goods

by Inland Waterways. It has been issued in Geneva on 26th May, 2000 during the occasion of a

Diplomatic Conference held under the joint auspices of the United Nations Economic

Commission for Europe (UNECE) and the Central Commission for the Navigation of Rhine

(CCNR). It contains all the requirements for the design and construction of inland vessels

involved during the transport of dangerous goods. It entered into force on 29th February, 2008.

Refer to (A.D.N. Regulations, 2015).

The objectives are:

To ensure a high level of safety for international carriage of dangerous goods by inland

waterways;

To effectively contribute to the protection of the environment by preventing any

pollution resulting from accidents or incidents during such carriage; and

To facilitate transport operations and promote international trade in dangerous goods.

2.2 Carriage of Dangerous Goods by Inland Waterways

Within the context of A.D.N. Regulations, the followings are the type of dangerous goods that

are allowed to be carried by inland navigation:

Gases compressed, liquefied or dissolved under pressure;

Flammable liquids;

Oxidizing substances;

Toxic substances;

Corrosive substances;

Miscellaneous dangerous substances and articles.

The vessels which carry these dangerous substances listed above have to be met with certain

criterion. The rules required for constructing such vessels are presented in Chapter 9.3 of

A.D.N. Regulations. It documents various design requirements such as materials, protections,



hold spaces, cargo tanks, ventilation, engine room, piping system, fire system, electrical

installations, ship stability, and so on.

The rules are also divided according to the type of vessels, namely, type G, C and N: (Refer to

A.D.N. Regulations 2015, Chapter 9.3)

Type G: tank vessel intended for the carriage of gases under pressure or under

refrigeration.

Type C: tank vessel intended for the carriage of liquids. (usually double hull with flush

deck)

Type N: tank vessel intended for the carriage of liquids. (usually with open or closed

cargo tanks)

2.3 Alternative Design Procedure and its Approaches

One of the interests of using alternative design approach is to check if it is possible to promote

structural crashworthiness while increasing the capacity of cargo tank. It is done by comparing

the risk of the cargo tank failure between conventional construction and alternative one. The

alternative design vessel will be fitted with the cargo tank whose capacity may exceed the

maximum allowable one (but not greater than 1000 m3). Also, the distance between the outer

side shell and the cargo tank may deviate from the minimum requirement except the fact that

the ship will be protected with a more crashworthy side structure. Within the scope of A.D.N.

Regulations, the risk of a more crashworthy construction (alternative design) should be equal

to or lower than the risk of a conventional construction. Only then, a higher safety may be

approved and the vessel will be permitted. Details about the alternative construction can be

found in A.D.N regulation 2015, Section 9.3.4.

Referring to A.D.N., the risk of cargo tank rupture due to ship collision can be described by

Equation (1) below:

𝑅 = 𝑃. 𝐶 ( 1 )

where

R : risk [m2];

P : probability of cargo tank rupture; and


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C : consequence (measure of damage) of cargo tank rupture [m2].

The probability of cargo tank rupture P depends on the probability distribution of the available

collision energy which the structures of the struck ship can absorb without any damage to the

cargo tank. This probability can be reduced by improving the structural crashworthiness of the

struck ship. The consequence of cargo tank rupture C can be defined as an affected area around

the struck ship.

There are 13 steps to calculate the probability of cargo tank rupture and the associated collision

energy absorbing capacity. Only the summary of those steps will be described in this thesis.

Step 1 includes preparation of a reference design and the associated alternative design. The

reference design should have at least the same dimensions (length, width, depth, displacement)

as the alternative design. Both designs should comply with the minimum requirements of a

recognized classification society.

In step 2, the vertical and longitudinal collision locations are defined. The vertical locations are

determined by using minimum and maximum draughts of the colliding ships. Then, a number

of possible draught combinations can be represented by an enclosed rectangular area shown in

Figure 1. Each inclined line has the same draught difference. In this thesis, however, to assess

the possible maximum collision energy, only the highest points on each respective diagonal line

are selected for the analysis.

Figure 1 Definition of vertical striking positions (A.D.N. Regulations, 2015)



On the other hand, three locations are suggested to determine the longitudinal impact locations.

They are:

at bulkhead;

between two webs; and

at web.

Therefore, a total of 9 collision locations is required to be studied for Type C vessels.

In step 3, the weighting factors representing the relative probability of the typical impact

locations are defined. The total weighting factor for each collision location is the product of the

factor for vertical collision location by the factor for longitudinal collision location. The

assumptions for these weighting factors must be agreed by a recognized classification society.

In step 4, collision energy absorbing capacity is determined for each collision location defined

in the previous steps 2 and 3 with the use of Finite Element Analysis. This energy is the amount

of collision energy absorbed by the structure of the struck ship up to initial rupture of cargo

tank. The following two impact scenarios are considered:

Scenario I: Push barge bow with 55 degree collision angle

Scenario II: V-shape bow with 90 degree collision angle

In addition, the following assumptions are made for struck and striking vessels:

The struck vessel is considered at rest, while the striking ship has a constant speed of

10 m/s.

The bow of the striking ship is assumed to be rigid while the structure of the struck ship

is considered as a deformable one.

In total, 36 finite element computations have to be simulated corresponding to 9 impact

locations and 2 bow shapes, each case for reference design and alternative design.

In step 5, probability of exceedance is calculated using the collision energy absorbing capacity,

𝐸𝑙𝑜𝑐(𝑖). To calculate this probability, cumulative probability density functions (CPDF) are

provided at A.D.N. Section 9.3.4.3.1.5.6. It is given by Equation (2) as follows:

𝑃𝑥% = 𝐶1(𝐸𝑙𝑜𝑐(𝑖))3 + 𝐶2(𝐸𝑙𝑜𝑐(𝑖))2 + 𝐶3𝐸𝑙𝑜𝑐(𝑖) + 𝐶4 ( 2 )

where

Px% : probability of cargo tank rupture;


A.D.N. Regulations

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C1-4 : coefficients from table in A.D.N Section 9.3.4.3.1.5.6; and

Eloc(i): collision energy absorbing capacity (from FEA).

In step 6, weighted probabilities of the cargo tank rupture 𝑃𝑤𝑥% are calculated by multiplying

each cargo tank rupture probability 𝑃𝑥% by the weighting factors corresponding to the maximum

displacement of the vessel and the characteristic collision speed.

In step 7, the total probabilities of cargo tank rupture 𝑃loc(𝑖) are calculated by summing all

weighted probabilities of cargo tank rupture 𝑃𝑤𝑥% for each collision location considered.

In step 8, for both collision scenarios, the weighted total probabilities of cargo tank rupture

𝑃𝑤loc(𝑖) are calculated by the multiplication of the total probabilities of cargo tank rupture 𝑃𝑙𝑜𝑐(𝑖)

with the weighting factors 𝑤𝑓𝑙𝑜𝑐(𝑖).

The scenario specific total probabilities of cargo tank rupture 𝑃𝑠𝑐𝑒𝑛𝐼 and 𝑃𝑠𝑐𝑒𝑛𝐼𝐼 are calculated in

step 9. This is done according to the table given at A.D.N. Section 9.3.4.3.1.

Step 10 is the calculation of weighted value of the overall total probability of cargo tank rupture

𝑃𝑤 according to the following Equation (3):

𝑃𝑤 = 0.8 ∗ 𝑃𝑠𝑐𝑒𝑛𝐼 + 0.2 ∗ 𝑃𝑠𝑐𝑒𝑛𝐼𝐼 ( 3 )

At step 11, the overall probability of cargo tank rupture 𝑃𝑤 is denoted as Pn for the alternative

design and as Pr for the reference design.

At step 12, the ratio between the consequence Cn of a cargo tank rupture for the alternative

design and the consequence Cr of a cargo tank rupture for the reference design is determined

using the following Equation (4):

𝐶𝑛/𝐶𝑟 = 𝑉𝑛/𝑉𝑟 ( 4 )

where

Vn : maximum capacity of the largest cargo tank in the alternative design; and

Vr : maximum capacity of the largest cargo tank in the reference design.

Step 13 is the final step in which the ratio 𝑃𝑟⁄𝑃𝑛 is compared with the ratio 𝐶𝑛/𝐶𝑟. If 𝐶𝑛/𝐶𝑟 ≤

𝑃𝑟⁄𝑃𝑛, the alternative design is proved to be at least as safe as the reference design and the design

can be accepted.



2.4 Determination of the Collision Energy Absorbing Capacity

2.4.1 General

Finite Element Analysis (FEA) is used to determine the collision energy absorbing capacity.

The applied FE code should be capable of dealing with both geometrical and material non-

linear effects. Examples of the applicable codes include LS-DYNA, PAM-CRASH, ABAQUS

and so on. The calculations will be validated by a recognized classification society.

2.4.2 Creating the Finite Element Models

FE models should be developed for both reference design and alternative design. Each model

should be capable of capturing plastic deformations corresponding to the collision scenarios

considered. The section of the cargo area should be modelled under the supervision of a


All three translational degrees of freedom are to be restrained at both ends of the modelled

section. The global horizontal hull girder bending of the vessel is not considered in most

collision cases. Thus, for the evaluation of plastic deformation energy, only half beam of the

vessel needs to be considered with the constraint in the transverse displacements at the

centreline CL. After generating the FE model, it is imperative to perform a trial collision

calculation to make sure that there is no plastic deformation near the constraint boundaries or

else the model should be extended. The collided area of the structures should use a sufficiently

fine mesh, while a more coarse mesh is applied for the other parts of the model. The fineness

of the element mesh must be adequate to capture the realistic rupture of elements including

local folding deformations. The maximum element size used should not exceed 200 mm in the

collision areas. The ratio between the longer and the shorter shell element edge should be

smaller than the value of three. In addition, the ratio between element length and element

thickness must be greater than five. Other values shall be validated with the recognized

classification society.

Plate structures, such as shells, webs, stringers, etc. can be modelled as shell elements and

stiffeners as beam elements, also taking into account cut-outs and holes in the collision areas.

When making the FE simulations, the ‘node on segment penalty’ method shall be activated for

the contact option, for example, “contact_automatic_single_surface” in LS-DYNA, “self-

impacting” in PAM-CRASH and so on.


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2.4.3 Material Properties

Due to the extreme behaviour of materials and structures during a collision, a true stress-strain

relations shall be used to define the materials as shown in the following Equation (5):

𝜎 = 𝐶. 휀𝑛 ( 5 )

where

𝑛 = ln(1 + 𝐴𝑔);

𝐶 = 𝑅𝑚. (𝑒

𝑛)𝑛;

Ag = the maximum uniform strain related to the ultimate tensile stress Rm; and

e = the natural logarithmic constant.

The values Ag and Rm can be obtained from tensile tests.

If only the ultimate tensile stress Rm is known, for shipbuilding steel with a yield stress ReH of

not greater than 355 N/mm2, the following formula shall be used to approximate the Ag value:

𝐴𝑔 =1

0.24 + 0.01395. 𝑅𝑚 ( 6 )

If both Ag and Rm values from the tensile test are difficult to obtain when starting the

calculations, then minimum values defined by the recognized classification society shall be

used. If shipbuilding steel has a yield stress exceeding 355 N/mm2 or materials other than

shipbuilding steel are used, then material properties should be defined in accordance with a


2.4.4 Rupture Criteria

In order to capture the initial rupture of an element in an FEA, a threshold failure strain value

needs to be defined. This predefined value of failure strain will be used as a rupture criteria to

compare with the strain calculated in the finite element. The calculated strain can be effective

plastic strain, principal strain, or for shell elements, the strain in the thickness direction of this

element. If this value exceeds the rupture criteria, the element shall be deleted from the FE

model and the deformation energy in this element will no longer change in the next calculation

steps. The following Equation (7), suggested by (Lehmann and Peschmann, 2002), shall be used

to determine the threshold rupture strain value:



휀𝑓(𝑙𝑒) = 휀𝑔 + 휀𝑒 .𝑡

𝑙𝑒 ( 7 )

where

휀𝑓 : rupture strain;

휀𝑔 : uniform strain;

휀𝑒 : necking;

𝑡 : plate thickness; and

𝑙𝑒 : individual element length.

The values of uniform strain and the necking for shipbuilding steel with a yield stress ReH of

not exceeding 355 N/mm2 shall be taken from the following table:

Table 1 Values for uniform strain and necking for shipbuilding steel (𝑅𝑒𝐻 ≤ 355 N/mm2)

stress states 1-D 2-D

휀𝑔 0.079 0.056

휀𝑒 0.76 0.54

element type beam shell plate

Other rupture criteria may be used with the validation from the recognized classification society

if adequate tests can be provided.

2.4.5 Friction Energy

The collision energy absorbing capacity is determined by the sum of internal energy and friction

energy. The friction coefficient μc is defined by the following Equation (8):

𝜇𝑐 = 𝐹𝐷 + (𝐹𝑆 − 𝐹𝐷). 𝑒−𝐷𝐶|𝑣𝑟𝑒𝑙| ( 8 )

where

𝜇𝑐 = Coulomb friction coefficient;

FD = Dynamic coefficient of friction = 0.1;

FS = Static coefficient of friction = 0.3;

DC = Exponential friction decay coefficient = 0.01; and

|𝑣𝑟𝑒𝑙| = relative friction velocity of contact surfaces.


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3. LITERATURE REVIEW

3.1 Inland Navigation Accident Study

In the past, navigation using inland waterways was solely for the transportation of bulk cargo.

However, nowadays, inland waterways have been used for the transport of not only bulk cargo

but also containers, general and liquid cargo. Therefore, the increase in the inland waterways

navigation has resulted a considerable increase in the probability of collisions, grounding, and

of other undesired events. Regarding this aspect, (Vidan et al., 2012) has proposed a new

approach in order to increase the safety level of inland navigation.

According to Eurostat statistics, in 2013, there was a total of 144 inland water transportation

accidents in the 28 EU (European Unions) member states and 56 % of such accidents took place

in Romania while 17 % were in Austria (See Figure 2).

Figure 2 Number of accidents in inland water transportation in 8 EU countries, 2013 (Eurostat, 2015)

In addition, every year starting from 2005 to 2014, the highest number of accidents occurred in

Romania with the exception of 2010 during which there were 32 accidents in Romania and 38

in Hungary. As for Czech Republic, the number of accident cases decreased by 74 % from the

year 2005 to 2014 (from 23 in 2005 to 6 in 2014). (See Figure 3)



Figure 3 Inland navigation accidents for 8 EU member states (Eurostat, 2015)

Figure 4 Distribution of vessel types involved in ship collisions (Youssef, Kim and Paik, 2014)

Figure 4 shows different types of ships involved in collisions. As can be seen, most of the

vessels taking part in the collisions are tankers, bulk carriers, cargo vessels and containers.

Although there exists statistics of inland navigation accidents for some of the EU member

states, the available data still suffer from incompleteness. To recreate the accident scenarios,

surrounding accident conditions such as ship speed, loading condition, and environmental data


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are necessary. (Youssef et al., 2014) also mentioned that major efforts are still needed to build

up a database of ship collision and grounding accidents.

3.2 Existing Simplified Ship Collision Models and Associated Software

Since 1950s, ship collision models have been developed as the ships were needed to transport

radioactive materials. According to (Ship Structure Committee (SSC), 2002), the collision

analysis can be classified into three sub-models:

Internal sub-models of structural mechanics;

External ship dynamic sub-models; and

Coupled approach of internal and external sub-models.

There are various existing models that use different sub-models and coupling approaches.

3.2.1 Internal Sub-models of Structural Mechanics

Experimental approach or the correlation of actual collision data has been applied in order to

evaluate the internal mechanics of ship collision. (Minorsky, 1959) was the first to attempt a

simplified formulation of the ship resistance to collision. His formula was based on the

investigation of 27 ship-ship collisions. From these collisions, he was able to derive a relation

between damaged volume of the steel structure and the absorbed energy: (Figure 5)

∆𝐾𝐸 = 47.2𝑅𝑇 + 32.7 ( 9 )

where

ΔKE : energy absorbed by the struck ship [MJ]; and

RT : Resistance factor or damaged volume of steel structure of struck ship [m3].

The advantage of Minorsky’s formulation is its simplicity. However, it was only valid for large

energy collisions. There was no influence of material properties, side structural arrangement

and deformation mode in the assessment of total absorbed energy.



Figure 5 Minorsky’s Correlation (Minorsky, 1959)

Many experiments have also been carried out to analyse ship collisions since the early 1960s.

For example, during the period of 1967 to 1976, Germany conducted 12 ship model tests. A 7-

year project on the prediction of tanker structural failure and oil spillage was carried out in

Japan from 1991 to 1997. The purpose was to analyse the dynamic process of structural damage

and the process of oil spill and water ingress through the damaged hull. A series of full-scale

collision experiments was carried out in Netherland in 1991 (Carlebur, 1995). See Figure 6.

So far the experimental results were proved to be quite accurate but their application was limited

by the necessity of expensive production of side structure and striking bow. Thus, a lot of

researchers and scientists tried to find various simplified ways to deal with the ship collision.

The usual approach is to decompose the struck ship into various substructures or components,

such as plates, stiffeners, web frames and panels, etc. In the paper of (Le Sourne et al., 2012),

it was mentioned that the individual structural members could be classified into three categories,

namely, the web girders, the side panels and the intersection elements. The theoretical models

of each of these components can be found in literature. Some examples of these documents

include (Wierzbicki, 1995), (Wang and Ohtsubo, 1997), (Amdahl, 1983), (Zhang, 1999),

(Zhang, 2002), (Simonsen, 1997) and so on.


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Figure 6 Full-scale collision experiment in Netherlands. Figure available from: (Zhang, 1999)

Using the above mentioned simplified approaches, closed form analytical formulations of the

resistance of each unit may be derived and by combining all individual resistances, a global

evaluation of the ability of a ship to withstand an impact with another vessel was formulated.

3.2.2 External Ship Dynamics Sub-models

There are various approaches to deal with the ship external dynamic behaviour during collision.

The approaches may be classified into two categories:

One or two degree of freedom models; and

Three degree of freedom models.

3.2.2.1 One or two degree of freedom models

One degree of freedom model is the simplest approach to deal with external dynamic of ship

collision proposed by (Minorsky, 1959) in which the surge velocity of the striking ship and the

sway velocity of the struck ships are in the same direction. Additional hypothesis are that the

kinetic energy in the longitudinal direction of struck ship is small, the collision is assumed to

be fully inelastic and the rotations are neglected for both colliding ships. In this method, the

worst case scenario for the crashworthiness evaluation of the vessels has been considered while

keeping the conservation of momentum to derive the formula for the sway velocity of struck



ships. Using the velocities, the absorbed kinetic energy in the struck ship in transverse direction

can be expressed as follows:

∆𝐾𝐸 =𝑀𝐴 𝑀𝐵

2𝑀𝐴 + 1.43 𝑀𝐵 (𝑉𝐵 𝑠𝑖𝑛 ∅)2 ( 10 )

where

ΔKE : total energy absorbed in collision;

MA : mass of the struck ship;

MB : mass of the striking ship; and

VB : velocity of the striking ship at impact.

Another approach to deal with the dynamics of ship collision is the computer program named

DAMAGE which was developed at Massachusetts Institute of Technology (MIT). Additional

degree of freedom and yaw motion of struck ship has been considered. The software can be

used to predict structural damage for grounding or right angle ship-ship collisions with

deformable side and deformable bow. One main advantage of DAMAGE is its modern

graphical user interface (GUI) that allows for making the analysis of ship structural

crashworthiness with no particular background in that field. However, one of the drawbacks is

that DAMAGE cannot be applied for collision with oblique striking angles or for struck ships

with initial velocity.

3.2.2.2 Three degree of freedom models

Three degree of freedom model was developed by (Hutchison, 1986). He generalized the

Minorsky’s method by considering all horizontal degree of freedom; surge, sway and yaw. The

virtual mass matrices were developed for both struck and striking ships, including the added

mass terms. Using these matrices and the velocity vector, the kinetic energy and momentum of

the ships were determined. (Rawson et al., 1998) also used similar model. Recently, the

Simplified Collision Model (SIMCOL) has been developed with the support of the Society of

Naval Architects and Marine Engineers (SNAME) and Ship Structure Committee (SSC). It

provides a simultaneous time-stepping solution of external ship dynamics and internal

mechanics. (Pedersen and Zhang, 1998) also provides expressions for absorbed energy

uncoupled with internal mechanics. By analysing the motions and impulses around the impact

point, the absorbed kinetic energy for longitudinal and transverse directions relative to the


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struck ship is derived with the assumption of small rotation and constant ratio of absorbed

plastic deformation energy. This approach has been used in the Technical University of

Denmark (DTU) collision simulation model.

3.2.3 Coupled Approach of Internal and External Sub-models

When internal mechanics and external dynamics couple, both effects are taken into account in

one simulation model. This approach provides more accurate result of ship collisions. It is,

however, very complicated to consider the simulation with large water domain which will

require a lot of time and challenges. So, a simple and computationally fast method that includes

all the significant phenomena is needed for the numerical simulation of external dynamics of

ship collision.

(Brown, 2002) proposed a two-dimensional coupled method and compared the calculated

deformation energy with that evaluated with the decoupled approach of (Pedersen and Zhang,

1998). (Pill and Tabri, 2011) presented a coupled approach for the simultaneous analysis of

inner mechanics and external dynamics with finite element (FE) code LS-DYNA. The obtained

simulated results were compared with experimental results and good agreement was achieved.

However, in their simulation method, the restoring forces, the gravity force and the

hydrodynamic damping were not included. The added masses also need to be considered for all

motion components to simulate a wider range of collision scenarios.

(Le Sourne et al., 2012) presented a user-friendly rapid damage assessment tool named SHARP

for ship collision. In this tool, the upper bound theorem was applied to calculate resistant forces

and internal energies of structural elements involved in the collision process. The crushing

forces are calculated based on super-element theory, allowing for the calculation of roll, yaw

and pitch moments at the centre of gravity of the colliding ships. The results are then transferred

to Mitsubishi Collision (MCOL). MCOL is an external dynamic program used to determine the

striking and struck ship dynamics by solving the hydrodynamic force equations and returns the

positions, velocities and accelerations of their centres of gravity to the internal mechanics

solver, also see (Le Sourne et al., 2001). With that approach based on 6 Degrees-of-Freedom

(DOF) movements, it is possible to take into account ships large rotations as well as gyroscopic

effects and hydrodynamic damping (wave and viscous damping).



4. SHIP COLLISION THEORY

4.1 General

When two ships collide, the kinetic energy possessed by their motions is partly transformed

into the deformation energy in the structural elements of striking and struck ships. The process

will continue until the speed of both vessels become equal. The main laws governing the

dynamics and kinematics during the process are the conservation of momentum and the

equilibrium of force and energy.

Generally, the mechanics of ship collision can be divided into two main parts:

Internal mechanics and

External dynamics.

The internal mechanics involves structural behaviour in the striking bow and the side structure

of the struck ship. The structural crashworthiness such as material yielding, crushing, folding,

fracture, and so on are evaluated. Deformations taking place are usually many times larger than

the structural thickness and the energy is mainly dissipated in relatively localized regions and

is usually in the form of an inelastic straining. On the other hand, the external dynamics deals

with the rigid body global motion of the colliding ships and their interaction with the

surrounding water. Refer to (Paik, 2007) for further reference.

As the purpose of this thesis is to compare the analysis results of SHARP with LS-DYNA, it is

very important to understand the basis of these two main approaches. SHARP is developed

using an analytical approach based on Super-Element Theory while LS-DYNA is developed

using a numerical approach based on Finite Element Theory. Thus, in this section, the basic

theories underlying Finite Element and Super-Element Methods will be explored.

4.2 Finite Element Theory

4.2.1 General Equation (Le Sourne, 2015)

A recent development in computing technology has made it possible to use finite element

analysis in ship collision problems which especially require to solve non-linear matrix equation

system. The dynamic equation system which involves movement of the structural nodes can be

represented by the following discrete Equation (11):


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[𝑀]. {��(𝑡)} + [𝐶]. {��(𝑡)} + [𝐾]. {𝑢(𝑡)} = {𝐹(𝑡)} ( 11 )

where

{��(𝑡)}, {��(𝑡)} 𝑎𝑛𝑑 {𝑢(𝑡)} : nodal acceleration, velocity, and displacement of the nodal vector

matrix;

[𝑀] : structural mass matrix;

[𝐶] : damping matrix;

[𝐾] : stiffness matrix; and

{𝐹(𝑡)} : total force vector matrix.

4.2.2 The Newmark Method (Le Sourne, 2015)

To solve Equation (11), a direct integration method known as Newmark Method is applied. It

solves the solution at time step 𝑡𝑛+1 = 𝑡𝑛 + ∆𝑡 when the solution at time step 𝑡𝑛 is known.

The initial conditions are:

𝑢(0) = 𝑢0 and ��(0) = ��0.

To get the approximate displacement and velocity at the next time step 𝑡𝑛+1, Taylor’s series

developments are used as follows:

𝑀��𝑛+1 + 𝐶��𝑛+1 + 𝐾𝑢𝑛+1 = 𝐹𝑛+1 ( 12 )

𝑢𝑛+1 = 𝑢𝑛 + ∆𝑡��𝑛 +∆𝑡2

2[(1 − 2𝛽)��𝑛 + 2𝛽��𝑛+1] ( 13 )

��𝑛+1 = ��𝑛 + ∆𝑡[(1 − 𝛾)��𝑛 + 𝛾��𝑛+1] ( 14 )

Where 𝛽 and 𝛾 are Newmark’s constants that will determine solution system of Equation (12).

For example, when 𝛽 value is zero, the corresponding integration scheme is said to be explicit.

On the other hand, it is said to be implicit if 𝛽 is not equal to zero.

Displacement and velocity predictors are defined so that the solution depends only on the

known quantities calculated at time step 𝑡𝑛.



��𝑛+1 = 𝑢𝑛 + ∆𝑡��𝑛 +∆𝑡2

2(1 − 2𝛽)��𝑛 ( 15 )

��𝑛+1 = ��𝑛 + ∆𝑡(1 − 𝛾)��𝑛 ( 16 )

Then, by substituting those predictors into Equations (12), (13) and (14), the following systems

of equations are obtained:

(𝑀 + 𝛾∆𝑡𝐶 + 𝛽∆𝑡2𝐾)��𝑛+1 = 𝐹𝑛+1 − 𝐶��𝑛+1 − 𝐾��𝑛+1 ( 17 )

𝑢𝑛+1 = ��𝑛+1 + 𝛽∆𝑡2��𝑛+1 ( 18 )

��𝑛+1 = ��𝑛+1 + 𝛾∆𝑡��𝑛+1 ( 19 )

Thus, initial acceleration becomes: (𝑀 + 𝛾∆𝑡𝐶 + 𝛽∆𝑡2𝐾)��0 = 𝐹0 − 𝐶��0 − 𝐾𝑢0.

4.2.3 Explicit Scheme (Le Sourne, 2015)

The system is said to be explicit if the above Equation (17) is solved by using 𝛽 = 0.

Considering central difference scheme (𝛾 =1

2) with undamped structural system, the following

equations are derived:

𝑀��𝑛+1 = 𝐹𝑛+1𝑒𝑥𝑡 − 𝐹𝑛+1

𝑖𝑛𝑡 ( 20 )

un+1 = un+1 ( 21 )

un+1 = un +1

2∆tun+1 ( 22 )

where

𝐹𝑛+1𝑒𝑥𝑡 : the vector of the external loads applied to the structure at time 𝑡𝑛+1;

𝐹𝑛+1𝑖𝑛𝑡 : the vector of internal forces and can be expressed as:

𝐹𝑛+1𝑖𝑛𝑡 = 𝐾𝑢𝑛+1 = ∫ 𝐵𝑇(𝜎𝑛+1)𝑑𝑣

𝑉 ; where 휀 = 𝐵(𝑢).

In the case of an elastic problem, 𝜎𝑛+1 is calculated from the increment of the deformation (Δɛ)

between tn and tn+1. Then,


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∆𝑢 = 𝑢𝑛+1 − 𝑢𝑛 = ∆𝑡��𝑛 +∆𝑡2

2��𝑛 ( 23 )

∆휀 = 𝐵(∆𝑢) ( 24 )

𝜎𝑛+1 = 𝜎𝑛 + 𝐻∆휀 ( 25 )

where H is the Hooke matrix.

If mass matrix M is diagonal, then the system is decoupled. This scheme is known as explicit

integration scheme and widely used in LS-DYNA, ABAQUS explicit, DYTRAN, etc.

4.2.4 Implicit Scheme (Le Sourne, 2015)

If 𝛽 is not equal to zero, then the equations can be generalized as follows:

(1

𝛽∆𝑡2𝑀 +

𝛾

𝛽∆𝑡𝐶 + 𝐾) 𝑢𝑛+1 = 𝐹𝑛+1 − 𝐶��𝑛+1 − 𝐾��𝑛+1 ( 26 )

��𝑛+1 =𝑢𝑛+1 − ��𝑛+1

𝛽∆𝑡2 ( 27 )

��𝑛+1 = ��𝑛+1 + 𝛾∆𝑡��𝑛+1 ( 28 )

In the above equations, the Newmark constants β = 0.25 and γ = 0.5 are usually applied and the

method is known as medium acceleration method. However, this scheme of solving the

equations needs the system matrix to be inverted and recalculated for each time step, so it can

sometimes require a huge computational effort.

In general, the implicit formulation is applied for slow speed dynamic problems while the

explicit scheme is more useful for high speed dynamic problems such as vehicles collisions.

However, the explicit solver is only conditionally stable and so a very small time step as well

as a large number of iterations are necessary in order to maintain the computational convergence

and stability.

4.2.5 LS-DYNA and MCOL

For the ship-ship collision analysis, LS-DYNA finite element explicit code can be utilized by

coupling with outer collision dynamics program MCOL. The main reason for using the explicit



methodology is that high level of non-linearity, contact, friction and rupture processes are

taking part in ship collision. Therefore, so as to reduce the required computational efforts and

to ease the convergence of the solutions, rather than implicit methods, explicit methodologies

are more suitable as mentioned by (Wu et al., 2004).

Figure 7 shows ship collision simulation using LS-DYNA/MCOL. In this type of simulation,

only the collision area of both ships are meshed and the remaining parts are modelled by using

rigid bodies described by inertia matrix and the centre of mass position. The hydrodynamic

matrices such as stiffness, inertia, and damping are prepared as inputs. The crushing forces are

first calculated in LS-DYNA using the methodologies explained previously. Then, the results

are transmitted to MCOL in which the rigid ship motion equations are solved as described by

Equation (29). The obtained new position 𝑥, velocity �� and acceleration �� of ship centres of

gravity are then transmitted from MCOL to LS-DYNA for the next integration time step. In this

way, it is possible to consider both external dynamics and internal mechanics for ship collision

problems. Referring to (Le Sourne et al., 2003)

[𝑀 + 𝑀∞]�� + 𝐺�� = 𝐹𝑊(𝑥) + 𝐹𝐻(𝑥) + 𝐹𝑉(𝑥) + 𝐹𝐶 ( 29 )

where

x : the earth-fixed position of the centre of mass of the ship;

𝑀 : the structural mass matrix;

𝑀∞ : the added mass matrix;

𝐺 : gyroscopic matrix;

𝐹𝑊 : wave damping force vector;

𝐹𝐻 : restoring force vector;

𝐹𝑉 : viscous force vector; and

𝐹𝐶 : contact force vector.


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Figure 7 LS-DYNA/MCOL collision simulation system (Le Sourne et al., 2003)

4.2.6 Advantages and Disadvantages of using LS-DYNA/MCOL

The advantage of using LS-DYNA/MCOL is its relative accuracy and in some cases, it may

even replace the model experiments. For example, as can be seen in Figure 8, the LS-DYNA

simulation result is superposed on the photo of the real ship hull after collision and the accuracy

of the software can be clearly observed. On the other hand, one major drawback is that to obtain

reliable results, the mesh size should be particularly small. This makes the computation time to

be very long. As the structure of the ship is already a complicated construction, a large number

of elements are required for modelling and as a result, the computation may take several

hundreds of hours to complete.

Figure 8 Comparison of LS-DYNA/MCOL simulation with reality (Le Sourne et al., 2003)



4.3 Super Element Theory

4.3.1 General Equations

The basic idea of using super-element method consists of splitting the vessel into several

structural macro-components also known as super-elements. A closed-form expression giving

the resistant force as a function of the element indentation is used to characterize these elements.

During the collision process, the energy absorption, collision forces and the penetration of the

striking ship are evaluated along with the activation of the super-elements involved in the

process. This is done according to the upper-bound theorem which states that “if the work rate

of a system of applied loads during any kinematically admissible collapse of a structure is

equated to the corresponding internal energy dissipation rate, then that system of loads will

cause collapse of the structure.” (Jones, 1997).

Mathematically, the maximal force causing the collapse of a given super-element with volume

V can be expressed by equating the external energy and the internal energy rates as follows:

(Available from: Buldgen et al., 2012)

��𝑒𝑥𝑡 = 𝐹. �� ( 30 )

��𝑖𝑛𝑡 = ∭ 𝜎𝑖𝑗 . 𝜖��𝑗 . 𝑑𝑉

𝑉

( 31 )

From (30) and (31), upper-bound theorem writes :

𝐹. �� = ∭ 𝜎𝑖𝑗 . 𝜖��𝑗 . 𝑑𝑉

𝑉

( 32 )

where

��𝑒𝑥𝑡 : external energy rate;

��𝑖𝑛𝑡 : internal energy rate;

𝐹 : maximal force responsible for the collapse of a given super-element;

�� : penetrating speed of the striking ship;

𝜎𝑖𝑗 : stress tensor of the super-element; and

𝜖��𝑗 : strain rate tensor of the super-element.


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To solve the Equation (32), the following hypotheses were made:

Materials of the elements are assumed to be perfectly rigid-plastic to avoid strain

hardening and strain rate effects.

The total internal energy rate is the sum of the contribution of bending and membrane

effects which are assumed to be completely uncoupled.

For a plate in a plane-stress, the bending effects are assumed to be confined in a certain

number m of plastic hinge lines.

For example, with the assumptions made above, the bending energy rate ��𝑏 and membrane

energy rate ��𝑚 of a plate with is impacted out of its plane can be determined with the help of

the following two formulae:

��𝑏 = 𝑀0 ∑ ��𝑘𝑙𝑘

𝑚

𝑘=1

��𝑚 =2𝜎0𝑡𝑝

√3 ∬ √𝜖11

2 + 𝜖222 + 𝜖12

2 + 𝜖11𝜖22 𝑑𝐴

𝐴

( 33 )

where,

𝑀0 : fully plastic bending moment;

𝐴 : area of the plate;

𝑡𝑝 : thickness of the plate;

��𝑘 : rotation of the hinge number k; and

𝑙𝑘 : length of the hinge number k.

Solving the above equations, however, still presents a number of challenges, one of which is

how to obtain the strain rate tensor. To calculate this, the displacement fields which are close

enough with those observed on impact trials or on numerical simulations are chosen. One

problem with the upper-bound method is that it may overestimate the resistance if the

displacement fields are not in good agreement with the reality.

To be able to apply the above method, the considered vessels need to be divided into simple

structures (the so-called super-elements) and displacements fields are chosen for each of them

according to the collision scenario to be simulated, namely, right angle collision and oblique

angle collision. As in the case of right angle collision simulation, the structure of the struck ship

can be represented by four types of super-elements as follows: (Lützen et al., 2000)



Super Element SE1: a rectangular plate simply supported on four edges and will be

subjected to an out-of-plane deformation during collision (See Figure 9a). For example,

inner and outer side plating and longitudinal bulkheads.

Super Element SE2: a rectangular plate simply supported on three edges with the last

one being free edge and will be subjected to an in-plane loading during collision. The

plate will deform like a concertina with successive folds until fracture along with the

tearing of supported edges (See Figure 9b). For example, decks, transverse bulkheads,

web girders, frames, bottom and inner-bottom.

Super Element SE3: a beam subjected to a perpendicular transverse force. It will

collapse in two different phases; firstly, the occurance of three plastic hinges and

secondly, behaviour like a plastic string (See Figure 9c). For example, small stiffeners

such as longitudinals.

Super Element SE4: X-T-L form intersections which will be crushed axially until they

are completely deformed along with their initial length during collision (See Figure 9d).

For example, the junctions of vertical and horizontal structural members.

(a) Plate subjected to out-of plane deformation (c) Beam impacted eccentrically

(b) Plate subjected to in-plane deformation

(d) X-T-L form intersections

Figure 9 Illustrations of super-elements for perpendicular collisions (Le Sourne et al., 2012)


A.D.N. Regulations

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For the oblique angle collision case, the structural elements are divided into six different super-

elements as follows (Buldgen et al., 2012):

Super Element SE1: a plate simply supported by four edges and submitted to an out-

of-plane impact with oblique angle (See Figure 10a). For example, side shell, inner side

shell, longitudinal bulkhead.

Super Element SE2: a vertical plate simply supported on three edges with the

remaining free edge. Collision is occurred on the free edge at an angle other than 90

degree (See Figure 10b). For example, transverse bulkhead.

Super Element SE3: this element is similar to SE2 except collision is occurred inside

the structure and the modes of deformation are different (See Figure 10c). For example,

transverse bulkhead, web girders, frames, etc.

Super Element SE4: beam element which is considered to be clamped at both ends

(See Figure 10d). For example, longitudinal stiffeners.

Super Element SE5: this element is absolutely similar to the X-T-L form intersections

already mentioned above. The only difference is that the collision angle is assumed to

be different from 90 degree (See Figure 10e). For example, junction of vertical and

horizontal structural members.

Super Element SE6: a horizontal plate, simply supported on three edges and free on

the last one. Structure is similar to vertical one considered in SE2 and SE3. Collision is

assumed to occur at the unsupported edge with a certain angle in the horizontal plane

(See Figure 10f). For example, weather deck.

With these super-elements mentioned above, the structural components of most typical ships

can be modelled and their individual behaviour can be sufficiently evaluated. Each of these

elements has a closed-form expression and it is possible to derive an analytical formulation for

the estimation of the collision resistance. More details of the formula derivations can be found

in (Buldgen et al., 2012).

Generally, throughout the derivation stages, the bow of the striking ship is assumed to be rigid.

However, as in the case of the struck ship side structure being more rigid, then the bow of the

striking ship can be assumed to be deformable with approval from a recognized classification

society. The method for the evaluation of bow crushing force was developed by (Simonsen and



Ocakli, 1999) which is based on a modification of (Amdahl, 1983). They considered that the

striking bow is composed of angles, T-sections, and cruciforms. With the use of theoretical

consideration of energy dissipated during plastic deformation of these elements, a formula for

the average crushing strength can be expressed as follows:

𝜎𝑐 = 2.42 [𝑛𝐴𝑇𝑡2

𝐴]

0.67

[0.87 + 1.27𝑛𝑐 + 0.31𝑛𝑇

𝑛𝐴𝑇(

𝐴

(𝑛𝑐 + 0.31𝑛𝑇)𝑡2)

0.25

]

0.67

( 34 )

where

𝜎𝑐 : the average crushing strength of the bow;

𝜎0 : the flow stress;

t : the average plate thickness of the cross-section under consideration;

A : the cross-sectional area of deformed material;

𝑛𝑐 : the number of cruciform;

𝑛𝑇 : the number of T-sections; and

𝑛𝐴𝑇 : the number of angle and T-sections.

The total crushing force Fc is then obtained by multiplying this strength by the associated cross-

sectional area A of the deformed material as 𝐹𝑐 = 𝜎𝑐𝐴.

4.3.2 SHARP Tool

SHARP is a powerful software which has been developed using C++ program so as to analyze

ship collision rapidly. In SHARP, the internal mechanics are coupled with an adaptive version

of MCOL described in (Le Sourne et al., 2012). The crushing resistances are calculated with

the use of Super Element Theory mentioned in the previous section 4.3.1. The input parameters

such as structural design of struck ship, data of the striking bow, and different collision

scenarios are defined using a graphical user interface as shown in Figure 11.


A.D.N. Regulations

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Figure 10 Descriptions of super-elements for oblique collisions (Le Sourne et al., 2012)



Figure 11 Graphical user interface of SHARP

The definition of the struck ship structure can be limited to the impacted area, consisting of the

surfaces and their associated scantlings. In the case of defining the striking ship bow geometry,

a simplified model of the fore part of the ship which also includes both the bow and the bulb is

used. However, for estimating the bow’s crushing resistance, only longitudinal structural

members are required to model as the method implemented in SHARP does not consider

transverse structural elements of the bow or bulb.

To consider the external dynamic effects during collision, hydrodynamic matrices of both

struck and striking ships need to be prepared using a seakeeping software such as the one

developed by Bureau Veritas and named HydroStar. As can be seen in Figure 12, the crushing

force is calculated using super-element method and roll, yaw, and pitch moments are

determined at the centre of gravity of both ships. These results are then transmitted to an

external dynamic program MCOL which returns new acceleration, velocity, and position of

each ship. The simulation terminates when the surge velocity of the striking ship is equal to the

sway velocity of the struck ship. The outputs can be post-treated as crushing force and absorbed

energy in terms of penetration, the hydrodynamic forces acting on the ship side, and graphical

animations of the collision process.


A.D.N. Regulations

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Figure 12 Workflow diagram of SHARP (Le Sourne et al., 2012)

Yes No



5. LS-DYNA AND SHARP SIMULATIONS

In this section, the numerical and analytical simulation procedures carried out by using both

LS-DYNA finite element code and SHARP analytical solver will be presented.

5.1 LS-DYNA/MCOL Simulation Procedures

5.1.1 General

In general, the numerical simulations in LS-DYNA/MCOL consist of three main steps:

Pre-processing using FEMB (Finite Element Model Builder);

Running LS-DYNA collision simulation coupled with MCOL; and

Post-processing by LS-DYNA post-processor LS-PRE/POST.

The required hydrodynamic properties can be determined by using additional hydrodynamic

software such as HydroStar and ARGOS. In this thesis, the same input data obtained from the

previous EMSHIP master thesis (Uzögüten, 2016) will be used.

The Finite Element simulation with LS-DYNA software has been carried out according to the

following flow chart (See Figure 13).

Figure 13 Flow-chart of LS-DYNA simulation process

3D Modelling and Meshing

Define Elements, Materials and

Parts

Define Boundary Conditions

Define Collision Scenarios

Define Contacts Computation

Controls

Solution Controls

Run the AnalysisResults and Post-

processing


A.D.N. Regulations

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5.1.2 Modelling and Meshing

As can be seen in Figure 13, the first step for the LS-DYNA simulation is to build finite element

3D models for both colliding vessels. In this thesis, the struck and striking ships were modelled

and meshed by using FEMB (Finite Element Model Builder).

5.1.2.1 Struck Ship: Type C Double Hull Tanker

The struck ship is a typical Type C Double Hull tanker which has the following characteristics:

Length overall: 125 m;

Breadth: 11.4 m;

Draught: 4.5 m;

Depth: 6 m;

Displacement: 5863.3 tonnes.

In Figure 14, finite element model of Type-C inland tanker is shown. Note that only three cargo

holds were modelled. The rest of the ship was taken into account by defining a rigid body on

the two end bulkheads that were characterized by the ship’s true mass, inertia and the centre of

gravity. The size of the maximum element, the ratio between element length and thickness, and

the ratio between longer and shorter shell element edge were defined in accordance with the

A.D.N. Regulations. However, only reference design has been modelled in this thesis since the

main purpose is to validate the SHARP tool by comparing the obtained results.

Figure 14 Finite Element model of struck ship (Type C inland double hull tanker)



5.1.2.2 Striking ships: V-shape bow and Push barge bow

Two striking ship bows were considered according to the A.D.N. Regulations, namely:

V-shape bow and

Push barge bow.

These two bow shapes were modelled according to the geometries given by A.D.N. Regulation

at section 9.3.4.4.8. Figure 15 shows the finite element models of the striking ships. Note that

only the fore part of the striking ship needs to be modelled. The rest of the striking ship was

represented by a rigid body with associated inertia, true mass and centre of gravity. In addition,

it was not needed to model the detailed structure of the striking bow as it will be considered as

a rigid body as recommended by A.D.N. Regulations at section 9.3.4.4.6.2.

To be able to define the required hydrodynamic properties, two real ships were chosen, namely,

Touax for the push barge bow and Odina for the V-shape bow. They have the following

characteristics:

Table 2 Main characteristics of the striking ships

V-shape bow Push barge bow Units

Length overall 85.95 88.5 m

Breadth 10.95 11.4 m

Draught 3.65 3.4 m

Depth 4.6 4.32 m

Displacement 3040.6 3228.7 tonnes

(a) Push-barge bow

(b) V-shape bow

Figure 15 Finite Element models of striking ship bows


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5.1.3 Elements, Materials and Parts

5.1.3.1 Elements

According to A.D.N. Regulations, plate structures such as side shells, inner side shells, web

frames, etc. were modelled as shell elements and stiffeners such as bottom longitudinals, deck

longitudinals, etc. were modelled as beam elements.

Belytschoko-Tsay formulation was used for the shell elements as it is more computationally

efficient than Hughes-Liu shell elements. Five integration points were considered throughout

the thickness of each shell element so as to capture the realistic plastic deformations. As for the

beam elements, Hughes-Liu beam element formulation was applied as this type of beam

provides an out-of-plane bending which is not provided by truss beam elements. Refer to

(Hallquist, 2006) for further details.

5.1.3.2 Materials

The material of the struck ship is Grade A shipbuilding steel with the following properties:

Young Modulus: 210 000 MPa;

Yield Strength: 250 MPa;

Ultimate Strength: 512 MPa.

In LS-DYNA modelling, two materials were defined as follows:

piecewise-linear-plasticity material and

rigid material

Piecewise-linear-plasticity material can be defined with or without considering a threshold

value for the failure strain. The rigid material was defined in order to take into account the

remaining part of the struck ship which was not included in the modelling.

With the use of piecewise-linear plasticity material, an elasto-plastic behaviour can be

represented and the corresponding stress-strain relation can be obtained by using the following

formula suggested by A.D.N. Regulation:



𝜎 = 𝐶. 휀𝑛 ( 35 )

where

𝑛 = ln(1 + 𝐴𝑔);

𝐶 = 𝑅𝑚. (𝑒

𝑛)𝑛;

Ag = the maximum uniform strain related to the ultimate tensile stress Rm; and

e = the natural logarithmic constant.

Using Equation (35), an arbitrary stress-strain curve was plotted and shown in Figure 16. Note

that the elastic behaviour of the material is only represented by 250 MPa and any values lower

than this were not considered as the deformations taking place during collision were usually

very high.

Figure 16 Arbitrary stress-strain curve for elasto-plastic material

The required material failure strain for the material was determined according to the formula

suggested by A.D.N. Regulations (see also Lehmann and Peschmann, 2002):

휀𝑓(𝑙𝑒) = 휀𝑔 + 휀𝑒 .𝑡

𝑙𝑒 ( 36 )

where

휀𝑓 : rupture strain;

0.0E+00

1.0E+08

2.0E+08

3.0E+08

4.0E+08

5.0E+08

6.0E+08

0 0.05 0.1 0.15 0.2 0.25

Str

ess

(N/m

^2

)

Plastic Strain

Arbitrary Stress-Strain Curve


A.D.N. Regulations

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휀𝑔 : uniform strain;

휀𝑒 : necking;

𝑡 : plate thickness; and

𝑙𝑒 : individual element length.

To use Equation (36), the following two assumptions were made:

First, the structures that were considered to fail due to excessive tension include side

shell, sheer strake, bilge plate, inner side shell, longitudinal bulkhead and webs. Note

that web frames do not fail by tension, however, they can fail by excessive shearing

especially at the connections of webs with weather deck or bottom plating.

Secondly, the parts which were subjected to compression such as deck, bottom, double

bottom, etc. were considered to still possess enough strength to resist the collision

without tearing even after plastic deformation. Therefore, for those parts, failure strain

was not considered.

With these two assumptions, the failure strain can be calculated for the concerned parts (See

Table 3). The definitions of parts and sections will be described in the next section 5.1.3.3.

Table 3 Material failure strain calculation

Part no. Item 𝒕

[m]

𝒍𝒆

[m] 𝜺𝒇

2 Web frame (upper part) 0.0064 0.126 0.08

6 Web frame (lower part) 0.008 0.126 0.09

5 Inner side shell 0.0075 0.1325 0.09

7 Outer side shell 0.0095 0.1325 0.09

9 Bilge plate 0.0115 0.1325 0.10

10 Sheer strake 0.0235 0.1325 0.15

14 Side longitudinals 0.0100 0.1325 0.14

15 Side longitudinals 0.0100 0.1325 0.14

The values of 휀𝑔 and 휀𝑒 required for the calculations were taken from Table 1 described in

Section 2.4.4. As can be seen, the values of the failure strain determined from Equation (36)

have some underestimations when they were compared with the reality. According to (Le

Sourne, 2015), a “classical” rupture strain value of 20 % was adopted in this thesis for the



simulations of LS-DYNA. Regarding this matter, also refer to (Simonsen, 2000), (Lehmann

and Peschmann, 2002), (Naar, 2002) and (Kitamura, 2002) for more references.

The material of the striking ship is Grade-A shipbuilding steel with the following properties:

Young Modulus: 210 000 MPa;

Yield Strength: 250 MPa;

Ultimate Strength: 512 MPa.

Note that according to A.D.N. Regulations, a rigid material was used to model the striking ship

bows.

5.1.3.3 Parts

Parts in LS-DYNA are used to define material information, properties of the section used,

hourglass type, thermal properties, and a flag for part adaptivity. Each part is comprised of

elements that have the same properties. In this way, same structural components can be grouped

under the same part. For example, bottom for part 33, weather deck for part 28, side shell for

part 7 and so on have been applied in the current LS-DYNA models. The following diagram

shows the way the keywords are organized in order to model in LS-DYNA:

Figure 17 Organization of keywords to define structural parts in LS-DYNA

In addition to the PART command, the PART_INERTIA option allows the inertial properties

and initial conditions to be defined instead of calculating them from the finite element mesh.

This option, however, can be applied for the rigid material only. Thus, in this case, the two

constraint boundaries and the striking ships were defined by using that command.


A.D.N. Regulations

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5.1.4 Boundary Conditions

Boundary conditions are imposed on the two transverse bulkheads which are located at both

ends of the struck ship model. As mentioned in the previous section 5.1.3, PART_INERTIA

command was used to define the associated true mass, inertia and centre of gravity for the

remaining part of the struck ship. The striking ship was also treated as a rigid body. At each

time step, the crushing forces were calculated in LS-DYNA and then were transferred to an

outer dynamic program named MCOL which will then calculate the translational movement as

well as rotational movement of the ship.

One problem with MCOL is that it is not parallelized, i.e., the calculations cannot be made

simultaneously in different processors of the computers. Generally, LS-DYNA uses very small

time steps (usually microseconds) and thus, the simulation needs millions of calculation steps.

Therefore, it is impossible for MCOL to perform all calculation steps with only one processor

or else the simulation will take several hundreds of hours to finish. To solve this issue, MCOL

sub-cycling option can be activated as it permits the MCOL to perform the calculations only at

every N cycle of LS-DYNA calculations. Since the evolution of the hydrodynamic forces is a

lot slower than the evolution of the stresses and strains in the structure, using such option will

not affect the final simulation results. For example, the hydrodynamic forces will not change a

lot during one millisecond while the stresses in the structure may change a lot in one

millisecond.

In order to determine how many calculation steps are required for the MCOL program, a

convergence test needs to be performed. The following test scenarios were chosen to perform

the convergence test for MCOL:

Case 2 (V-shape bow : 90 deg : Between webs : Mid-depth of struck ship);

Case 3 (Push barge bow : 55 deg : At web : Mid-depth of struck ship); and

Case 4 (Push barge bow : 55 deg : At bulkhead : Above deck of struck ship).

The collision scenarios mentioned above were taken from the next Section 5.1.5.

Cases 2 and 3 in the above scenarios were considered without rupture strain and case 4 with the

rupture strain. Different MCOL sub-cycling steps (100, 200 and 400) were considered for each

case, making a total of 9 simulations as follows (See Table 4):



Table 4 Convergence tests for MCOL sub-cycling steps

Test Simulation MCOL calculation

Case 2 without rupture strain 100 200 400

Case 3 without rupture strain 100 200 400

Case 4 with rupture strain 100 200 400

As shown in Table 5, the results of MCOL sub-cycling steps are given for each test case. Note

that the striking ship was considered at a constant speed 10 m/s for the convergence tests. The

obtained deformation energies and penetrations are plotted against time (See Appendix A).

Table 5 Results of convergence tests for MCOL

MCOL Deformation energy Penetration

Steps [J] Error % [m] Error %

Case 2 (V-shape bow : 90 deg : Between webs : Mid-depth of struck ship)

100 1.01E+08 4.31

200 1.01E+08 0% 4.36 1%

400 9.79E+07 3% 4.14 5%

Case 3 (Push barge bow : 55 deg : At web : Mid-depth of struck ship)

100 8.72E+07 3.6

200 8.71E+07 0% 3.74 4%

400 8.67E+07 0% 3.77 1%

Case 4 (Push barge bow : 55 deg : At bulkhead : Above deck of struck ship)

100 5.13E+07 3.09

200 5.32E+07 4% 3.19 3%

400 5.36E+07 1% 3.19 0%

In the above table, the error percentage is determined by using the following formulation:

𝐸𝑟𝑟𝑜𝑟 % =𝑀𝐶𝑂𝐿2𝑁 − 𝑀𝐶𝑂𝐿N

𝑀𝐶𝑂𝐿N ( 37 )

where, N = MCOL calculation steps = 100 or 200.

According to the results of the convergence tests shown in Table 5, the following deductions

can be made:

Case 2 has the same results for MCOL100 and MCOL200 calculation steps (0 %

difference for the deformation energy and 1 % for the penetration).


A.D.N. Regulations

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Therefore, it was decided to use MCOL sub-cycling step of 200 as it can give the converged

results for all simulations. The detailed comparisons of the graphs for different MCOL sub-

cycling steps can be found in Appendix A.

5.1.5 Collision Scenarios

The following five scenarios have been defined in LS-DYNA in order to compare the results

with SHARP:

Table 6 Collision scenarios

Scenarios Bow

Type

Collision Angle

[deg] Longitudinal Position

Vertical

Position

Case 1 V-shape 90 At web Under deck

Case 2 V-shape 90 Between webs Mid-depth

Case 3 Push barge 55 At web Mid-depth

Case 4 Push barge 55 At bulkhead Above deck

Case 5 V-shape 90 At web Above deck

In Table 6 shown above, the longitudinal position and vertical position refer to the locations of

the impact point on the struck ship. These locations can be again expressed in terms of

coordinate system in 3D plane (i.e., in terms of X, Y and Z coordinates) as shown in Table 7.

Table 7 Location of the impact points in LS-DYNA

Scenarios Impact Locations [m] Striking

Bow Type

Collision Angle

[deg] X Y Z

Case 1 21.55 5.76 5.65 V-shape 90

Case 2 22.67 5.76 3.72 V-shape 90

Case 3 16.14 5.78 3.89 Push barge 55

Case 4 24.10 5.78 6.24 Push barge 55

Case 5 21.55 5.76 6.37 V-shape 90



Note that in LS-DYNA, the origin point of the global coordinate system was located at the

intersection of the Centreline, the Baseline and 200 mm horizontally from the first bulkhead of

the struck ship model. When defining Y impact location, a margin distance was taken into

account which was defined by the sum of half thickness of struck ship’s side shell, half thickness

of striking ship’s bow and some additional margin distance (about 10-20 mm). A typical

collision simulation setup of LS-DYNA (case 1) is shown in Figure 18.

Figure 18 Typical collision simulation in LS-DYNA (Case 1)

Among those five cases mentioned above, cases 1 to 3 were defined using exactly the same

scenarios used in previous EMSHIP Master thesis (Uzögüten, 2016) in which the scenarios

were defined by following A.D.N. Regulations. However, the vertical impact locations for cases

4 and 5 will be slightly modified in this thesis. Because, the positions defined by (Uzögüten,

2016) were a bit too high for the striking ships and as a result, there were significant vertical

reaction forces, leading the simulation to undesirable condition. (See Figure 19)

This is because when simulating in LS-DYNA, the gravity loading is usually ignored for both

struck and striking ships in order to save time and avoid complexity in the simulation process.

This simplification will not affect the results unless the vertical reaction forces become

important. Therefore, in order to prevent the vertical forces from becoming very large, the

position of the striking ship was lowered by about 800 mm while keeping the draft combination

points to remain inside of the rectangular area bounded by maximum and minimum draughts

of colliding vessels. (See Figure 20)


A.D.N. Regulations

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Figure 19 Undesirable effect (Conceptual diagram)

(a) Push barge bow (b) V-shape bow

Figure 20 Definitions of the vertical impact locations (A.D.N. Regulations, 2015)

Table 8 Draft combinations of struck and striking ships

Case Bow Type Struck Ship [m] Striking ship [m]

Case 1 V-shape 4.5 3.5


Case 3 Push barge 2.72 3.4

Case 4 Push barge 4.5 2.43




In Figure 20, minimum and maximum draughts of striking and struck ships are shown. It can

be observed that even though the vertical positions of case 4 and case 5 were modified, the

choice of the draft combination was ensured to predict the worst case collision scenario, i.e., to

select the possible maximum displacements, in accordance with the A.D.N. regulations.

Hereby, the LS-DYNA simulations can be divided into two categories:

Simulations without rupture strain using a constant striking ship’s speed of 3 m/s; and

Simulations with rupture strain using a constant striking ship’s speed of 10 m/s.

The first category of the aforementioned LS-DYNA simulations aims at checking the validity

of software SHARP without any rupture strain. When rupture strain is not considered, it would

be more realistic to use a lower speed, 3 m/s, instead of using 10 m/s as proposed by the A.D.N.

The aim of the second category is to observe if SHARP tool can be applied for the A.D.N.

Regulations as a replacement of the conventional FE software. Therefore, a total of 10 LS-

DYNA simulations will be performed in the framework of this thesis.

To determine the hydrodynamic properties required for the rigid body calculation, the coastal

area of Belgium (Scheldt estuary – Zeebrugge) was chosen as the investigated incident area

(Figure 21). According to the wave data (12875 measured waves) in this region, the most

probable wave period is approximately 5.25 seconds and the wave frequency is about 1.197

rad/sec. The values of wave damping matrices were taken for this wave period and “.mco” files

were generated for different collision scenarios. The “.mco” files applied in this master thesis

were taken from the previous master thesis (Uzögüten, 2016).

Figure 21 Scheldt estuary – Zeebrugge (available from: Google Map)

Zeebrugge


A.D.N. Regulations

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5.1.6 Contact Type and Friction

Using ‘node on segment penalty’ method, the following two contact options were defined in

LS-DYNA.

CONTACT_AUTOMATIC_GENERAL_ID and

CONTACT_AUTOMATIC_SURFACE_TO_SURFACE.

The first option is to create the self-contact between each part of the struck ship. For example,

the contact between side shell and web frame, local folding of weather deck and bottoms and

so on. The second option is to create the contact between striking and struck ships. Depending

on the scenarios, the contact definition can change especially when failure is considered. In

order to get a rough idea of the collided part and behaviour of the elements involved, it is

important to run some test simulations and make some modifications in the input file if needed.

The friction considered in LS-DYNA is calculated by using the Coulomb friction relation given

by the following Equation (38):

𝜇𝑐 = 𝐹𝐷 + (𝐹𝑆 − 𝐹𝐷). 𝑒−𝐷𝐶|𝑣𝑟𝑒𝑙| ( 38 )

where

𝜇𝑐 = Coulomb friction coefficient;

FD = Dynamic coefficient of friction = 0.1;

FS = Static coefficient of friction = 0.3;

DC = Exponential friction decay coefficient = 0.01; and

|𝑣𝑟𝑒𝑙| = relative friction velocity of contact surfaces.

According to the scenarios simulated in this thesis, the friction coefficients can be computed as

follows:

With 90 degree collision angle ==> |𝑣𝑟𝑒𝑙| = 0 m/s and 𝜇𝑐 = 0.3.

With 55 degree collision angle ==> |𝑣𝑟𝑒𝑙| = 5.74 m/s and 𝜇𝑐 = 0.29.

In SHARP, the Coulomb friction coefficient 𝜇𝑐 has already been set at a predefined value of

0.3. Although there is no option to modify this coefficient in the current version of SHARP,

there is no problem as this is the same value recommended by A.D.N. Regulations.



5.2 SHARP/MCOL Simulation Procedures

5.2.1 General

In general, simulation in SHARP program consists of the following six main steps:

Figure 22 Simulation procedures for SHARP/MCOL

5.2.2 Modelling and Meshing

As shown in Figure 22, the first step of simulating in SHARP involves developing collision

models for both struck and striking ship.

5.2.2.1 Modelling of the struck ship

This step consists of hull form generation and structural modelling. Hull form modelling was

done by defining a parametric model based on the definitions of three sections (aft, middle and

forward) and longitudinal lines. Each section can be modified by shifting 6 control points which

are connected between the sections through longitudinal lines.

After modelling of the hull form, the structures were modelled. This includes defining the ship

surfaces such as decks, bulkheads, hulls and so on and the corresponding scantlings. A fixed

frame spacing in meters was determined before the start of the modelling and only starboard

side needed to be modelled. The other side was automatically created by the software by

Modelling Define materials

Define collision scenarios

Generate hydrodynamic matrices for

MCOL

Run the analysisPost process the

results


A.D.N. Regulations

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generating symmetrical surfaces about the centreline. The complete SHARP model of struck

ship is shown in Figure 23.

Figure 23 Complete SHARP model of struck ship

However, it should be noticed that when modelling structures in SHARP, some details cannot

be modelled such as holes and corrugated bulkheads. To solve this issue, an equivalent plate

thickness has been applied for those specific structures. The equivalent plate thickness was

determined based on the fact that the material volume of the actual and equivalent plate is the

same. The following formula depicts the required equivalent thickness:

𝑡𝑒𝑞 =𝐴𝑎𝑐𝑡𝑢𝑎𝑙𝑡𝑎𝑐𝑡𝑢𝑎𝑙

𝐴𝑎𝑐𝑡𝑢𝑎𝑙 + 𝐴ℎ𝑜𝑙𝑒

( 39 )

where,

𝑡𝑒𝑞 : equivalent thickness of the plate;

𝑡𝑎𝑐𝑡𝑢𝑎𝑙 : actual thickness of the plate;

𝐴𝑎𝑐𝑡𝑢𝑎𝑙 : actual area of the plate; and

𝐴ℎ𝑜𝑙𝑒 : total area of the holes on the plate.

In this thesis, a virtual horizontal deck was required to use as a limit for other surfaces. The

thickness of that surface was assigned as zero so that it would not be included in the calculation.

However, it is found out that this could impose some problems in the meshing process of

SHARP whose influence will be analysed in details in the next section of this thesis.

As can be seen in Figure 24a, SHARP will automatically divide the shell plating into two parts

when virtual plating is used, creating two side shell super-elements instead of one. Usually the

side shell super-element is bounded by two bulkheads at the end, by weather deck at the top



and by the ship’s bottom (See Figure 25b). By considering the virtual deck, this assumption

will change completely and can somehow affect the results. This is illustrated in Figure 25

which highlights the difference in the basic assumption of SHARP. As can be seen, a side shell

should normally be bounded by four clamped ends. However, the presence of the virtual deck

caused an extra clamp end at the position of the deck which could later result in a more rigid

side shell. Therefore, it is imperative to check the effects of the virtual deck in more details.

(a) With virtual deck (b) Without virtual deck

Figure 24 Side shell becoming two super-elements due to virtual deck (Body plan view)

(a) Two side shell super-elements

each with four fixed ends

(b) One side shell super-element

with four fixed ends

Figure 25 Comparison of side shell super-element with and without virtual deck (profile view)


A.D.N. Regulations

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5.2.2.2 Modelling of striking ship

In SHARP, only the fore part of the striking ships was modelled. Although it was possible to

model the striking ship structural configurations in SHARP, only the geometry of the bow was

modelled in this study as A.D.N. demands a rigid striking bow. On the other hand, SHARP is

also able to perform simulations with deformable striking bows.

The geometry of the striking ship bow is a parametric model defined by 9 parameters shown in

Figure 26. The symbols used in the figure are explained in Table 9. As can be seen in the figure,

the deck and bottom are defined by using ellipses and the bulb is assumed to be an ellipsoid.

Figure 26 Model of the striking ship bow in SHARP (Besnard, 2014)

Table 9 Definitions of the parameters used in the SHARP bow model (Besnard, 2014)

Identification of the parameter Notation

Semi major axis of the deck R1d

Semi minor axis of the deck R2d

Semi major axis of the bottom R1b

Semi minor axis of the bottom R2b

Depth D

Length of the bulb RL

Vertical radius of the bulb RV

Horizontal radius of the bulb RH

Distance between the bulb tip and the foremost part of the bow RD



(a) Push barge bow (b) V-shape bow

Figure 27 Models of striking ships in SHARP

Figure 27 shows the models of the two striking ship bows. By comparing these pictures with

finite element models presented in Figure 15, it can be observed that the V-shape bow could be

modelled quite accurately while it was not possible to get an exactly similar bow shape for the

push barge given by A.D.N. So as to obtain a similar push barge bow, the longitudinal curvature

of the ellipse was greatly reduced so that the weather deck would be a flattened curve shape.

Moreover, due to the limitation of the modelling of the knuckles, only one side angle can be

defined. This angle, however, will not be the first point of impact. The first impact point will

be at some point near that angle since the bow has been tilted to 55 degree.

In Figure 28, the intended impact location is defined according to the direction of the striking

ship although the initial impact point will be at the knuckle of the bow. Without making an

adjustment, the original striking ship model of SHARP cannot have the same shape as LS-

DYNA around initial impact point. Therefore, an extra distance of 0.95 m has been added to

the striking ship longitudinal position so that the shape of the bow around knuckle (around

initial impact point) would be as close to the LS-DYNA model as possible.

Figure 28 Adjustments in the push barge bow position in SHARP (Top view)


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Figure 29 highlights the difference in bow shapes between the two models which should also

be taken into account when evaluating the results.

(a) Difference in bow shape (Top view) (b) Difference in bow shape (Profile view)

Figure 29 Comparison of the push barge bow models between LS-DYNA and SHARP

5.2.3 Materials and Rupture Strain

In SHARP, the material properties are characterized by the following parameters:

Young modulus E [MPa];

Yield stress S0 [MPa];

Rupture toughness Rc [N/mm]; and

Rupture strain Ec.

As the material of the struck ship is shipbuilding steel – Grade A that has yield strength of 250

MPa and ultimate strength of 512 MPa, the lower limit 250 [MPa] was taken as the material

yield stress S0 (See Figure 30). The young modulus was taken as 210000 [MPa] while rupture

toughness was taken as 500 [N/mm].

Although SHARP is able to make simulations with or without considering a rupture criteria,

the rupture strain value Ec is still required to define. Therefore, in the case without rupture

strain, very high value of Ec such as 1000 has to be applied. The reason is to prevent any shell

rupture in SHARP and sometimes it is found out that Ec value of 1 or 2 is not enough to prevent

this. With Ec = 1000, the prevention of shell rupture was ensured. As in the case with rupture

strain, the rupture strain value of 0.2 calculated in Table 3 of section 5.1.3.2 was applied.



Figure 30 Stress-strain curves considered for LS-DYNA and SHARP simulations

Figure 30 shows the comparison of stress-strain relation considered in LS-DYNA and SHARP

simulations. As can be seen in the figure, a true stress-strain relation is not applied in SHARP

but rather a plastic flow stress which remains constant until the rupture of the shell. In this

context, an average yield stress of (𝜎0 =𝜎𝑦+𝜎𝑢

2= 317.5 𝑀𝑃𝑎) has been considered in the

master thesis of (Uzögüten, 2016). However, under the assumption of very mild steel for the

inland vessels, only the yield stress up to 250 MPa has been considered in the framework of

this thesis.

5.2.4 Collision Scenarios

The same scenarios used in LS-DYNA will be applied for SHARP as well. However, in order

to take into account the variation inherent to the Super-Element Method, additional 8 collision

locations need to be created around the real impact point. So, for each LS-DYNA simulation, 9

simulations of SHARP will be analysed, making it a total of 90 scenarios. The total energy

absorbing capacity will be taken as the average results of these 9 simulations. The obtained

results were compared numerically as well as graphically and presented in the next section.

Figure 31 shows how those additional impact points can be considered in SHARP.


A.D.N. Regulations

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Figure 31 Impact locations on side shell in SHARP

In the above figure, the values shown are calculated using the structural information of the

struck ship as follows:

Impact point for X distance change (longitudinal) : ± 𝑊𝑒𝑏 𝑓𝑟𝑎𝑚𝑒 𝑠𝑝𝑎𝑐𝑖𝑛𝑔

2

Impact point for Z distance change (vertical) : ± 𝑆𝑡𝑖𝑓𝑓𝑒𝑛𝑒𝑟 𝑠𝑝𝑎𝑐𝑖𝑛𝑔

2

where, web frame spacing is 1.59 m and the stiffener spacing is 0.5 m.

Note that in SHARP, the impact locations were defined by using X and Z (longitudinal and

vertical coordinate) of the global coordinate system whose origin is located at the aft extreme

of the struck ship and at the interception of the ship’s baseline and centreline. In addition, it was

not necessary to determine Y coordinate in SHARP for the collision position as it will

automatically be calculated, taking into account the margin between the two ships. Figure 32

shows typical diagram of the collision simulation (case 1) defined and modelled by SHARP.

Figure 32 Typical collision scenario modelled in SHARP (case 1)



6. COMPARISON AND ANALYSIS

SHARP tool has already been validated for ocean-going tankers and FPSO application cases,

see (Paboeuf et al., 2015). However, in order to validate the use of SHARP program for inland

vessel structure, the following results have been compared between LS-DYNA and SHARP

calculations:

Penetration into the struck ship, and

Struck ship deformation energy.

6.1 Simulations without Rupture Strain

The main focus on this study is to check if SHARP results correspond well with LS-DYNA

without considering the rupture. The striking ship was considered to have a constant speed of 3

m/s for both simulations. Thus, it should be noted that the simulations presented in this Section

do not exactly follow the A.D.N. Regulations. However, the validation tests regarding the

A.D.N. Regulations will be presented in the following Section 6.2.

6.1.1 Case 1 (V-shape bow : 90 deg : At web : Under deck of struck ship)

Table 10 shows the penetration and deformation energy calculated from LS-DYNA when the

tanker has been collided perpendicularly by V-shape bow with a speed of 3 m/s. The impact

point considered in this simulation is at web and just under deck of the struck ship. The results

were taken at 1.2 sec which is at the end of the simulations.

Table 10 Results calculated by LS-DYNA – Case 1 (without rupture strain)

Simulation Time [sec] Penetration [m] Deformation energy [MJ]

1.2 1.1 8.5

In Figure 33, the extent of damage in LS-DYNA after the collision is shown. It can be observed

that not only the side shell but also the deck is damaged due to the impact. The reason why the

weather deck deforms without being collided is that in LS-DYNA, the elements are

simultaneously activated, i.e., there is an interaction between different structural components,

for example, side shell and weather deck in this case. This is usually the case for inland vessels

when the two colliding ships have nearly the same height. Another reason can be that the

thickness of the weather deck (9.75 mm) is quite small compared to the sheer strake thickness


A.D.N. Regulations

71


which is 23.5 mm. Thus, it is obvious that the deformation of the thicker plate (the sheer strake)

has caused the deformation in the thinner one, the weather deck.

Figure 33 Extent of damage in LS-DYNA – Case 1 (without rupture strain)

Table 11 below presents the results of penetration into the struck ship and the deformation

energy calculated by SHARP at 9 impact locations. The extent of damage in SHARP is shown

in Figure 34. The impacted elements are shown in yellow colour while the destroyed elements

are in red. As there is no red colour, it can be said that there is no shell rupture. Moreover, it is

found out that the deck super-element has not been activated at the end of the simulation. This

is because in SHARP, the super-elements are independently activated only upon contact.

Table 11 Results calculated by SHARP – Case 1 (without rupture strain)

Simulations No. Penetration [m] Deformation Energy [MJ]

Simulation 1 0.68 8.70









Average 0.78 8.44

Standard deviation 0.07 0.25



Figure 34 Extent of damage in SHARP – Case 1 (without rupture strain)

The results of LS-DYNA and SHARP are compared numerically as well as graphically and

shown in Table 12 and Figure 35 respectively.

Table 12 Comparison of the results – Case 1 (without rupture strain)

Penetration [m] Deformation Energy [MJ]

LS-DYNA 1.1 8.5

SHARP (average) 0.78 8.44

% Difference 27% 1%

Figure 35 Comparison of the results – Case 1 (without rupture strain)

0.00E+00

2.00E+06

4.00E+06

6.00E+06

8.00E+06

1.00E+07

0.00 0.30 0.60 0.90 1.20 1.50

Def

orm

atio

n E

ner

gy [

J]

Penetration [m]

Struck ship - Deformation Energy (Case 1)

LS-DYNA

Simulation 1

Simulation 2

Simulation 3

Simulation 4

Simulation 5

Simulation 6

Simulation 7

Simulation 8

Simulation 9


A.D.N. Regulations

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As can be seen in Figure 35, SHARP results do not agree very well with LS-DYNA and it is

found out that SHARP model seems to be more rigid. However, the final deformation energy

is more or less the same in both simulations, only showing a discrepancy of 1 %. The

discrepancy regarding the final penetration is about 27 %. This is because the coupling effect

between the side shell and the weather deck creates different boundary conditions for the side

shell considered in LS-DYNA and SHARP. Since the weather deck has been deformed in LS-

DYNA, this makes the side shell in LS-DYNA to behave like a plate with three clamped ends

and one moving end (at the weather deck). On contrary, considering the SE1 super-element in

SHARP solver, all the four edges of the side shell are supposed to be clamped, causing the side

shell to behave more rigidly than in LS-DYNA.

In Table 13, deformation energies for each structural component are calculated and expressed

as percentages of the total energy and compared between LS-DYNA and SHARP. The results

are also given for SHARP with one side shell super-element in order to see the influence of

virtual deck. The presence of virtual deck can split the side shell super-element into two parts

and this has already been explained in Section 5.2.2.1. Note that among the 9 SHARP

simulations, the results of SHARP shown in Table 13 are the results of simulation 1 in which

the real impact point was considered. See Section 5.2.4 to recall the impact scenarios in SHARP.

Table 13 Comparison of energy absorption – Case 1 (without rupture strain)

PARTS LS-DYNA

SHARP

(Two side shell super-

elements)

SHARP

(One side shell super-

element)

E (MJ) % E (MJ) % E (MJ) %

Total Energy 8.5 8.71 8.87

Side Shell 3 35% 7.22 83% 7.61 86%

Inner Shell 0.13 2% 0 0% 0 0%

Web Frame 2.6 31% 1.47 17% 1.25 14%

Double Bottom 0 0% 0 0% 0 0%

Bottom 0 0% 0 0% 0 0%

Weather Deck 1.8 21% 0 0% 0 0%

Stiffeners 0.5 6% 0.02 0% 0.01 0%

Others 0.47 5% 0 0% 0 0%

Penetration (m) 1.1 0.68 0.64



According to the results from Table 13, the following analyses can be made:

Firstly, it can be observed that the presence of virtual deck does not cause much

difference in the final results of SHARP because all the results of SHARP with two side

shell super-elements and one side shell super-element are approximately the same.

In addition, it can be observed that in LS-DYNA, most proportion of the total

deformation energy was dissipated in side shell, web frame and weather deck (35%,

31% and 21% respectively). On the other hand, in SHARP, almost all of the total energy

was absorbed by the side shell, amounting to more than 80 % of the total energy. This

can be explained by the different assumptions on the behaviour of the elements

considered in LS-DYNA and SHARP. As already explained, the finite elements are

simultaneously activated when collision occurs whereas super-elements in SHARP are

activated only upon contacts. Therefore, the side shell in SHARP, which does not break

due to the fact that the rupture is not considered in the simulation, will behave like a

barrier that prevents the striking ship from hitting other elements. On contrary, the

deformation of the side shell in LS-DYNA will cause the deformation in other structural

components due to the coupling effect.

In addition, it can be observed that the weather deck in LS-DYNA has absorbed 21 %

of the total energy while the one in SHARP does not absorb any energy at all. This

coupling effect between weather deck and side shell is usually found in inland ship

collisions. An analytical formulation to consider this effect has already been developed

by (Buldgen et al., 2013) but still not implemented in SHARP yet.

All in all, the results of case 1 are highlighting the significance of the coupling effect

when simulating a collision on an inland vessel occuring just under its weather deck.

6.1.2 Case 2 (V-shape bow : 90 deg : Between webs : Mid-depth of struck ship)

Table 14 shows the penetration and deformation energy calculated from LS-DYNA simulation

when the tanker has been collided by V-shape bow at an angle of 90 degree with a constant

speed of 3 m/s. The location of the impact was considered between the webs and at mid-depth

of the struck ship.


A.D.N. Regulations

75




1.2 1.1 9.5


In Figure 36, the extent of damage in LS-DYNA after impact is shown. It can be observed that

in addition to the bending of the side shell, the weather deck also bent slightly. Table 15 presents

the results calculated by SHARP at 9 impact locations. The damage extent in SHARP at the

end of the simulation is shown in Figure 37. The impacted elements are shown in yellow colour

while the destroyed elements are in red. Although some red parts can be seen at the inner shell,

it is later found out to be the graphic error. This is also shown in Table 17 when the energy

absorbed by the inner shell is only 0.02 MJ which is negligible in comparison with total energy.


Simulation No. Penetration [m] Deformation Energy [MJ]










Average 1.11 8.57





The end simulation results calculated by LS-DYNA and the average results obtained from all 9

simulations of SHARP are given in Table 16. It is observed that the penetration has only 1 %

discrepancy whereas the deformation energy has 10 % discrepancy.



LS-DYNA 1.1 9.5


% Difference 1% 10%

In Figure 38, these results are again compared graphically. It can be observed that the trends of

both simulations are approximately the same. Nevertheless, after about 0.5 m penetration, the

deformation energy results of LS-DYNA became lower than those of SHARP. Then, it

suddenly increased again around 1 m penetration. It has been found out that this sudden increase

in the energy in LS-DYNA comes from the web frames. However, this is not possible for

SHARP because, as already explained, the side shell super-element in SHARP will absorb

almost all of the total energy while preventing the striking ship from hitting other super-

elements. This can be clearly observed in Table 17 in which the deformation energy of each

structural component is shown as a percentage of the total energy.

Note that there is elastic energy deformation in LS-DYNA, that is, the shell goes backward after

the collision. This is because the speed and mass of the striking ship is small, resulting in the

low initial kinetic energy. However, for the comparison, the final result of LS-DYNA which

takes into account both elastic energy and plastic energy was used.


A.D.N. Regulations

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PARTS LS-DYNA

SHARP

(With two side shell

super-elements)

SHARP

(With one side shell

super-element)

E (MJ) % E (MJ) % E (MJ) %


Side Shell 4.2 44% 8.14 95% 7.61 92%

Inner Shell 0.2 2% 0.02 0% 0.15 2%

Web Frame 3.5 37% 0.3 4% 0.31 4%

Double Bottom 0.1 1% 0 0% 0.02 0%

Bottom 0.06 1% 0 0% 0 0%

Weather Deck 0.3 3% 0 0% 0 0%

Stiffeners 0.76 8% 0.09 1% 0.18 2%

Others 0.38 4% 0.01 0% -0.01 0%


According to the results from Table 17, the followings could be deduced:

The energy contribution of the side shell in LS-DYNA becomes higher in case 2,

amounting to 44 % of the total. This is because in this case, the point of impact, being

0.00E+00

2.00E+06

4.00E+06

6.00E+06

8.00E+06

1.00E+07

1.20E+07

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

Def

orm

atio

n E

ner

gy [

J]

Penetration [m]


LS-DYNA

Simulation 1

Simulation 2

Simulation 3

Simulation 4

Simulation 5

Simulation 6

Simulation 7

Simulation 8

Simulation 9



the mid-depth of the struck ship, is far from both weather deck and bottom. Therefore,

the energy dissipations of the weather deck and bottom are quite low (about 1-3 %) and

as a result, the side shell absorbs more energy in their places.

On the other hand, in SHARP, the side shell absorbs very large amount of energy (95%

of the total). This means that the striking ship will not collide many super-elements such

as inner shell and webs that are behind the side shell. That is why the webs in SHARP

dissipate very small energy (only about 0.3 MJ) as compared with LS-DYNA in which

the energy dissipated by the webs is about 3.5 MJ.

The total energy and the penetration values of both SHARP results are in good

agreement with LS-DYNA. The result of SHARP (with only one side shell super-

element) is slightly more conservative than that of SHARP (with two side shell super-

elements). This is because with the assumption of two side shell super-elements, the

shell becomes more rigid as there will be an additional clamped end at the connection

point. (Refer to Section 5.2.2.1)

All in all, SHARP results in case 2 are quite satisfactory. It can be said that the

assumptions made in LS-DYNA and SHARP are also the same in this case as the deck

and bottom do not deform a lot. Therefore, it can be concluded that SHARP is more

accurate when the coupling effect remains negligible. Of course, this coupling effect

depends on the location of the impact point and the initial kinetic energy of the striking

ship.

6.1.3 Case 3 (Push barge bow : 55 deg : At web : Mid-depth of struck ship)

In Table 18, the penetration and deformation energy at the end of the simulation calculated by

LS-DYNA is presented. In this case, the tanker has been impacted by the push barge striking

ship at an angle of 55 degree with a constant speed of 3 m/s. The impact point is located at web

and at mid-depth of the struck ship.



1.2 0.65 6.65


A.D.N. Regulations

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In Figure 39, the extent of damage after impact is shown. It can be observed that the damage

on the side shell is very small and extremely localized. As a consequence, the weather deck and

bottom are only very slightly deformed.


Table 19 presents SHARP results of penetration into the struck ship and the deformation energy

at 9 impact locations. The damage extent after impact is shown in Figure 40. As there are only

yellow parts in the figure, it can be said that SHARP does not result any rupture in the structures.












Average 1.10 6.70





In Table 20 and Figure 41, the results of LS-DYNA and SHARP are compared numerically as

well as graphically. As can be seen, there is a large discrepancy (about 69 %) between the

penetration results of LS-DYNA and the average result of SHARP. The deformation energy,

however, matches very well, only showing 1 % discrepancy. When observing Figure 41, it

appears that the large discrepancy in the penetration is due to the presence of elastic energy

during collision. Note that the energy post-processed in LS-DYNA and used for the comparison

includes both elastic and plastic energies.



LS-DYNA 0.65 6.65


% Difference 69% 1%


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As can be seen in Figure 41, if the elastic energy part is ignored, the maximum penetration in

LS-DYNA is around 0.85 m. Therefore, the discrepancy value will become a lot smaller

(approximately 30 %). Moreover, as can be seen, all of the results of SHARP are always higher

in the penetration, i.e., at the same deformation energy, the damage penetration in SHARP is

always higher than the one calculated by LS-DYNA. However, the slopes of these curves are

approximately the same. The reason is probably due to the many simplifications made when

modelling the push barge. As a result, the damage extent obtained from LS-DYNA and SHARP

are not exactly the same and it can be seen that SHARP has more damage extent. (Refer to

Figure 39 and Figure 40)

In Table 21, the distributions of energy for each structural component are presented. The results

are also given for SHARP (with one side shell super-element). Note that the results of SHARP

in Table 21 are only those of simulation 1 in which real impact point was considered.

According to the results shown in Table 21, the following important points could be extracted:

In LS-DYNA, the side shell absorbs maximum amount of the total energy (60 %) while

the webs and stiffeners absorb about 18 % and 14 % respectively. However, in SHARP,

the largest proportion of the total energy was dissipated only in the side shell (more than

80 %) and the rest were only absorbed by the webs (about 10 %).

0.00E+00

1.00E+06

2.00E+06

3.00E+06

4.00E+06

5.00E+06

6.00E+06

7.00E+06

8.00E+06

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

Def

orm

atio

n E

ner

gy [

J]

Penetration [m]


LS-DYNA

Simulation 1

Simulation 2

Simulation 3

Simulation 4

Simulation 5

Simulation 6

Simulation 7

Simulation 8

Simulation 9




PARTS LS-DYNA

SHARP


super-elements)

SHARP


super-element)

E (MJ) % E (MJ) % E (MJ) %


Side Shell 4 60% 5.88 86% 5.48 82%

Inner Shell 0 0% 0.09 1% 0.2 3%

Web Frame 1.2 18% 0.7 10% 0.83 12%

Double Bottom 0.09 1% 0 0% 0 0%

Bottom 0 0% 0 0% 0 0%

Weather Deck 0.12 2% 0 0% 0 0%

Stiffeners 0.9 14% 0.16 2% 0.2 3%

Others 0.34 5% 0.01 0% 0 0%


The stiffeners in SHARP only absorbs 3 % of the total energy which is very small as

compared with LS-DYNA. This highlights the difference in the damage extent obtained

from LS-DYNA and SHARP due to the bow shape difference. It seems that the bow

model in SHARP has more in the longitudinal extent of damage but less in the vertical

extent of damage as compared with LS-DYNA.

In this case, the virtual deck have caused some changes in the final results. It can be

seen that the results with one side shell super-element is slightly more conservative than

those with two side shell super-elements.

One important aspect for the case 3 would be to investigate whether the discrepancies

are due to the bow shape difference or due to the coupling effect and the corresponding

boundary conditions for the side shell. However, in this case, since the location of

impact is at the mid-depth of the struck ship and the initial kinetic energy of the striking

ship is quite low, the deck and bottom do not deform a lot in LS-DYNA. In other words,

the simulation has only weak coupling effect. Therefore, in this case, it can be concluded

that the discrepancy is mainly due to the difference in the bow shape models. Therefore,

it is suggested to improve the user interface of SHARP which could consider a more

precise description of the push barge model.


A.D.N. Regulations

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6.1.4 Case 4 (Push barge bow : 55 deg : At bulkhead : Above deck of struck ship)

Table 22 shows the penetration and deformation energy computed by LS-DYNA simulation

when the tanker has been collided by push barge bow at an angle of 55 degree with a speed of

3 m/s. The location of the impact point is at bulkhead and just above deck of the struck ship.



1.2 0.6 4.3

In Figure 42, the extent of damage after impact is shown. It is found out that not only the side

shell deforms but also the deck has been crushed by the striking ship.

Table 23 presents the results of penetration into the struck ship and the deformation energy

calculated by SHARP at 9 impact locations.

The damage extent for SHARP is illustrated in Figure 43. It can be seen that only the weather

deck and upper part of the side shell are taken part in the collision process, which is just as the

same as LS-DYNA. The impacted elements are shown in yellow colour while the destroyed

elements are in red. As there is no red colour, it can be said that there is no shell rupture.


Simulations No. Penetration [m] Deformation Energy [MJ]










Average 0.55 4.64







shown in Table 12 and Figure 44 respectively.



LS-DYNA 0.6 4.3


% Difference 8% 8%


A.D.N. Regulations

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As can be seen in Table 12, both penetration and deformation energy of SHARP show 8 % of

discrepancy in comparison with LS-DYNA. However, the results of SHARP are slightly less

conservative. Note that the penetration result of LS-DYNA is the final value at the end of the

simulation, i.e., at 1.2 seconds.

As can be seen in Figure 44, the structures in SHARP are slightly more rigid. The reason is

probably due to the simplification in the push barge model. Moreover, the side shell super-

element in SHARP has a virtual deck which will divide the side shell and create an extra

clamped end at the connection point. As a consequence, the shell in SHARP is slightly stiffer

than the one in LS-DYNA.

Table 25 shows the comparison of the deformation energy dissipated in each structural

component of the struck ship between LS-DYNA and SHARP. The results of SHARP (with

only one side shell super-element) are also given in order to check if the virtual deck causes

much influence in the results or not.

According to the results from Table 25, the followings could be deduced:

By observing the LS-DYNA results, it can be seen that most of the energy is absorbed

by the weather deck (about 40 % of the total). Other large amount of energy is

distributed to side shell and web frames, amounting to 30 % and 23 % respectively.

0.00E+00

5.00E+05

1.00E+06

1.50E+06

2.00E+06

2.50E+06

3.00E+06

3.50E+06

4.00E+06

4.50E+06

5.00E+06

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

Def

orm

atio

n E

ner

gy [

J]

Penetration [m]


LS-DYNA

Simulation 1

Simulation 2

Simulation 3

Simulation 4

Simulation 5

Simulation 6

Simulation 7

Simulation 8

Simulation 9




PARTS LS-DYNA

SHARP


super-elements)

SHARP


super-element)

E (MJ) % E (MJ) % E (MJ) %


Side Shell 1.3 30% 3.54 76% 1.42 31%

Inner Shell 0.05 1% 0 0% 0 0%

Web Frame 1 23% 0.26 6% 0.8 17%


Bottom 0 0% 0 0% 0 0%

Weather Deck 1.7 40% 0.86 18% 2.38 52%

Stiffeners 0.2 5% 0 0% 0.01 0%

Others 0.05 1% 0 0% 0 0%


When observing SHARP results, the total energy of both results are almost the same.

Nonetheless, the rest of the results are not the same and the reason is due to the fact that

the shell becomes less rigid in the case with “one side shell SE”. Since “two side shell

SE” will have an extra clamped end due to the presence of virtual deck during modelling

of the struck ship in SHARP, it is obviously more rigid, leading to less penetration

results. This effect has been explained in the previous cases as well. It can be seen that

the results of SHARP with “one side shell SE” corresponds better with LS-DYNA than

the results of SHARP with “two side shell SE”.

The penetration result obtained from SHARP with “one side shell SE” was almost twice

larger than LS-DYNA. However, this could be improved if the equivalence thickness

between 9.5 mm and 23.5 mm was considered. Currently, “one side shell SE” has been

modelled using 9.5 mm as the thickness.

However, using such option still imposes some difficulties as every time the user wants

to consider only “one side shell SE”, one has to skip the user interface and manually

configure the super-elements in the input file. To conclude, it is suggested to make some

improvements in the user interface of SHARP so that even with the presence of virtual

deck, the side shell super-element will not be divided into two.


A.D.N. Regulations

87


6.1.5 Case 5 (V-shape bow : 90 deg : At web : Above deck of struck ship)

Table 26 shows the results of penetration and deformation energy calculated from LS-DYNA

when the tanker has been impacted by V-shape bow at an angle of 90 degree with 3 m/s. The

impact point was considered at web and just above deck of the struck ship. In Figure 45, the

view of damage extent after impact is shown. It can be observed that the side shell was deformed

and the weather deck was crushed due to the collision.



1.2 0.7 5.2

Table 27 presents the results of penetration into the struck ship and the deformation energy

calculated by SHARP at 9 impact locations. The damage extent after impact is illustrated in

Figure 46. In SHARP, the impacted elements are shown in yellow colour while the destroyed

elements are in red. As there is no red colour, it can be said that there is no shell rupture. The

web frames visible are only the results of graphic errors when making the animation.












Average 0.61 5.90



shown in Table 28 and Figure 47 respectively. It can be seen that both penetration and

deformation energy have discrepancy of about 13 %.







LS-DYNA 0.7 5.2


% Difference 13% 13%

According to Figure 47, it is obvious that LS-DYNA structures are less stiff than the structures

in SHARP because larger penetration was obtained in LS-DYNA. The reason for such

discrepancy is due to the presence of virtual deck when modelling the struck ship structures in

SHARP. This effect is highlighted by the distribution of energy in each structural component

as shown in Table 29.


A.D.N. Regulations

89



As can be seen in Table 29, the energy distributions for each structural component are given in

terms of total energy and compared with LS-DYNA. Note that the value of LS-DYNA

presented in Table 29 includes elastic deformation.


PARTS LS-DYNA

SHARP


super-elements)

SHARP


super-element)

E (MJ) % E (MJ) % E (MJ) %


Side Shell 0.8 15% 3.82 65% 1.34 23%

Inner Shell 0.1 2% 0 0% 0 0%

Web Frame 1.2 23% 0.92 16% 2.36 40%


Bottom 0 0% 0 0% 0 0%

Weather Deck 2.8 54% 1.16 20% 2.12 36%

Stiffeners 0.1 2% 0 0% 0.02 0%

Others 0.2 4% 0 0% 0 0%


0.00E+00

1.00E+06

2.00E+06

3.00E+06

4.00E+06

5.00E+06

6.00E+06

7.00E+06

0.00 0.20 0.40 0.60 0.80 1.00

Def

orm

atio

n E

ner

gy [

J]

Penetration [m]


LS-DYNA

Simulation 1

Simulation 2

Simulation 3

Simulation 4

Simulation 5

Simulation 6

Simulation 7

Simulation 8

Simulation 9



According to Table 29, the following conclusions can be made:

In LS-DYNA, the side shell, webs and the weather deck are components which absorb

most proportion of the total energy while among them, the maximum amount is

dissipated in the weather deck (about 54 % of the total).

When observing SHARP results, the two simulations lead to different results. The

SHARP simulation with “one side shell super-element” leads to more penetration and

less deformation energy. However, the reason is the same as for case 4 because in this

modelling, only the thickness of 9.5 mm is used instead of considering equivalent

thickness.

All in all, in terms of penetration as well as energy distribution, it is obvious that the

results of SHARP simulation with “one side shell super-element” are in better accord

with LS-DYNA than the ones which considered “two side shell super-elements”. This

improvement should be considered when updating the user-interface of SHARP, i.e., to

be able to use virtual deck without causing any extra effect to the side shell super-

element. Moreover, it is obvious that in case 5, the discrepancy is coming from the

virtual deck since the striking bow model used in this simulation is the V-shape bow

which has almost the same geometry with LS-DYNA.

6.1.6 Overall Analysis

According to the results from case 1 to case 5 (from Section 6.1.1 to 6.1.5), it can be observed

that the modelling of the virtual deck, i.e., the use of two side shell super-elements instead of

only one, can change the final results in some cases. Because, with the presence of virtual deck,

the side shell super-element becomes more rigid and as a consequence, in most of the cases

(except cases 2 and 3), the penetrations calculated by SHARP are less than those calculated by

LS-DYNA. Regarding this matter, the user interface of SHARP needs to be improved so that

the virtual deck will not cause any extra effect on the side shell super-element.

Another important point to consider is the coupling effect between the structural elements such

as deck, bottom and side shell because inland vessels usually have similar depths and thus, the

deformation of the side shell can cause the deformation in the weather deck and/or bottom even

though these components are not directly impacted. An analytical formulation to consider such


A.D.N. Regulations

91


effect has been developed by (Buldgen et al., 2013), but has not been implemented in SHARP

yet.

In addition, the bow shape geometries of the striking ship in SHARP, especially the push barge,

do not match exactly with the push barge model in LS-DYNA which takes the bow shape

definition from A.D.N. Regulations. Such difference in the bow shape can lead to discrepancy

which can be very large, for example, case 3 (about 69 %).

Moreover, the presence of elastic energy should also be noticed as this could make the side

shell in LS-DYNA to bounce back a lot at the end of the simulation. This happens when the

initial kinetic energy of the striking ship is quite low. Nevertheless, since SHARP can only

consider the completely rigid-plastic material, it can be said to be a more conservative approach

in that case.

The discrepancies of all results for all cases are summarized in Table 30. Note that in this table,

all results were taken at the end of the simulation time, i.e., when there was no more

deformation, and the results of SHARP were the results with two side shell super-elements

(with the presence of virtual deck).

Table 30 Summary of result discrepancy (cases without rupture strain)

Cases Penetration Deformation energy

1 27% 1%

2 1% 10%

3 69% 1%

4 8% 8%

5 13% 13%

6.2 Simulations considering Rupture (A.D.N. Regulations)

According to the A.D.N. Regulations, the probability of cargo tank rupture is determined by

using the energy absorption capacity of the struck vessel until the initial rupture of its cargo

tank. Therefore, the main focus in this section is to analyse and compare the results of SHARP

with those of LS-DYNA by defining every parameter exactly as suggested by the A.D.N.

Regulations. The comparisons will be made at 1 m penetration (not at the end of the simulation

time), that is, only when the initial rupture of the cargo tank occurs.




Figure 48 compares the damage extent in LS-DYNA and SHARP at 1 m penetration. As can

be seen, the deck is crushed in LS-DYNA whereas it has not been activated in SHARP. This

coupling effect usually occurs when both striking and struck vessels have the same height. In

addition, the red part in SHARP simulation is showing that the side shell super-element has

been destroyed although in LS-DYNA, the side shell still remains unperforated.

(a) LS-DYNA (b) SHARP

Figure 48 Comparison of damage extent in LS-DYNA and SHARP – Case 1 (With rupture strain)

In Table 31, the comparison of the results of total deformation energy between LS-DYNA and

SHARP is presented when the penetration is at 1 m. It can be observed that there is a

discrepancy of 9 % and SHARP results are less than LS-DYNA in this case. Note that the

SHARP results given in Table 31 are the average value of all the results calculated at 9 impact

locations.

Table 31 Comparison of the results – Case 1 (With rupture strain)

Deformation Energy [MJ]

LS-DYNA 6.22

SHARP (average) 5.69

% Difference 9%

The results are also compared graphically in Figure 49 and good agreement is found between

LS-DYNA and SHARP. Also, SHARP results are slightly more conservative in this case.

However, with the knowledge gained from the previous simulations (Refer Section 6.1), the

following additional analyses could be made:


A.D.N. Regulations

93


Figure 49 Comparison of the results – Case 1 (With rupture strain)

Firstly, there is a virtual deck which splits the side shell super-element of SHARP into

two. This causes an extra clamped end in the middle of these two elements and as a

result, the shell becomes more rigid. (Refer to Section 5.2.2.1)

Secondly, the weather deck in LS-DYNA was crushed during the collision. As a

consequence, the side shell in SHARP is bounded by four clamped ends while it behaves

like a plate with only three clamped ends and one moving end in LS-DYNA due to the

fact that the weather deck deforms.

Such combined effects from the first and the second might have caused the side shell in

SHARP to be stiffer than what it actually should be (before its rupture), leading to better

results in comparison with LS-DYNA. However, one has to be aware that if the

developments suggested in the previous sections were considered, then the results

would not be the same and in this case, they may become much smaller than LS-DYNA.

In this context, the behaviour of the side shell super-element becomes significant. In

SHARP, it is assumed that when the failure strain of the side shell exceeds the

predefined criterion, the associated resistant force is directly imposed to zero in the next

calculation step. However, in LS-DYNA (in reality as well), the resistant force will

slowly decrease until it reaches zero.

0.00E+00

1.00E+06

2.00E+06

3.00E+06

4.00E+06

5.00E+06

6.00E+06

7.00E+06

8.00E+06

0.00 0.20 0.40 0.60 0.80 1.00

Def

orm

atio

n E

ner

gy

[J]

Penetration [m]


LS-DYNA

Simulation 1

Simulation 2

Simulation 3

Simulation 4

Simulation 5

Simulation 6

Simulation 7

Simulation 8

Simulation 9



Therefore, to conclude case 1, it is important to consider how to correctly represent the

decreasing slope of the side shell resistance so that the loose of stiffness in the side shell

super-element caused by the developments could be properly compensated.


Figure 50 shows the damage extent in LS-DYNA and SHARP at 1 m penetration. As can be

seen, the weather deck in LS-DYNA is only slightly deformed whereas it has not been impacted

at all in SHARP. More importantly, it is found out that the side shell has been completely

destroyed in SHARP while it is still unperforated in LS-DYNA. So, it is obvious that the side

shell super-element fails too rapidly in SHARP and, as a consequence, the side shell resistance

drops to zero too quickly.



In Table 32, the results of total deformation energy obtained from LS-DYNA and SHARP at 1

m penetration are compared. It can be observed that there is a very large discrepancy (about 82

%) in the total deformation energies computed by SHARP and LS-DYNA. Note that the

SHARP results given in Table 32 are the average result of all 9 simulations of SHARP.



LS-DYNA 5.29


% Difference 82 %


A.D.N. Regulations

95



Figure 52 Comparison of the crushing force in LS-DYNA and SHARP (Case 2)

The results are also compared graphically and shown in Figure 51. It appears that SHARP

results are much less, approximately 5 times, than LS-DYNA results. Although it is

conservative, the result discrepancy is still very large. The reason is due to the premature failure

of the side shell super-element in SHARP. As shown in Figure 52, the evolution of crushing

0.00E+00

1.00E+06

2.00E+06

3.00E+06

4.00E+06

5.00E+06

6.00E+06

7.00E+06

0.00 0.20 0.40 0.60 0.80 1.00

Def

orm

atio

n E

ner

gy

[J]

Penetration [m]


LS-DYNA

Simulation 1

Simulation 2

Simulation 3

Simulation 4

Simulation 5

Simulation 6

Simulation 7

Simulation 8

Simulation 9

0.00E+00

1.00E+07

2.00E+07

3.00E+07

4.00E+07

5.00E+07

6.00E+07

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Cru

shin

g F

orc

e [N

]

Time [sec]

SHARP lsdyna



force in SHARP is a lot smaller (about 10 times) than LS-DYNA. In addition, the crushing

force in LS-DYNA slowly decreases until it reaches zero while in SHARP, the side shell does

not participate in the overall struck ship resistance at all after its failure. This is the development

that is mainly needed to consider for the side shell super-element in SHARP in order to correctly

represent the decreasing slope of its resistance when it begins to fail. Also, investigations should

be made why the side shell super-element fails so rapidly.


Case 3 is the scenario in which the tanker has been impacted by push barge. The angle of impact

considered is 55 degree together with the constant striking speed of 10 m/s. The location of

impact point is at web and at mid-depth of the struck ship. Failure modelling of 20 % was used

for both LS-DYNA and SHARP simulations.

In Figure 53, the damage extent in LS-DYNA and SHARP at 1 m penetration are compared. It

can be observed how the difference in the bow shape geometry can lead to different results.

Even though both figures are taken at the same damage penetration of 1 m, the longitudinal

extent of damage is small in LS-DYDA (See Figure 53a). On contrary, the longitudinal extent

of damage is larger in SHARP (Figure 53b). Thus, more elements will participate in the

collision in SHARP while only a few elements will resist the collision in LS-DYNA. This

makes the assumptions between the two approaches to be completely different.




A.D.N. Regulations

97


Table 33 shows the comparison of the total deformation energy between LS-DYNA and

SHARP when the penetration is 1 m. It can be observed that there is a discrepancy of 27 % in

which SHARP results are higher than LS-DYNA results. Note that the SHARP results given in

Table 33 are the average value of the results calculated at 9 impact locations.



LS-DYNA 4.4

SHARP (average) 5.6

% Difference 27 %


The results are also compared graphically and shown in Figure 54. According to the figure, it

can be seen that all SHARP results correlate well with the LS-DYNA. However, the results

calculated by SHARP are higher than LS-DYNA at 1 m penetration. As already mentioned, due

to the difference in geometry of the striking ship bow, the longitudinal extent of damage is not

the same even though both results are taken at the same penetration value.

It can be predicted that the results of SHARP will become higher after 1 m penetration because

the webs and inner shell have already participated in the collision process while in LS-DYNA,

only the side shell and very few elements have taken part in the collision. For this case, if a

0.00E+00

1.00E+06

2.00E+06

3.00E+06

4.00E+06

5.00E+06

6.00E+06

7.00E+06

8.00E+06

0.00 0.20 0.40 0.60 0.80 1.00

Def

orm

atio

n E

ner

gy

[J]

Penetration [m]


LS-DYNA

Simulation 1

Simulation 2

Simulation 3

Simulation 4

Simulation 5

Simulation 6

Simulation 7

Simulation 8

Simulation 9



more precise bow shape could be considered, SHARP results would become a lot smaller due

to the fact that the side shell is very rapidly destroyed.


Case 4 is the scenario in which the tanker has been collided by a push barge which has a constant

speed of 10 m/s at 55 degree collision angle. The point of impact is located at bulkhead and just

above deck of the struck ship. The failure strain used for both LS-DYNA and SHARP

simulations is 20 %. As can be seen in Figure 55, while the shell in LS-DYNA breaks only a

little, the whole side shell has already failed in SHARP.



Table 34 shows the comparison of the total deformation energy between LS-DYNA and

SHARP when the penetration is 1 m. Note that the SHARP results presented are the average

value of the results calculated at 9 impact locations.



LS-DYNA 10.8

SHARP (average) 3.9

% Difference 64 %

The results are also compared graphically and shown in Figure 56. According to the figure, a

discrepancy of 64 % is observed while the value calculated by SHARP is less than the one

calculated by LS-DYNA. The main reason is the same as case 2 in which the contribution of


A.D.N. Regulations

99


the side shell super-element in the overall struck ship resistance is many times smaller than that

of LS-DYNA. This should be investigated in the future.



In this case, the tanker has been impacted perpendicularly by the V-shape bow with a constant

speed of 10 m/s. The location of impact is considered at web and just above deck of the struck

ship. The failure strain used for both LS-DYNA and SHARP simulations is 20 %. Figure 57

shows the damage penetration extracted with LS-DYNA post processer, LS-PRE/POST and by

SHARP graphical interface respectively. Only the upper part of the side shell super-element in

SHARP seems to have ruptured.

Table 35 shows the comparison of the results of total deformation energy between LS-DYNA

and SHARP when the penetration is 1 m. It can be seen that there is a discrepancy of only 1%

with SHARP result being slightly more conservative. Note that the value presented for SHARP

is only the average value of the results calculated at 9 impact locations.

0.00E+00

2.00E+06

4.00E+06

6.00E+06

8.00E+06

1.00E+07

1.20E+07

0.00 0.20 0.40 0.60 0.80 1.00

Def

orm

atio

n E

ner

gy [

J]

Penetration [m]


LS-DYNA

Simulation 1

Simulation 2

Simulation 3

Simulation 4

Simulation 5

Simulation 6

Simulation 7

Simulation 8

Simulation 9







LS-DYNA 7.12


% Difference 1 %


0.00E+00

2.00E+06

4.00E+06

6.00E+06

8.00E+06

1.00E+07

1.20E+07

0.00 0.20 0.40 0.60 0.80 1.00

Def

orm

atio

n E

ner

gy

[J]

Penetration [m]


LS-DYNA

Simulation 1

Simulation 2

Simulation 3

Simulation 4

Simulation 5

Simulation 6

Simulation 7

Simulation 8

Simulation 9


A.D.N. Regulations

101


The results are also compared graphically as shown in Figure 58. According to the figure, it can

be said that all SHARP results correlate well with LS-DYNA. The trends of both approaches

are almost similar. This is because in this case, the geometry of the bow shape is similar and

also there are some factors, as explained in case 1 (Section 6.2.1) which could make the side

shell in SHARP to be stiffer than what it actually should be. It would be interesting to see what

the consequences will be if all the developments suggested were to be considered.


Studying the simulations where the rupture has been considered (from Section 6.2.1 to 6.2.5),

the following overall analyses could be made:

The location of the impact point and the associated striking bow are the deciding factors

in the agreement of the results. For example, if V-shape bow is used instead of the push

barge, the results should be the same. However, it is found out that only cases 1 and 5

are found to be in good accords with LS-DYNA while there is a very large discrepancy

of about 82 % for case 2. The reason is due to the difference in the locations of the

impact point considered. As both cases 1 and 5 considered the impact point around the

vicinity of the weather deck, the results are quite good because the deck super-element

contributes more in the collision rather than the side shell super-element. As for case 2,

however, the results do not match well because the impact point considered is at the

mid-depth of the struck ship where the side shell super-element plays a more important

role. Since the side shell fails too prematurely, this causes an underestimation in the

overall struck ship resistance. This highlights the need to consider more stiffness as well

as the behaviour after side shell rupture in the solver of SHARP. In the paper of

(Kitamura, 2002), it was stated that a simplified analytical approach should consider the

post rupture-initiation/propagation behaviour of the side shell in order to correctly

represent the overall resistance and the energy absorption capability of the struck ship.

Regarding the bow shape model, the push barge bow cannot be modelled as exactly as

the one defined by A.D.N. Regulations due simply to the fact that SHARP still needs

more surface tools to allow for a more precise bow shape description. This leads to some

discrepancies as compared with LS-DYNA, for example, cases 3 and 4.

The summary of all the result discrepancies with the failure strain can be seen in Table 36. Note

that both LS-DYNA and SHARP results are taken and compared only at the penetration length



of 1 m (not at the end of the simulations), i.e., only when the initial rupture of the cargo tank

occurs, in accordance with the A.D.N Regulations.

Table 36 Summary of result discrepancy (cases with rupture strain)

Cases Deformation energy

1 9%

2 82%

3 27%

4 64%

5 1%

6.3 Additional Simulations with Modified Rupture Strains

In the previous sections, comparisons have been made between LS-DYNA numerical approach

and SHARP analytical approach only up to 1 m penetration. According to the results, it has

been found out that the side shell super-element of SHARP fails too rapidly and, as its resistance

drops suddenly to zero, does not resist sufficiently. Therefore, in this section, the rupture strain

value considered in SHARP will be tuned in order to correctly model the loose of stiffness in

the side shell and the simulations will be run again. The obtained results will be compared with

LS-DYNA. Note that 20 % failure strain was used in LS-DYNA simulations for every

comparison. A list of new rupture strain values considered in SHARP simulations is given in

Table 37.

Table 37 Different rupture strain values considered in SHARP

Cases Rupture strain Ec

Case 1 2

Case 2 5

Case 3 0.5

Case 4 3

Case 5 3


Table 38 presents the comparison of the results from LS-DYNA and an average result computed

from all 9 impact locations of SHARP. Both results are taken at the end of the simulations, i.e.,


A.D.N. Regulations

103


when there is no more deformation. The results are also compared graphically as shown in

Figure 59.

Table 38 Comparison of the results – case 1 (with modified rupture strain)


LS-DYNA 4.5 111


% Difference 3% 24%

Figure 59 Comparison of the results– case 1 (with modified rupture strain)

According to the results, it can be seen that SHARP results are very close to the LS-DYNA

ones. The discrepancy for the penetration is 3 % while the discrepancy for the deformation

energy is 24 %. In both results, SHARP is less because in LS-DYNA, when collision occurs,

the weather deck was crushed and thus, absorbed some amount of energy during the process.

On the other hand, the weather deck in SHARP has not been impacted at all. This is because in

SHARP, the elements are independently activated when collision occurs. (See Figure 60 and

Figure 61)

In addition, the crush of the weather deck in LS-DYNA has caused different boundary

conditions for the side shell considered in LS-DYNA and SHARP. In other words, the side shell

in LS-DYNA behaves like a plate with three clamped ends and one moving end (at the weather

0.00E+00

2.00E+07

4.00E+07

6.00E+07

8.00E+07

1.00E+08

1.20E+08

0.00 1.00 2.00 3.00 4.00 5.00

Def

orm

atio

n E

ner

gy

[J]

Penetration [m]


LS-DYNA

Simulation 1

Simulation 2

Simulation 3

Simulation 4

Simulation 5

Simulation 6

Simulation 7

Simulation 8

Simulation 9



deck). On contrary, the side shell in SHARP is considered as four clamped ends. Hence, before

the side shell fails, the deformation energy value of SHARP is higher than LS-DYNA, i.e.,

around 1 m damage penetration.

Figure 60 View of the deformation of weather deck and bottom in LS-DYNA

Figure 61 View of the activated elements in SHARP (weather deck has not been impacted at all)

The results are also compared as the percentages of the total energy shown in Table 39. Note

that the values of SHARP presented in this table are taken only from the simulation 1 among

the 9 simulations of SHARP. Also, the results of SHARP with the virtual deck (with two side

shell super-elements) have been provided in this table because the sensitivity is not very high

due to the very fast velocity of the striking ship.


A.D.N. Regulations

105


Table 39 Comparison of the energy dissipation – case 1 (with modified rupture strain)

PARTS LS-DYNA SHARP

E (MJ) % E (MJ) %

Total Energy 111 86.2

Side Shell 29 26% 10.2 12%

Inner Shell 10.4 9% 4.22 5%

Web Frame 12.8 12% 10.6 12%

Double Bottom 7.8 7% 0.24 0%

Bottom 4.7 4% 0 0%

Weather Deck 18 16% 0 0%

Stiffeners 5.8 5% 60.9 71%

Others 22.5 21% 0.04 0%

Penetration [m] 4.5 4.16

According to the results from Table 39, the following analyses could be made:

In LS-DYNA, the energy is well distributed between different structural components.

In SHARP, however, most of the total energy (about 71 %) is dissipated in stiffeners

which seems to be unrealistic. The reason for this should be investigated and improved

in the near future.

It can be observed that the weather deck in LS-DYNA absorbs a good amount of energy

(about 16 %) whereas the weather deck in SHARP has not been impacted at all. This

coupling effect between deck, bottom and side shell can usually be observed in the

collision of inland vessels.

In addition, it should be noticed that even with the modified failure strain, the side shell

super-element in SHARP fails more rapidly than in LS-DYNA. The amount of energy

dissipation can be compared, accounting for 29 MJ in LS-DYNA but only 10.2 MJ in

SHARP. This highlights the need to improve the modelling of the failure of the side

shell in SHARP.




The results of SHARP and LS-DYNA for case 2 are compared in Table 40. Note that both

results are taken at the end of the simulations and SHARP result is the average result of all 9

impact scenarios. The results are also compared graphically in Figure 62. As can be seen,

SHARP results correspond well with LS-DYNA. The discrepancy is 2 % for the penetration

and 18 % for the deformation energy.



LS-DYNA 4.4 103


% Difference 2% 18%


In this case, however, LS-DYNA results are higher in both penetration and deformation energy.

The reason is the same with case 1 in which the weather deck also deformed in LS-DYNA even

though it was not impacted. Figure 63 presents LS-DYNA view of the damage extent when the

weather deck was deformed due to the impact. In Figure 64, the view of the damage extent in

SHARP is presented.

0.00E+00

2.00E+07

4.00E+07

6.00E+07

8.00E+07

1.00E+08

1.20E+08

0.00 1.00 2.00 3.00 4.00 5.00 6.00

Def

orm

atio

n E

ner

gy [

J]

Penetration [m]


LS-DYNA

Simulation 1

Simulation 2

Simulation 3

Simulation 4

Simulation 5

Simulation 6

Simulation 7

Simulation 8

Simulation 9


A.D.N. Regulations

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Figure 63 View of the bending of weather deck due to deformation of the side shell

Figure 64 View of the activated super-elements in SHARP (The weather deck has not been collided)

In Table 41, the energy dissipation of each structural element is shown as a percentage of the

total energy. It can be observed that energy is well distributed in LS-DYNA for each component

while in SHARP, stiffeners absorb more than half of the total energy (about 66 %). The reason

for this should be investigated as already mentioned in case 1. Another important fact found

when observing Table 41 is that the webs are found to have destroyed and can only absorb 1.44

MJ which is very small (by about 8 times smaller) as compared with LS-DYNA. This effect

was not seen in case 1 as the striking ship position is just under deck of struck ship. The

sensitivity of the collision position of the web should be investigated.




PARTS LS-DYNA SHARP

E (MJ) % E (MJ) %


Side Shell 28.5 28% 21.4 26%

Inner Shell 9 9% 4.12 5%

Web Frame 12.3 12% 1.44 2%

Double Bottom 14 14% 0.02 0%

Bottom 9.9 10% 1.16 1%

Weather Deck 5.2 5% 0 0%

Stiffeners 6.3 6% 55.2 66%

Others 17.8 17% -0.04 0%



In Table 42, the results calculated by SHARP and LS-DYNA are compared numerically. Note

that in this case, the results are not the end simulation results but instead, the ones taken at 5.8

m penetration damage. The reason is that the striking ship has already penetrated more than half

the breath of the struck ship and in this case, SHARP simulation is forced to stop. Nevertheless,

there is only 1 % discrepancy in the deformation energy calculated from LS-DYNA and

SHARP at 5.8 m penetration.



LS-DYNA 5.8 29


% Difference - 1%


A.D.N. Regulations

109



In Figure 65, it can be seen that the trends of LS-DYNA and SHARP are similar before 1 m

penetration and after 4 m penetration. It is observed that LS-DYNA curve goes up suddenly at

the penetration value of about 5.8 m. This is due to the striking ship reaching the centreline

bulkhead of the struck ship.

In addition, it is observed that LS-DYNA results show the decreasing positive slope because

the side shell which has ruptured will continue to resist the collision (See Figure 66). On the

other hand, in SHARP, after the side shell breaks, nothing is there to resist the collision anymore

and the crushing resistance is assumed to have dropped to zero. The side shell crushing

resistances obtained from LS-DYNA and SHARP are compared in Figure 67.

According to Figure 67, it is obvious that the side shell impact resistances calculated from LS-

DYNA and SHARP are very different in nature as well as in amplitudes. It is seen that the

resistance given by LS-DYNA is almost 6 times larger than the one calculated by SHARP. This

is due to the fact that the penetration is very localized which leads to a very rapid rupture of the

side shell in SHARP while this is not the case in LS-DYNA.

0.00E+00

5.00E+06

1.00E+07

1.50E+07

2.00E+07

2.50E+07

3.00E+07

3.50E+07

4.00E+07

0.00 1.00 2.00 3.00 4.00 5.00

Def

orm

atio

n E

ner

gy

[J]

Penetration [m]


LS-DYNA

Simulation 1

Simulation 2

Simulation 3

Simulation 4

Simulation 5

Simulation 6

Simulation 7

Simulation 8

Simulation 9



Figure 66 View of the side shell which has ruptured being still there and resisting the collision – case 3

Figure 67 Comparison of the crushing resistance of the side shell between LS-DYNA and SHARP

Table 43 highlights the amount of energy dissipation in each of the structural component in LS-

DYNA and SHARP. Note that the values presented in the table are taken at 5.8 m penetration

for both simulations. It can be seen that in this case too, the stiffeners in SHARP absorb very

high amount of energy, accounting for 79 % of the total, which seems to be unrealistic. The

web in LS-DYNA has 17 % energy dissipation while the web in SHARP has 10 %.


A.D.N. Regulations

111



PARTS LS-DYNA SHARP

E (MJ) % E (MJ) %


Side Shell 7.26 25% 1.54 5%

Inner Shell 3.57 12% 1.73 5%

Web Frame 5.04 17% 3.44 10%

Double Bottom 0.09 0% 0 0%

Bottom 0.05 0% 0.14 0%

Weather Deck 0.09 0% 0 0%

Stiffeners 3.4 12% 26.3 79%

Others 9.5 34% 0.05 1%



Table 44 presents the comparison of the results calculated by LS-DYNA and SHARP. Note that

both results in this case were taken at the end of the simulation time and SHARP results are the

average one calculated from all 9 simulation results. It is found out that there is 4 % discrepancy

in the penetration and 21 % discrepancy in the deformation energy.



LS-DYNA 3.61 55.5


% Difference 4% 21%

In Figure 68, the results are again compared graphically. It can be observed that with the

modified rupture strain, all SHARP results are in good accord with LS-DYNA and slightly

more conservative too.



Figure 68 Comparison of the results – case 4 (with modified rupture strain)

Table 45 compares the amount of energy dissipation in each of the structural component in LS-

DYNA and SHARP in the form of percentages. Note that the values of SHARP shown in this

table are only the results of simulation 1 in which the real impact point was considered.

Surprisingly, in this case, the side shell in SHARP absorbs more than half of the total energy.

Table 45 Comparison of the energy dissipation – case 4 (with rupture strain)

PARTS LS-DYNA SHARP

E (MJ) % E (MJ) %

Total Energy 55.5 45.8

Side Shell 8 14% 23.7 52%

Inner Shell 3 5% 0.34 1%

Web Frame 5.5 10% 8.42 18%


Bottom 0 0% 0 0%

Weather Deck 21.6 39% 6.6 14%

Stiffeners 1.7 3% 6.6 14%

Others 15.68 28% -0.01 0%


0.00E+00

1.00E+07

2.00E+07

3.00E+07

4.00E+07

5.00E+07

6.00E+07

0.00 1.00 2.00 3.00 4.00

Def

orm

atio

n E

ner

gy

[J]

Penetration [m]


LS-DYNA

Simulation 1

Simulation 2

Simulation 3

Simulation 4

Simulation 5

Simulation 6

Simulation 7

Simulation 8

Simulation 9


A.D.N. Regulations

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However, with the modified value of rupture strain, it is understandable that the behaviour of

side shell are different for different cases. In this case, the rupture strain value used is ‘3’ which

makes the side shell to become more resistant. This in turn has caused a decrease of energy

dissipation in the stiffeners. This case somehow highlights that if the side shell super-element

was correctly modelled, the stiffeners would correspond correctly. Nevertheless, modelling of

both structural failure, i.e., stiffeners and side shell, are to be investigated more in the future.

The energies dissipated by the web frames are found to be not too different from LS-DYNA,

showing 5.5 MJ in LS-DYNA and 8.4 MJ in SHARP.


The results of case 5 are compared in Table 46. It can be seen that there is 10 % discrepancy

for penetration and 6 % discrepancy for deformation energy. Note that both simulation results

are taken at the end of the simulation time.



LS-DYNA 3 56.4


% Difference 10% 6%

Figure 69 Comparison of the results – case 5 (with modified rupture strain)

0.00E+00

1.00E+07

2.00E+07

3.00E+07

4.00E+07

5.00E+07

6.00E+07

7.00E+07

0.00 1.00 2.00 3.00 4.00

Def

orm

atio

n E

ner

gy

[J]

Penetration [m]


LS-DYNA

Simulation 1

Simulation 2

Simulation 3

Simulation 4

Simulation 5

Simulation 6

Simulation 7

Simulation 8

Simulation 9



In Figure 69, the results are again compared graphically and a good agreement is found between

LS-DYNA and SHARP results. However, between the penetration damage of 0.5 m and 2 m,

SHARP results are found to be a bit higher (almost twice) than LS-DYNA results. The reason

is probably due to the behaviour of the side shell super-element. At the start of the collision, it

will have more stiffness due to the high rupture strain value (Ec = 3) used in this SHARP

simulation. The stiffness will abruptly decrease when the calculated strain exceeds the criteria,

and in this case, it is obvious that the overall deformation energy will decrease too. However,

this makes the results of LS-DYNA and SHARP to be in better comparison.

In Table 47, the comparison of the energy dissipation is given in the form of percentages of the

total energy. It can be observed that the energy distributions of different structural components

are in quite good agreement with LS-DYNA except for stiffeners and weather deck.

The weather deck of SHARP absorbs 1.6 times less energy than the weather deck of LS-DYNA

does. As in the case for stiffeners, similar to the previous simulations, the energy dissipation of

stiffeners in SHARP is very high (about 45 % of the total energy). Therefore, it could be said

that the extra energy absorbed by other elements in LS-DYNA such as brackets, deck transverse

beams, etc. seemed to have been compensated by the extra energy absorbed by the stiffeners in

SHARP.


PARTS LS-DYNA SHARP

E (MJ) % E (MJ) %

Total Energy 56.4 60.2

Side Shell 13.5 24% 12.5 21%

Inner Shell 5.5 10% 3.42 6%

Web Frame 6.9 12% 6.65 11%


Bottom 0.15 0% 0 0%

Weather Deck 16.2 29% 9.94 17%

Stiffeners 3 5% 27.3 45%

Others 10.85 19% -0.01 0%

Penetration [m] 3 3.43


A.D.N. Regulations

115



According to the results from case 1 to case 5 (from Section 6.3.1 to Section 6.3.5), it can be

observed that with the tuned rupture strain, the results of SHARP correspond better with LS-

DYNA except for case 3. However, it should be noted that cases 3 and 4 use the push barge

bow whose shape has been modelled in SHARP with a lot of geometrical simplifications.

In most of the cases except in cases 3 and 5, the dissipated energies calculated by LS-DYNA

are found to be higher (around 20%) than those as assessed by SHARP. This is due to the fact

that, for inland vessels, in which the height of struck and striking ships are similar, the weather

deck and the bottom are simultaneously deformed in LS-DYNA even if they are not directly

impacted. On contrary, the super-elements are independently activated upon contact in SHARP.

In other words, some coupling between decks, bottom and side shell needs to be taken into

account even though they are not being impacted. Theoretical developments have already been

performed and presented in (Buldgen et al., 2013) but not implemented in SHARP solver yet.

The summary of penetration and deformation energy at the end of the simulation, i.e., when

there is no more deformation, is given in Table 48 below. The values presented for SHARP are

obtained by averaging the 9 scenario results.

Table 48 Result discrepancy of the simulations (cases with modified rupture strain)

Cases Penetration Deformation energy

1 3% 24%

2 2% 18%

3* - 1%

4 4% 21%

5 10% 6%

*Note that case 3 is the only case in which the comparison is made at the 5.8 m penetration damage.

All things considered, one of the interesting facts about this study is how to adapt the failure

modelling for the super-elements in order to correctly simulate the ship collision. In Appendix

B, the failure strain sensitivity check has been performed by applying different values of rupture

strain Ec in SHARP simulations and the results are compared with LS-DYNA.



7. CONCLUSIONS AND RECOMMENDATIONS

In this master thesis, some validation tests for a simplified analytical tool SHARP have been

performed by comparing the results with non-linear finite element explicit code, LS-DYNA.

The modelling of the colliding ships involved and the associated scenarios have been defined

within the scope of A.D.N. Regulations.

Generally, the simulations can be divided into two categories:

Simulations without modelling rupture at constant striking ship’s speed of 3 m/s; and

Simulations accounting for rupture at constant striking ship’s speed of 10 m/s.

According to the results obtained, the following conclusions and recommendations could be

made:

The use of the virtual deck which is defined with zero thickness to serve as a geometrical

limit during modelling of the struck ship is found to have caused some effect in the side

shell super-element of SHARP. As a consequence, the side shell behaves more rigidly

than it should be and this leads to some inconsistent results especially in cases where

rupture is disregarded. Therefore, it is recommended to improve the user interface of

SHARP in order to correctly characterize the actual structural behaviour of the super-

elements.

The coupling effect that occurs when the weather deck and bottom are not heavily

constructed as compared with the side shell and/or when the depths of the colliding ships

are similar (usually for inland ships) has not been considered in SHARP since the

application of the tool is originally intended for the collisions of FPSO and ocean-going

tankers. Analytical formulations have been developed by (Buldgen et al., 2013) and in

the future version of SHARP, it will become possible to take into account such effect.

Also, the geometrical simplifications that have to be made when modelling the push

barge has led to some discrepancy in the results. Therefore, more vessel lines and/or

surface tools are suggested to implement in the SHARP modelling interface to allow for

a more precise description of the barge bow shape.

In addition, a premature failing of the side shell super-element is observed when the

same rupture strain as LS-DYNA is applied. Moreover, it is also important to take into

account the post rupture behaviour of the side shell super-element to avoid an


A.D.N. Regulations

117


underestimation in the overall struck ship resistance. In this thesis, see Section 6.3, this

lack of resistance in the side shell super-element has been compensated by defining a

larger rupture criterion. Nevertheless, this matter regarding the adaptation of rupture

strain for the super-element still requires an intensive research as the individual element

length le mentioned in A.D.N. cannot be applied for the super-elements due to the

methodology itself.

Regarding the material properties, a true stress-strain relation following the power law

has been applied for the LS-DYNA along with the consideration of elasto-plastic

material. On the other hand, a rigid-plastic material associated to a constant plastic flow

stress is defined in SHARP. However, neglecting the elastic part of the deformation can

sometimes have significant effect when the collision event involves smaller vessels with

slow speed applications.

Finally, the behaviour of the stiffeners that have not failed even in the event of shell

plating rupture should be investigated.

Considering all these aforementioned facts, it is obvious that the SHARP program needs more

developments in the solver as well as in the user interface. Nevertheless, SHARP still promises

a potential considering the time required for the simulations (a few seconds) as compared with

the Finite Element simulations (a few days). Also, the user interface of SHARP is very easy to

use since a full structural model can be generated within a few days unlike the building of Finite

Element models that usually requires tremendous effort and an immense amount of time.

To conclude, in the near future after all the developments will have been considered, SHARP

might become an effective as well as a reliable tool that can substitute the conventional finite

element method in terms of rapidity and simplicity when it comes to ship collision analysis.



ACKNOWLEDGEMENTS

First of all, I would like to give my wholehearted thanks to all the teachers and mentors who

have thought me and guided me to be in the right direction and to be able to proudly stand in

this current position.

Secondly, I would like to express my profound gratitude towards Prof. Hervé Le Sourne, my

thesis supervisor at l'Institut Catholique d'Arts et Métiers (ICAM), for sharing his insights and

valuable expertise with me to perform a successful study.

Thirdly, I would like to convey my genuine thanks to Stéphane Paboeuf, another supervisor of

mine from Bureau Veritas Marine & Offshore Division in Nantes, who always provided me

with precious advices and guidance throughout my internship period.

I would also like to deeply thank ICAM for their support with necessary computation power

which has let me finish all my LS-DYNA simulations in time. In addition, I would like to show

my appreciation to Bureau Veritas teams that welcomed me with open arms, creating an

atmosphere of warmth and friendliness.

Moreover, my deepest gratitude goes to Prof. Philippe Rigo, a coordinator of the EMSHIP

program, for inviting me to Europe and giving me a chance to participate in this challenging

master program in the first place. He is again the reviewer of this master thesis that deserves

him another round of my sincere regards.

Also, I would like to say great thanks to my parents for giving me encouragement and

motivation every time I needed it.

Last but not least, I would like to place on record my sense of gratitude to all the people, who

have directly or indirectly lent a helping hand in the development of this thesis.

This thesis was developed in the frame of the European Master Course in “Integrated Advanced

Ship Design” named “EMSHIP” for “European Education in Advanced Ship Design”, Ref.:

159652-1-2009-1-BE-ERA MUNDUS-EMMC.

Ye Pyae Sone Oo

Wednesday, 11 January 2017.

Carquefou, France.


A.D.N. Regulations

119


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Besnard, N., 2014. SHARP 2 V1.0 User Guide. La Ciotat: PRINCIPIA.

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APPENDIX



A. CONVERGENCE TESTS FOR MCOL SUB-CYCLING


Figure A - 2 MCOL convergence test for penetration (case 2 - without rupture strain)

0.0E+00

2.0E+07

4.0E+07

6.0E+07

8.0E+07

1.0E+08

1.2E+08

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Def

orm

atio

n E

ner

gy

[J]

Time [sec]

Deformation energy Vs TimeCase 2 (V-shape bow : 90 deg : Between webs : Mid-depth of struck ship)

MCOL_100 MCOL_200 MCOL_400

0.0

1.0

2.0

3.0

4.0

5.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Pen

etra

tio

n [

m]

Time [sec]

Penetration Vs TimeCase 2 (V-shape bow : 90 deg : Between webs : Mid-depth of struck ship)

MCOL100 MCOL_200 MCOL_400


A.D.N. Regulations

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Figure A - 4 MCOL convergence test for penetration (case 3 - without rupture strain)

0.0E+00

2.0E+07

4.0E+07

6.0E+07

8.0E+07

1.0E+08

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Def

orm

atio

n E

ner

gy

[J]

Time [sec]

Deformation energy Vs TimeCase 3 (Push barge bow : 55 deg : At web : Mid-depth of struck ship)


0.0

1.0

2.0

3.0

4.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Pen

etra

tio

n [

m]

Time [sec]

Penetration Vs TimeCase 3 (Push barge bow : 55 deg : At web : Mid-depth of struck ship)




Figure A - 5 MCOL convergence test for deformation energy (case 4 - with rupture strain)

Figure A - 6 MCOL convergence test for deformation energy (case 4 - with rupture strain)

0.0E+00

1.0E+07

2.0E+07

3.0E+07

4.0E+07

5.0E+07

6.0E+07

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Def

orm

atio

n E

ner

gy

[J]

Time [sec]

Deformation energy Vs TimeCase 4 (Push barge : 55 deg : At bulkhead : Above deck of struck ship)


0.0

1.0

2.0

3.0

4.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Pen

etra

tio

n [

m]

Time [sec]

Penetration Vs TimeCase 4 (Push barge : 55 deg : At bulkhead : Above deck of strcuk ship)



A.D.N. Regulations

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B. CASE SENSITIVITY OF RUPTURE STRAIN

B.1 Case 1 (V-shape bow : 90 deg : At web : Under deck of struck ship)

Table B - 1 Evaluation of energy distribution using different rupture strains – Case 1

PARTS LS-DYNA

SHARP* SHARP

Ec = 0.2 Ec = 0.5

E (MJ) % E (MJ) % E (MJ) %

Total Energy 111 29.5 81.3

Side Shell 29 26% 1.26 4% 5.06 6%

Inner Shell 10.4 9% 1.26 4% 1.85 2%

Web Frame 12.8 12% 12.7 43% 11.8 15%

Double Bottom 7.8 7% 0.65 2% 0.39 0%

Bottom 4.7 4% 0 0% 0 0%

Weather Deck 18 16% 0 0% 0 0%

Stiffeners (Side) 5.8 5% 13.6 46% 62.2 77%

Others 22.5 20% 0.03 0% 0 0%


SHARP SHARP SHARP SHARP

Ec = 1 Ec = 2 Ec = 3 Ec = 5

E (MJ) % E (MJ) % E (MJ) % E (MJ) %

85.6 86.2 86.8 87.7

6.77 8% 10.2 12% 14.7 17% 21.9 25%

2.7 3% 4.22 5% 7.05 8% 9.44 11%

10.7 13% 10.6 12% 10.5 12% 10.4 12%

0.33 0% 0.24 0% 0.21 0% 0.13 0%

0 0% 0 0% 0 0% 0 0%

0 0% 0 0% 0 0% 0 0%

65.1 76% 60.9 71% 54.3 63% 45.8 52%

0 0% 0.04 0% 0.04 0% 0.03 0%

4.39 4.16 4 3.8

*Results taken at 1 sec of collision simulation time.

Ec : Rupture Strain

E : Deformation energy [MJ]



B.2 Case 2 (V-shape bow : 90 deg : Between webs : Mid-depth of struck

ship)


PARTS LS-DYNA

SHARP* SHARP

Ec = 0.2 Ec = 0.5

E (MJ) % E (MJ) % E (MJ) %

Total Energy 103 20.1 77.7

Side Shell 28.5 28% 0.65 3% 1.79 2%

Inner Shell 9 9% 1.35 7% 1.75 2%

Web Frame 12.3 12% 2.3 11% 1.66 2%

Double Bottom 14 14% 0.05 0% 0.02 0%

Bottom 9.9 10% 2.75 14% 1.5 2%

Weather Deck 5.2 5% 0 0% 0 0%

Stiffeners 6.3 6% 13 65% 71 91%

Others 17.8 17% 0 0% -0.02 0%



Ec = 1 Ec = 2 Ec = 3 Ec = 5

E (MJ) % E (MJ) % E (MJ) % E (MJ) %

80.9 81.8 82.1 83.3

3.48 4% 8.45 10% 11.7 14% 21.4 26%

4.22 5% 4.34 5% 4.03 5% 4.12 5%

1.52 2% 1.47 2% 1.43 2% 1.44 2%

0.02 0% 0.02 0% 0.02 0% 0.02 0%

1.26 2% 1.22 1% 1.2 1% 1.16 1%

0 0% 0 0% 0 0% 0 0%

70.4 87% 66.3 81% 63.8 78% 55.2 66%

0 0% 0 0% -0.08 0% -0.04 0%

4.76 4.65 4.59 4.34


Ec : Rupture Strain



A.D.N. Regulations

129


B.3 Case 3 (Push barge : 55 deg : At web : Mid-depth of struck ship)


PARTS LS-DYNA*

SHARP* SHARP*

Ec = 0.2 Ec = 0.5

E (MJ) % E (MJ) % E (MJ) %


Side Shell 12 23% 0.7 4% 1.54 4%

Inner Shell 7 13% 1.2 7% 2.11 6%

Web Frame 8.8 17% 3.94 22% 3.83 10%

Double Bottom 0.9 2% 0 0% 0 0%

Bottom 0.5 1% 0.13 1% 0.14 0%

Weather Deck 0.12 0% 0 0% 0 0%

Stiffeners 6 11% 11.8 66% 29.8 80%

Others 17.38 33% 0.03 0% -0.02 0%

Penetration (m) 7 7.7 6.7

SHARP* SHARP SHARP SHARP

Ec = 1 Ec = 2 Ec = 3 Ec = 5

E (MJ) % E (MJ) % E (MJ) % E (MJ) %

44 66.5 67.8 69.7

2.4 5% 6.15 9% 4.79 7% 6.28 9%

4.02 9% 7.51 11% 6.75 10% 8.73 13%

3.97 9% 4.49 7% 3.61 5% 3.28 5%

0.01 0% 0.02 0% 0.01 0% 0 0%

0.16 0% 0.2 0% 0.26 0% 0.33 0%

0 0% 0 0% 0 0% 0 0%

33.5 76% 48.1 72% 52.4 77% 51.1 73%

-0.06 0% 0.03 0% -0.02 0% -0.02 0%

7.3 6.8 5.69 5.1


Ec : Rupture Strain




B.4 Case 4 (Push barge : 55 deg : At bulkhead : Above deck of struck ship)


PARTS LS-DYNA

SHARP* SHARP*

Ec = 0.2 Ec = 0.5

E (MJ) % E (MJ) % E (MJ) %


Side Shell 8 14% 2.62 8% 6.19 16%

Inner Shell 3 5% 0.58 2% 1.24 3%

Web Frame 5.5 10% 11.3 35% 13.7 36%

Double Bottom 0.02 0% 3.64 11% 2.75 7%

Bottom 0 0% 0 0% 0 0%

Weather Deck 21.6 39% 10.7 33% 7.46 19%

Stiffeners 1.7 3% 3.58 11% 7.11 18%

Others 15.68 28% 0.08 0% 0.05 0%



Ec = 1 Ec = 2 Ec = 3 Ec = 5

E (MJ) % E (MJ) % E (MJ) % E (MJ) %

43.3 44.3 45.8 47.4

14.2 33% 17.5 40% 23.7 52% 28.8 61%

0.9 2% 1.02 2% 0.34 1% 0.15 0%

10 23% 9.12 21% 8.42 18% 7.44 16%

0.84 2% 0.5 1% 0.15 0% 0 0%

0 0% 0 0% 0 0% 0 0%

7.11 16% 6.96 16% 6.6 14% 7.86 17%

10.2 24% 9.21 21% 6.6 14% 3.09 7%

0.05 0% -0.01 0% -0.01 0% 0.06 0%

4.44 4.16 3.74 3.22


Ec : Rupture Strain



A.D.N. Regulations

131


B.5 Case 5 (V-shape bow : 90 deg : At web : Above deck of struck ship)


PARTS LS-DYNA

SHARP* SHARP

Ec = 0.2 Ec = 0.5

E (MJ) % E (MJ) % E (MJ) %


Side Shell 13.5 24% 1.86 4% 3.11 5%

Inner Shell 5.5 10% 0.72 1% 1.05 2%

Web Frame 6.9 12% 9.04 18% 6.8 11%

Double Bottom 0.3 1% 1.38 3% 0.62 1%

Bottom 0.15 0% 0 0% 0 0%

Weather Deck 16.2 29% 25.9 52% 15.4 26%

Stiffeners 3 5% 10.7 22% 33 55%

Others 10.85 19% -0.1 0% 0.12 0%

Penetration (m) 3 7.05 4.44


Ec = 1 Ec = 2 Ec = 3 Ec = 5

E (MJ) % E (MJ) % E (MJ) % E (MJ) %

59.2 59.7 60.2 60.9

4.8 8% 8.22 14% 12.5 21% 20.7 34%

1.04 2% 1.95 3% 3.42 6% 2.43 4%

6.74 11% 6.52 11% 6.65 11% 6.49 11%

0.51 1% 0.41 1% 0.4 1% 0.29 0%

0 0% 0 0% 0 0% 0 0%

11.5 19% 10.7 18% 9.94 17% 10.9 18%

34.6 58% 32 54% 27.3 45% 20.1 33%

0.01 0% -0.1 0% -0.01 0% -0.01 0%

3.75 3.6 3.43 3.14


Ec : Rupture Strain
