Finite Element Analysis of Offshore Jacket Structure Subjected to … · 2018-12-04 · Finite...

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Finite Element Analysis of Offshore Jacket Structure Subjected to Deformable Vessel

Collisions

Jose Babu Maliakel

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 ICAM, FRANCE 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. Herve Lesourne, ICAM-NANTES, FRANCE

Reviewer: Prof. Philippe Rigo, University of Liege

Nantes, February 2014

P 2 Jose Babu Maliakel

Master Thesis developed at ICAM-Nantes, France

Finite Element Analysis of Offshore Jacket Structure Subjected to Deformable Vessel Collisions

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“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014

ABSTRACT

Collisions between ships and offshore wind energy turbines (OWTs) represent a substantial

danger to the environment. It ought to be taken into account that in a collision event, areas of

the ship structure are damaged. The possibility of leakage of cargo is supplementary to the

structural damage to the offshore structure. Hence arises a need for accurate finite element

analysis to precisely access the extent of damage that may result as a consequence of such a

collision.

Experimental impact tests on H-Brace structure which were conducted by the University of

Ulsan, Korea to better understand the behavior of these simple tubular structure to impact loads.

The diameter-thickness ratios used for the experimental testing were similar to that of the

tubular members that are presently being used in the offshore industry. Geometrical values of

the same has been used by the author to develop a finite element models of H-Brace structures

to conduct a numerical study into the behavior of these tubular structures. After a numerical

parametric study was conducted on the H-Brace structure by varying tubular thickness,

diameter and boundary conditions, finite element simulations subjecting a 4-legged jacket

structure to collision from offshore supply vessel and bulk carrier was carried out to

comprehend the local and global deformation characteristics of 4-legged jacket in case of high

energy collisions. Bow impact was considered for offshore supply vessel and broadside impact

was considered for bulk carrier. A parametric study was also conducted by varying jacket leg

thickness to study its effect on the force-deformation and energy-deformation relationships of

the impacted jacket and the striking ship. Subsequently the results pertaining to local

indentation of impacted member was compared to recommended design curves by NORSOK.

LS-DYNA finite element code were used for the simulations.



PREFACE

This master thesis topic was decided by Prof.Herve Le sourne – ICAM Nantes, France and

allocated to the author. The work on the thesis began in July 2013.

The work conducted was part of the wider framework of the CHARGEOL Project, which deals

with the development of calculation tools with the objective to study the behavior of an offshore

wind turbine supporting structure when it is submitted to accidental loads: seism, ship

collisions, strong wave impacts, etc.

The partners of this project are:

Hydrocean for waves impact analyses

GEM Laboratory (ECN) for the seismic numerical studies

IFFSTAR Laboratory for the seismic tests

BUREAU VERITAS for validation of developed tools.

STX FRANCE, leader of the project, builder of the jackets and future user of the

developed tools

ICAM for collision numerical studies and for the development of a simplified tool

which will help to dimension the jacket submitted to a ship collision

The mechanical engineering department of ICAM (LE2M) will be involved in the development

of a ship collision analysis tool which will be used by STX Solution and BUREAU VERITAS

at the pre-design stage of a jacket. This tool is based on the super-element method which has

been developed by ICAM in collaboration with University of Liege (ANAST laboratory).

Hence all the data generated through the numerical simulations will be used for the development

and validation of this analytical tool based on the superelement method. The work scope of the

author involves numerical simulation only. The superelement based analysis tool is developed

by other specific members of the CHARGEOL Project team.


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DECLARATION OF AUTHORSHIP

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

as the result ofmy 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 the University of ICAM Nantes-France

Date: 20-01-2014 Signature



Table of Contents

1. Introduction ............................................................................................................................... 11

2. Accidental collisions – Design principles ................................................................................. 18

2.1. General ....................................................................................................................................... 18

2.2. Energy perspective ..................................................................................................................... 18

2.3. Force – deformation relationships .............................................................................................. 19

3. Calculation methods .......................................................................................................................... 20

3.1. Deformation Modes .................................................................................................................... 20

3.2. Local Deformation of Tubular Members ................................................................................... 21

4. Superlement theory............................................................................................................................ 23

5. Non-linear FEA using LS-DYNA ..................................................................................................... 28

5.1. LS-DYNA – General information .............................................................................................. 28

5.2. Solution Methodology ................................................................................................................ 28

5.2.1. Stability and Time-Step ....................................................................................................... 29

5.3. Shell elements ............................................................................................................................ 29

5.4. Material models .......................................................................................................................... 30

5.4.1. Piecewise Linear Plasticity ................................................................................................. 30

5.4.2. Rigid Material ..................................................................................................................... 30

5.5. Contact definition between colliding surfaces ........................................................................... 31

6. H- BRACE Structure ......................................................................................................................... 32

6.1. General ....................................................................................................................................... 32

6.2. H-Brace & Striker Finite Element Model .................................................................................. 33

6.2.1. Model Verification ............................................................................................................... 36

6.2.2. Mesh and Elements .............................................................................................................. 36

6.2.3. Boundary Conditions ........................................................................................................... 36

6.2.4. Material Properties ............................................................................................................. 37

6.3. FEA Results ................................................................................................................................ 38

6.3.1. H-STRUCTURE perpendicular & oblique impact simulations ........................................... 38

6.3.2. Parametric Study ................................................................................................................. 39

6.3.3. Effect of Boundary Conditions ............................................................................................ 39

6.3.4. Effect of brace thickness ...................................................................................................... 42

6.3.5. Effect of brace diameter ...................................................................................................... 46

7. Jacket model ...................................................................................................................................... 50


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7.1. General ....................................................................................................................................... 50

7.2. FE Model .................................................................................................................................... 50

7.2.1. Mesh and Elements .............................................................................................................. 50

7.2.2. Boundary Conditions ........................................................................................................... 51


8. OSV Bow Model ............................................................................................................................... 53

8.1. General ....................................................................................................................................... 53

8.2. FE Model .................................................................................................................................... 55

8.2.1. Model Verification ............................................................................................................... 55


8.2.4. Impact Location ................................................................................................................... 56

8.3. FE Simulation Results – Impact Location 1 ............................................................................... 57

8.3.1. Available Strain Energy ...................................................................................................... 57

8.3.2. Force-Deformation relationship ......................................................................................... 57

8.3.3. Effect of thickness ................................................................................................................ 61

8.3.4. Energy Dissipation Characteristics .................................................................................... 64

8.3.5. Resistance to Local Indentation .......................................................................................... 69

8.4. FE Simulation Results – Impact Location 2 ............................................................................... 72

8.4.1. Force Deformation Relationship ......................................................................................... 72

9. Bulk Carrier Side Impact – 1 m/s ...................................................................................................... 75

9.1. General ....................................................................................................................................... 75

9.2. FE Model .................................................................................................................................... 78

9.3. FE Results – Impact Velocity 1 m/s ........................................................................................... 81

9.3.3. Effect of Leg Thickness ........................................................................................................ 85

9.4. FE Results – Impact Velocity 2 m/s ........................................................................................... 93

9.4.1. Force Displacement Relationship ....................................................................................... 93

10. DISCUSSIONS & CONCLUSIONS .............................................................................................. 96

11. FURTHER WORK.......................................................................................................................... 98

12. ACKNOWLEDGEMENTS ............................................................................................................ 99

13. REFERENCES .............................................................................................................................. 100

14. APPENDIX ................................................................................................................................... 102



LIST OF TABLES & FIGURES

Figure 1. Installed capacity - cumulative share by country [left], cumulative share by sea basin

[right] (Source:EWEA) ............................................................................................................ 12 Figure 2. EU 2012 targets (Source:EWEA) ............................................................................. 12 Figure 3.EU 2020 & 2030 targets (Source:EWEA) ................................................................. 13 Figure 4. Tripod Foundation (Source Alpha Ventus) .............................................................. 15 Figure 5. A jacket foundation.( Source Alpha Ventus) ............................................................ 16

Figure 6. Components of a Monopile Foundation ................................................................... 17 Figure 7. Gravity foundations (Source Luc van Braekel ) ....................................................... 17

Figure 8.Design Categories ...................................................................................................... 19 Figure 9.Force-Deformation Relationship ............................................................................... 19 Figure 10. Deformation Modes ................................................................................................ 20 Figure 11. Local denting model ............................................................................................... 21

Figure 12. Local denting resistance .......................................................................................... 21 Figure 13: Super-element types. Source: (Lutzen et al., 2000) ................................................ 24

Figure 14: Geometrical Variables for the Calculation of the Internal Energy on a Cylinder.

Source: Buldgen, Loïc and LeSourne, Hervé, “Impact on Cylinders”, 2013 .......................... 27 Figure 15. Work Scope & Progression ..................................................................................... 32

Figure 16. Actual H-Brace Models used by University of Ulsan ............................................ 33

Figure 17. Geometric Model of OWT-A2 ............................................................................... 34 Figure 18. Mesh of OWT-A2 at Joint Location [LEFT] & Impact Location [RIGHT] .......... 35 Figure 19. Striker Geometry ..................................................................................................... 35

Figure 20. FEA model of Striker A .......................................................................................... 35 Figure 21. Boundary conditions for impact analysis ................................................................ 37

Figure 22. OWT A2 force displacement curve ........................................................................ 40

Figure 23.OWT F2 force displacement curve .......................................................................... 40 Figure 24. Membrane Forces -OWT A2 .................................................................................. 41

Figure 25. Membrane Forces -OWT F2 ................................................................................... 41 Figure 26. Force-Displacement Curve for varying thickness- OWT F2 .................................. 42 Figure 27. Plastic Strain Plots for varying brace thicknesss .................................................... 45

Figure 28. Force v/s Local/Global Displacement curve. Thickness =2.1mm .......................... 45 Figure 29.Force v/s Local/Global Displacement curve. Thickness =4.1mm ........................... 46

Figure 30.Force v/s Displacement curve - Varying Diameter ................................................. 47 Figure 31. Force v/s Local Displacement curve. Thickness =3.1mm ...................................... 48

Figure 32. Force v/s Global Displacement curve. Thickness =3.1mm .................................... 49 Figure 33. FE mesh of Jacket Bottom ...................................................................................... 50 Figure 34. Jacket Model ........................................................................................................... 51 Figure 35. OSV Bow Geometry ............................................................................................... 53 Figure 36. OSV Bow FE Mesh ................................................................................................ 54

Figure 37. OSV Structural Configuration ................................................................................ 55 Figure 38. Impact Location 1 [Left] Impact Location 2 [Right] .............................................. 56 Figure 39. Force Deformation Characteristics : Varying Thickness ........................................ 58 Figure 40. Local Indentation. Thickness= 40mm [LEFT] Thickness=60mm [RIGHT] .......... 60


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Figure 41. Force v/s Displacemet [Local/Global] . Thickness =60mm ................................... 61

Figure 42.Force v/s Displacemet [Local/Global] . Thickness =50mm .................................... 61 Figure 43. Force v/s Displacemet [Local/Global] . Thickness =40mm ................................... 62 Figure 44. Plastic Strain Plot of Collision. Jacket Leg Thickness =40mm .............................. 63

Figure 45. Energy v/s Deformation Curve. Thickness =40mm ............................................... 65 Figure 46. Energy v/s Deformation Curve. Thickness =50mm ............................................... 65 Figure 47. Energy v/s Deformation Curve. Thickness =60mm ............................................... 66 Figure 48. Deformed Hull Shell ............................................................................................... 67 Figure 49. Deformed Deck Plate .............................................................................................. 68

Figure 50. Deformed Hull Shell Longitudinals ........................................................................ 68 Figure 51. . Comparison b/w NORSOK reistance curves against Numerical Simulation

Resistance Curves .................................................................................................................... 70 Figure 52. Deformed Leg Section. 40mm Thickness [left] 60mm Thickness [Right] ............. 70 Figure 53. Force Deformation Relationship Comparison b/w 2 impact locations ................... 72

Figure 54. Local Indentation Comparison b/w 2 impact locations, Thickness =40mm ........... 73 Figure 55 Local Indentation Comparison b/w 2 impact locations, Thickness =50mm............ 74

Figure 56. Local Indentation Comparison b/w 2 impact locations, Thickness =60mm.......... 74 Figure 57. Photo of Panamax Bulk Carrier .............................................................................. 75 Figure 58. Bulk Carrier FEM Model ........................................................................................ 76 Figure 59. Double Bottom Structure ........................................................................................ 76

Figure 60. Web Frames & Topside & Hopper Longitudinals .................................................. 77 Figure 61. FE Mesh of Bulk Carrier Hold ............................................................................... 78

Figure 62. FE Mesh of Bulk Carrier Hold ............................................................................... 79 Figure 63. Impact Location Bulk Carrier ................................................................................. 80 Figure 64. Force-Displacement Curve -Bulk Carrier Side Impact 1m/s .................................. 82

Figure 65. Plastic Strain Plot of one impacted Leg. 60mm Thickness [LEFT] & Thickness

40mm [RIGHT] ........................................................................................................................ 84 Figure 66. Local/Global Deformation Comparision. Thickness =40mm................................ 86 Figure 67. Local/Global Deformation Comparision. Thickness =50mm .............................. 86

Figure 68. Local/Global Deformation Comparision. Thickness =60mm................................ 87 Figure 69. Energy Displacement Curve . Thickness = 40mm ................................................. 88

Figure 70. Energy Displacement Curve . Thickness = 50mm ................................................. 89

Figure 71. Energy Displacement Curve . Thickness = 60mm ................................................. 89 Figure 72. Plastic Strain Plot of Jacket with leg Thickness=40mm, Post Collision ................ 90

Figure 73. Top view of Jacket Leg with 40mm Leg Thickness, Post Collision ...................... 91 Figure 74. Strain Plot of Ship & Jacket. Isometric View ......................................................... 91 Figure 75. Strain Plot of Ship Structural Members .................................................................. 92

Figure 76. Plastic Strain Plot. Thickness = 40mm. Time = 1s. [LEFT] Time= 2s [RIGHT] .. 93 Figure 79. Force Deformation Curves-Bulk Carrier Impact- 2m/s .......................................... 95

Figure 80. Energy -Displcement Graph - 15 Degrees ............................................................ 102 Figure 81. Force-Diplacement Graph - 15 Degrees ............................................................... 102

Figure 82. Energy -Displacement Graph - 30 Degrees .......................................................... 103 Figure 83. Force-Displacement Graph - 30 Degrees .............................................................. 103 Figure 84. Energy-Displacement Graph -45 Degrees ............................................................ 104 Figure 85. Force-Displacement Graph - 45 Degrees .............................................................. 104 Figure 86. Energy-Displacement Graph - 60 Degrees ........................................................... 105

Figure 87. Force-Displacement Graph - 60 Degrees .............................................................. 105



Table 1. Dimension of created FE Models. .............................................................................. 33 Table 2. Material Properties of H-Brace Models ..................................................................... 37 Table 3. FEA Result comparision for H-BRACE configurations ............................................ 38 Table 4. Oblique impact results -OWT A2 .............................................................................. 39 Table 5. OWT-F2-Strength Increase with Increasing Thickness. Displacement – 0.01m ....... 43

Table 6. OWT-F2-Strength Increase with Increasing Thickness. Displacement – 0.02m ....... 43 Table 7. Material Properties of Jacket ...................................................................................... 52 Table 8. Particulars of the Modelled OSV Bow ....................................................................... 54 Table 9. OSV Ship Particulars ................................................................................................. 54 Table 10. Material property of OSV Bow Structure ................................................................ 56

Table 11. Strength Increase vis a vis Thickness Increase. Displacement =0.05m ................... 59 Table 12. Strength Increase vis a vis Thickness Increase. Displacement =0.1m ..................... 59

Table 13. Displacement & Acceleration of the transition piece. ............................................. 63 Table 14. Energy Absorption Characteristics for OSV structural Members ............................ 67 Table 15. Bulk Carrier Particulars ............................................................................................ 75 Table 16. Particular's of the Model Bulk Carrier Cargo Hold ................................................. 77

Table 17. Material Properties of Bulk Carrier .......................................................................... 80 Table 18. Strength Increase Comparison for displacement 0.5m ............................................ 83

Table 19.Strength Increase Comparison for displacement 1m ................................................ 83 Table 20. Displacement and Accelerations of Transition Piece ............................................... 85 Table 21. Energy Dissipation Characteristics - Ship Structural Members ............................... 92


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1. Introduction

Energy security has consistently been top on the priority list for all the countries. However,

presently it is not just a question of achieving this energy security, but additionally a question

of exactly how it is achieved. At this point in time, this is especially relevant in Europe as huge

efforts are being made to accomplish a really environmentally friendly energy future centered

on indigenous, non-polluting and viable renewable systems. To this end an EU policy

framework on wind energy has been established and has been the driver for growth in this

relatively young industry. Since 1995, wind energy has played a growing and rapidly

accelerating role in the expansion of the renewable energy industry. The majority of the 84 GW

of wind power installed in the EU by the close of 2010 were added in the latter 10 years. This

substantial deployment of wind power has been a key component in decreasing greenhouse gas

emissions from the energy sector, with more wind power capacity being set up in the EU than

any other power generating system in the last 10 years, with the exception of gas. The European

Commission envisioned, in its 2008 Communication on offshore wind energy (Breu,

Guggenbichler, & Wollmann, 2008) that "offshore wind can and must make a substantial

contribution to meeting the EU's energy policy objectives through a very significant increase -

in the order of 30-40 times by 2020 and 100 times by 2030 - in installed capacity compared to

today." Some statistics regarding the cumulative share of different countries in the offshore

wind energy market is shown in Figure 1. The EU targets for the years of 2012, 2020 and 2030

has been illustrated in figures Figure 2 and Figure 3.

Offshore wind farms provide distinct benefits in comparison to farms in close proximity to

shore or on land. Offshore sites have better and more steady wind sources. A wind farm could

be situated over a big and wide open area with less noise restrictions. Bigger wind turbines up

to 5MW, 6 MW and 10MW can consequently be employed. These types of wind turbines can

generate power at a significantly higher capacity and yield compared to onshore. A

disadvantage utilizing offshore wind farms however, is the accident possibilities related to

collisions with large merchant vessels, offshore supply vessels etc. A safety area is generally

defined round the windfarms where the commuting ships should not enter. Nonetheless, all

kinds of offshoer installations requires some assistance for operation and maintenance. This

calls for support vessels to navigate close to the offshoe installations, and thus increasing the

risk of collisions. Ships that are trasiting close to the offshore installations may lose propulsion



and drift toward the offshore structures. Bad weather conditions can have similar effect on ships

which transit close to the windfarms.

Standardised design-curves and calculation methods are often employed in order to estimate

the resistance of the installations. A lot of of the standard design-approaches are centered on

some assumpsions of the actual problem. As a result, the procedures could possibly have

limitations in its use (Qvale, 2012). This is the principal reason why precise, although time

consuming finite element anslysis needs to be done.

Figure 1. Installed capacity - cumulative share by country [left], cumulative share by sea basin [right]

(Source:EWEA)

Figure 2. EU 2012 targets (Source:EWEA)


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Figure 3.EU 2020 & 2030 targets (Source:EWEA)

Onshore wind resources are at saturation point and due to various other issues and it is

imperative that the industry looks offshore for its wind energy requirement.

There are 4 types of foundation which are used in the offshore industry are :

Monopile Structure

Tripod Structures

Jacket Structures

Concrete Structures

Monopiles are large diameter, thick walled, steel tubulars that are driven into the seabed . Outer

diameters usually range from 4 to 6 m and typically 40–50% of the pile is inserted into the

seabed (Figure 6. Components of a Monopile FoundationFigure 6). The conditions of the soil at the

seabed, depth of the water, the design loads such as the wave loads, loads from the

superstructurem local environmental conditions determine the required depth of piling. If an

offshoer structure such as a wind turbine is to be installed in shallow water (<20m), monopiles

are preferred for foundations.



Tripods consist of a central steel shaft connected to three cylindrical steel tubes through which

piles are driven into the seabed (Figure 4). Tripods have more weight and due to its peculiar

geometry, it is quite expensive to manufacture as well.

Jacket foundations are an open lattice steel truss template consisting of a welded frame of tubular members extending from

tubular members extending from the mudline to above the water surface (

Figure 5). A pile is rammed through the jacket legs at the the extreme bottom of the jacket leg

to ensure strength of jacket. Jackets are robust and heavy structures and require expensive

equipment to transport and lift. Since the location of present windfarms are relatively close to

the shore and since the water depth is not too much, jacket structure are not widely used.

Gravity foundations are concrete structures that use their weight to resist wind and wave loading

(Figure 7). In comparision to monopiles, gravity foundations are relatively less expensive to

build albeit the installation costs are higher, largely due to the need for dredging and subsurface

preparation and the use of specialized heavy-lift vessels. Gravity foundations may also have an

advantage in ice-prone regions (Herndon, 2008).

At present, most of the offshore wind farms are quite close to the shore , however, due to an

increasing need to increase the number of windfarms, in order to meet the 2020 & 2030 EU

targets, the windfarms will have to be located further and further away from the shore, which

means that the water depth will increase. Hence there will be an increased usage of jacket

structures as foundations. This increases the probabilities of collisions from ships and collision

analysis of jacket structures will have increasing relevance.


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Figure 4. Tripod Foundation (Source Alpha Ventus)



Figure 5. A jacket foundation.( Source Alpha Ventus)


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Figure 6. Components of a Monopile Foundation

Figure 7. Gravity foundations (Source Luc van Braekel )



2. Accidental collisions – Design principles

2.1. General

The NORSOK STANDARD–004 (NORSOK, 2004) has been referred to extensively in this

chapter. Ship collisions are classified as accidental loads which can be defined in the following

way:

“Accidental actions are actions caused by abnormal operation or technical failure. They

include for instance fires and explosions, impacts from ships, dropped objects, helicopter crash

and change of intended pressure difference.” (Norsok, Federation, & Industry, 2007)

The general objective is to make sure that post a high energy impact, the 3 main aspects of the

offshore structure is retained (NORSOK, 2004):

Usability of escapeways

Integrity of shelter areas

Global load bearing capacity

2.2. Energy perspective

(NORSOK, 2004) differentiates in between three distinctive design classes pertaining to energy

dissipation (Figure 8):

Strength design.

The offshore structure is sturdy enough to endure the collision-force with small

deformation and the colliding vessel deforms and dissipate the vast majority of the

collision energy.

Ductility design.

The offshore structure experiences significant plastic deformations and absorbs the

majority of the collision energy and the striking ship will be sturdy.

Shared-energy design.

This means that that each of the offshore structure and colliding vessel play a significant

role for the dissipation of energy.


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Figure 8.Design Categories

As mentioned in (NORSOK, 2004), strength design or ductility design will offer definite

advantages from a purely calculation point of view since one can know for sure that 1 of the 2

structures involved in collisions will absorb a majority of the energy. As a result, one may use

simple analytical models and associated calculation procedures to calculate the damage caused.

2.3. Force – deformation relationships

Force-deformation relations as shown in Figure 9 depict the reaction forces of the 2 colliding

structures.

Figure 9.Force-Deformation Relationship

The strain energy dissipated in the collision is equivalent to the overall area underneath the two

curves:



3. Calculation methods

3.1. Deformation Modes

A number of deformation methods (Figure 10) could contribute to the energy dissipation

(Soreide, 1985):

Local deformation - bracing/leg

Global deformation - bracing & leg

Overall deformation of the platform

Local deformation of ship structure at impact location

Motions of the colliding ship/offshore structure

Figure 10. Deformation Modes


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3.2. Local Deformation of Tubular Members

Overall strength of the tubular structure in the jacket will be reduced by the local denting (Figure

11). As per (Skallerud & Amdahl, 2002), the consequences of denting are as follows:

Impact energy is absorbed by the impacted member at the initial contact point.

The localized denting reduces the real bending capability of the section and additionally

consequences in supplemental bending moment because of the axial force as a result of

the eccentricity created in the damaged segment.

As per (NORSOK, 2004) , the resistance to local denting of unstiffened tubular members can

be taken from Figure 12 or otherwise by equations.

Figure 11. Local denting model

Figure 12. Local denting resistance



Where,

R = Resistance to the denting process,

RC = Characteristic strength factor,

D = The diameter of the member,

T = The thickness of the member

B = The width of the collision contact region.

wd = The dent depth

fy = Yield Strength of tubular member

(NORSOK, 2004) mentions additionally that the curves in Figure 12 are invalid for small

indentation and ought not to be utilized to validate a design in which the dent damage is below

wd/d < 0.05.

Please note that throughout the thesis, in all force/energy displacement relationships, the

overall displacement is taken into account. Wherever local deformation or denting is

taken into account, it has been mentioned explicitly.

.


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4. Superlement theory

Studying the dynamics of a ship collision requires consideration of many factors. The study of

ship collisions can be divided into three categories: experimental, numerical simulations and

simplified analytical methods (Haris & Amdahl, 2013). Experimental studies are generally used

to validate the other two; however because of the high cost associated to them these are not

widely used to assess ship collisions.

The relative (as compared to the other two categories) straightforwardness of simplified

analytical methods is a very interesting characteristic of this solution. One of the earliest

attempts in presenting a simplified analytical solution to ship collisions was (Minorsky, 1959).

More recent studies has been carried out to calculate the crushing resistance and local denting

of web girders under localized loads (Hong & Amdahl, 2008).

Research has also been performed for impacted panels, and simplified methodologies to

calculate the crushing resistance of metal plates have been presented by (Ohtsubo & Wang,

1995; Wierzbicki, 1995; Zhang, 2002).

With the previously illustrated methodologies closed-form analytical formulations of the

resistance of each component of a ship’s structure (web girders, side panels and intersection

between these) can be obtained. Combining these, the overall capacity of a ship to withstand an

impact with another vessel can be calculated.

The super-element method, which was first proposed by (Lutzen, Simonsen, & Pedersen, 2000)

for perpendicular ship impacts by a rigid bow, divides the ship into large structural components

and estimates its crushing resistance according to the summation of the results from the different

parts. This produces the internal mechanics behavior of the ship, which must be coupled with

the external mechanics (the global ship motion considering its interaction with the fluid that

surrounds it) to obtain accurate results (Le Sourne, Besnard, Cheylan, & Buannic, 2012).



Therefore the structure of the impacted ship is divided into four types of super-elements (Lutzen

et al., 2000):

1. A rectangular plate simply supported on its four edges that experiences out of plane

deflections and ruptures when the deformations exceed the threshold value. It is used

for longitudinal bulkheads, inner and outer side platings.

2. A rectangular plate simply supported on three edges, with the last free and an in-plane

load in a right angle collision. The failure of this plate is characterized by successive

folds resembling a concertina. It serves to model bulkheads, web girders, frames, bottom

and inner bottom.

3. A beam with a force normal to its axis, with a two phase collapse. First it fails by a

mechanism of plastic hinges and later behaves like a plastic string, with a resistance

equal to zero after fracture.

4. X, T and L type intersections, which are used to model the intersection between

transverse bulkheads and mid-decks and transverse bulkheads and the weather decks.

When the axial reduction is equal to the length of the intersection, its load drops to zero.

Figure 13: Super-element types. Source: (Lutzen et al., 2000)


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The basic formulation is based on the evaluation of the external and internal energy rates of the

super-element in question. The external energy rate is evaluated with the following equation:

𝐸𝑒𝑥𝑡̇ = 𝐹 ∗ �̇� (Eq. 6)

Here, Ėext represents the external rate energy absorbed by the super-element, F represents the

resistance of the super-element and �̇� the penetration rate of the striking ship.

The internal energy rate is represented by:

𝐸𝑖𝑛𝑡̇ = ∫ ∫ ∫ 𝜎𝑖𝑗 ∗ 𝜖𝑖𝑗̇ ∗ 𝑑𝑉 (Eq. 7)

With V equal to the volume of the body, 𝜎𝑖𝑗 represents the stress tensor and 𝜖𝑖𝑗̇ is the strain rate

tensor. A series of simplifications are carried out to facilitate the analytical solution of the

previous equation. These include:

1. The material of the super-element is assumed to be perfectly rigid and the flow stress

σo is governed by the following equation:

𝜎𝑜 =𝜎𝑦 + 𝜎𝑢

2 (Eq. 8)

Where 𝜎𝑢 represents the ultimate stress and 𝜎𝑦 the yield stress. This average serves to

simplify the strain hardening effect.

2. The total internal energy rate has its initial contribution due to the bending internal

energy rate, which as the effects of flexion lie within defined plastic hinge lines m, is

equal to

𝐸�̇� = 𝑀𝑜 ∑ �̇�𝑘

𝑚

𝑘=1

𝑙𝑘 (Eq. 9)

Here, 𝑀𝑜 equals the plastic bending moment, 𝑙𝑘represents the length of the plastic hinge

and �̇�𝑘 accounts for the rotation.



3. A secondary component of the total energy rate is the membrane energy rate, which if

defined for a plate of a thickness equal to tp,

𝐸�̇� = 𝑡𝑝 ∬ 𝜎𝑖𝑗 ∗ 𝜖𝑖𝑗 ∗ 𝑑𝐴 (Eq. 10)

Here, A is the area of the plate creating the deformation. Considering a plane

stress state, the Von Mises yield criterion produces:

𝐸�̇� =2𝜎𝑜𝑡𝑝

√3∬ √𝜖𝑋𝑋̇

2 + 𝜖𝑌𝑌̇2 + 𝜖𝑋𝑌̇

2 + 𝜖𝑋𝑋̇ 𝜖𝑌𝑌̇ 𝑑𝑋𝑑𝑌 (Eq. 11)

Therefore, to obtain the total internal energy rate, the membrane energy rate and the bending

energy rate are added together:

𝐸𝑖𝑛𝑡̇ = 𝐸�̇� + 𝐸�̇� (Eq. 12)

The previously described simplified procedure was presented in (Le Sourne et al., 2012), which

also states that the most complex component of this calculation is the strain rate tensor 𝜖𝑖𝑗̇ which

is defined by displacement fields defined according to impact trials or numerical simulations.

This leads to overestimations of the resistance of the super-elements if the displacement fields

are not defined in an accurate manner.

The original super-element method was only valid for perpendicular collisions between ships,

however (Buldgen, Le Sourne, Besnard, & Rigo, 2012; Buldgen, Le Sourne, & Rigo, 2013a)

extended the methodology for oblique collisions between two ships and inclined ship sides and

(Buldgen, Le Sourne, & Rigo, 2013b) devised the super-element methodology for ship

collisions with lock gates.

The extension of the super-element method to simulate the collisions between striking ship

stems and a leg or brace of a jacket of an OWT was presented to the CHARGEOL project

partners by (Buldgen, Loïc and LeSourne, Hervé, “Impact on Cylinders”, 2013). The dynamics

of the collision are characterized by the following variables:


27


The length of the impacted cylinder L, its radius R, thickness tp, the inclination of the cylinder

ζ, the major and minor axes q and p in the uppermost deck of the striking stem (idealized as an

ellipse), the stem and side angles φb and Ψb respectively and the height of the stem model hb,

the relative inclination between the cylinder and the vessel α, the longitudinal position of the

stem Yp and its vertical position Zs, as shown in the following figure.

Figure 14: Geometrical Variables for the Calculation of the Internal Energy on a Cylinder. Source: Buldgen, Loïc and

LeSourne, Hervé, “Impact on Cylinders”, 2013

The cylinder can be defined as a series of smaller geometries which dissipate the membrane

and bending energy, which summed equal the total internal energy absorbed by the impacted

cylinder.

The current work aims to set the numerical grounds for the preliminary formulation of the

aforementioned super-element scheme for cylinders to OWT jackets. The development of the

project will be discussed in the following sections



5. Non-linear FEA using LS-DYNA

The stress-strain produced as a result of such a collision is normally in the plastic range. As a

result, non-linear FE analysis has to be employed to accurately determine the collision

behaviour. Hence LS-DYNA, which is a solver especially suited for crash/collision applications

is used. LS-DYNA uses a system of keywords for accurately defining the physical condition.

For example, there are keywords for defining materials, defining element types, initial

velocities, boundary conditions etc. Using different keywords one can significantly alter the

physical behaviour of the ship and the platform. In this chapter a few crucial keywords are

explained briefly.

5.1. LS-DYNA – General information

Livermore Software Technology Corporation (LSTC) is the company which has

created/developed this solver. Initially, the intended use was in military applications, like many

technologies/software’s which evolved at that time, and later diversified to include several other

industries (Livermore Technology Corporation, 2014).

Livermore Technology Corporation has developed a software package that can be used for

preprocessing and post processing. It is a powerful and easy to use and has been employed in

the course of this entire thesis for pre-processing and post-processing of the results.

5.2. Solution Methodology

The primary solution method of the bases of which LS-DYNA solver works, is the time

integration technique . The displacements in the case of a new time step is calculated on the

basis of accelerations, velocities and displacements at the preceding steps (Livermore

Technology Corporation, 2006).

The explicit method will be employed for the H-Brace impact simulations and ship-Jacket

collisions.


29


5.2.1. Stability and Time-Step

The time steps for all the simulations which has been carried out is in the range of 1E-6 s. As a

consequence, the simulation is very time consuming. Emphasis should be to get all the

keywords and parameters tight the first time.

The maximal permitted time step is limited by the element length, Ls, and the speed of sound,

c, as shown in equation 4-11 (Livermore Technology Corporation, 2006). Hence, the selection

of element size becomes extremely important. If the element size is too small the simulation

time will be very high, however, if the element size too big, the physical representation of the

results will not be accurate. The objective is to find a good balance between the two.

By default, the characteristic length is computed as (Livermore Technology Corporation, 2006):

β = 0 for quad shell elements and 1 for triangular shell elements

As = The shell element area

Li = The length of the element sides (Livermore Technology Corporation, 2006).

5.3. Shell elements

There are numerous shell element choices in LS DYNA. Belytschko-Lin-Tsay shell element is

the standard shell element type in LS-DYNA. This particular element is employed in all the

simulations. In terms of computation time, using this particular shell element type is

advantageous.



5.4. Material models

5.4.1. Piecewise Linear Plasticity

This particular material is referenced to as material model 24 - “MAT_PIECEWISE LINEAR

PLASTICITY”. This model provides elasto-plastic behavior along with strain rate effects and

does not use an equation of state (Livermore Technology Corporation, 2006).

Strain rate might well be taken care of by employing the Cowper-Symonds model that scales

the yield stress with the factor (Livermore Technology Corporation, 2006) :

ε= The strain rate

C = Cowper Symonds strain rate parameter

p = Cowper Symonds strain rate parameter

5.4.2. Rigid Material

This particular material is referenced to as material model 20- “MAT_RIGID” in LS DYNA.

This material transforms the elements to a rigid body, that is, simply no deformation. This

material needs a few input variables for example Young’s modulus, Poisson’s ratio and density

(Livermore Technology Corporation, 2006). All of these variables are utilized for figuring out

the sliding interface details for contact issues and ought to as a result be sensible values (Qvale,

2012).


31


5.5. Contact definition between colliding surfaces

This particular section details exactly the way contact is defined in LS DYNA. This section is

primarily structured on LS DYNA theory manual (Livermore Technology Corporation, 2006)

as well as the LS DYNA support web-pages (Livermore Technology Corporation, 2014).

Contact is defined by pinpointing areas that are that should be examined for penetration.

This is accomplished by defining segments of slave elements and master elements. One has the

option to define the slave and master contacts by using Node Sets, Part Sets, Parts or Shell

element sets. The methodology adopted by the author is to initially run a simulation by selecting

all the colliding parts as possible contact surface. After one run is complete, one can accurately

determine the exact contact areas, after which shell sets are used to accurately define contacts.

This will save some computation time. AUTOMATIC contact types has been utilized in the

simulations. The value of the shell thickness will be used as a value of contact thickness, if not

mentioned otherwise. The contact type referenced to as

“CONTACT_AUTOMATIC_SURFACE_TO_SURFACE” in LS DYNA is used for defining

contact involving ship and platform. For contact inside the ship or platform, the contact type

“AUTOMATIC_GENERAL” is used (Livermore Technology Corporation, 2006).



6. H- BRACE Structure

6.1. General

The primary reason for conducting the H-STRUCTURE impact simulation was to compare the

LS-DYNA numerical results with the results of the actual model test conducted by the

University of Ulsan (Cho, Seo, Cerik, & Shin, 2013), so that the LS-DYNA model developed

by ICAM can be validated. Once the validation is done, the numerical results of the H-

STRUCTURE will be used by ANAST laboratory for development of the super-elements.

Figure 15. Work Scope & Progression

Refer to Figure 15, the tasks highlighted in green represents the work done by the author. The

conclusions gained from the parametric studies and validation of the H-Brace structure was

used to set up the LS-DYNA collision model. The LS-DYNA collision model was jointly set

up by the supervisor, the author and Mr.Andres Barrera. The rigid ship collision simulations

has been done by a colleague of the author – Mr.Andres Barrera.

VALIDATION OF LS-DYNA MODEL

PARAMETRIC STUDY OF H-

BRACE STRUCTURE

SET UP LS-DYNA COLLISION MODEL

RIGID SHIP COLLISON

SIMULATIONS

DEFORMABLE SHIP COLLISION

SIMULATIONS

OBLIQUE IMPACT

SIMULATIONS

DATA SENT TO ANAST

LABORATORY FOR SUPERELEMENT DEVELOPMENT


33


6.2. H-Brace & Striker Finite Element Model

The finite element models of the H-Brace and Striker used in this LS-DYNA analysis was

created by the author. It is based on the H-Brace models used by the University of Ulsan (Figure

16), South Korea for their experiments (Cho et al., 2013). The geometric model was created in

AutoCAD modelling software and then meshed in PATRAN.

Figure 16. Actual H-Brace Models used by University of Ulsan

The brace and the chord is modeled with shell elements and striker was modeled as a rigid solid

body. Striker A has a mas of 295kg and striker B has a mas of 460 kg.

Table 1. Dimension of created FE Models.

DIMENSIONS OF THE TEST MODELS

Model L, m D, mm t, mm L/D D/t Striker Type Drop Height, m

OWT-A2 1.286 76.3 3.22 16.9 23.7 A 1004

OWT-A3 886 76.3 3.36 11.6 22.7 B 1402

OWT-B2 1286 89.1 3.56 14.4 25 B 1202

OWT-C3 886 114.3 4.02 7.8 28.4 B 1408

OWT-D1 1686 76.3 1.85 22.1 41.2 B 1203

OWT-E3 886 89.1 2.1 9.9 42.4 B 1404

OWT-F2 1286 114.3 2.1 11.3 54.4 B 1402



Where,

L = Length of the brace

D = Diameter of the brace

t = Thickness of the Brace

L/D = Length to Diameter Ratio

D/t = Diameter to Thickness Ratio

7 different H-Brace combinations with varying D/t ratios has been modelled and meshed.

Figure 17. Geometric Model of OWT-A2


35


Figure 18. Mesh of OWT-A2 at Joint Location [LEFT] & Impact Location [RIGHT]

Figure 19. Striker Geometry

Figure 20. FEA model of Striker A



6.2.1. Model Verification

Since the time of computation is quite big as it was mentioned in the previous chapter, we need

to ensure that, there are no issues pertaining to the FE model before we can begin a simulation.

The most crucial check is to delete all duplicate nodes. An edge check has been done to ensure

that only the free edges are the free edges of the chord. No duplicates nodes were found and

interconnectivity between parts was ensured.

6.2.2. Mesh and Elements

4-noded quadratic shell element have been employed for the brace and chord. Based upon on

very similar analysis identified in the literature, an element size of 5 to 10 times the plate

thickness will provide a fine portrayal of the physical effects, which includes shell-folding

effects (Qvale, 2012). A mesh size of 2mm is used at the joints and at the impact location and

a mesh size of 5mm is used in other areas. A gradual mesh sizing is used to have a smooth

connectivity between differently sized elements. This results in a total of 27632 elements for

brace and chord combined. A constant stress solid element is used to model the striker part. As

stated earlier, it will be treated as a rigid part.

6.2.3. Boundary Conditions

2 types of boundary conditions have been employed in this LS-DYNA simulation. The free

edges of the chord has been fixed in x, y, z, Rx, Ry and Rz, to mirror what has been done in the

experimental model test conducted by Ulsan University(Cho et al., 2013). For the striker,

rotational motion, that is Rx, Ry and Rz has been constrained.


37


Figure 21. Boundary conditions for impact analysis

6.2.4. Material Properties

The brace and chord is modelled using material model - piecewise linear plasticity. The material

properties is presented in Table 2. Cowper-Symonds strain rate model is used. The striker is not

allowed to deform as it has been modelled as a rigid model. The material properties are the

same as for the brace and chord material as listed below.

Table 2. Material Properties of H-Brace Models

MODEL UNITS

Yield Strength - OWT-A2 375.7 Mpa

Yield Strength - OWT-A3 375.7 Mpa

Yield Strength - OWT-B2 377.4 Mpa

Yield Strength - OWT-C3 360.9 Mpa

Yield Strength - OWT-D1 363.7 Mpa

Yield Strength - OWT-E3 394.1 Mpa

Yield Strength - OWT-F2 344.7 Mpa

Density 7850 kg/m3

Young's Modulus 210000 Mpa

Poisson's Ratio 0.3

Strain Rate Parameter, C 40.4

Strain Rate Parameter, P 5



6.3. FEA Results

6.3.1. H-STRUCTURE perpendicular & oblique impact simulations

dd is the local denting value and do is the overall bending value.

Table 3. FEA Result comparision for H-BRACE configurations

As can be seen from the Table 3, the local denting damage results agree with the actual

experimental model test results. However, comparing the values of overall bending damage,

the results are not coherent. After discussions with the supervisor, the author came to the

conclusion that the consistent under-prediction of the overall bending damage in the ICAM

numerical results could partly be due to the clamping ineffectiveness in the experimental model

test results and partly due to the fact that there are initial residual stresses in the joints due to

welding, which results in earlier plastification as compared to FE model. In the experimental

testing procedures, efforts have been made to completely clamp the chord during the test.

However, clamping effectiveness could have been overestimated. Further mesh refinement was

done to check whether, it would affect the results. The results continued to be the same inspite

of several attempts at mesh refinement. Hence, it was concluded that the maximum possible

accuracy has been attained for the H-BRACE impact simulations. After discussions with

supervisor, it was concluded that the uniform underprediction of overall bending damage would

be taken into account when developing the superelement’s and an allowance would be made

for the same. Taking into account the uniform under-prediction overall bending damage and

accurately conveying to the end user, of this particular inaccuracy, the H-BRACE simulations

were considered as validated.

Model ICAM RESULTS.

UNIVERSITY OF ULSAN NUMERICAL RESULTS

EXPERIMENTAL TEST RESULTS

dd .mm d0 .mm dd .mm d0 .mm dd .mm d0 .mm

OWT-A2 23.98 37.08 24.04 56.95 26.74 81.01

OWT-A3 33.84 31.44 36.7 76.31 30.76 67.23

OWT-B2 33.84 40.98 34.86 67.75 31.55 63.50

OWT-C3 43.18 9.83 49.36 28.75 34.25 27.75

OWT-D1 44.95 82.27 51.81 140.3 39.76 143.75

OWT-E3 62.6 27.55 74.69 76.51 58.03 59.73

OWT-F2 72 29.17 78.43 68.51 59.01 57.77


39


The next step involved conducting oblique impact tests for one H-brace configuration. The

results of the same has been shown below in Table 4.

Table 4. Oblique impact results -OWT A2

Model Local Denting Damage, dd , mm Overall Denting Damage, d0 , mm

OWT-A2-15O ANGLE 21.48 39.58

OWT-A2-30O ANGLE 18.08 34.16

OWT-A2-45O ANGLE 13.78 24.95

OWT-A2-60O ANGLE 6.88 22.24

The force-deformation relationships and energy deformation relationships for the above stated

oblique angle simulations have been given in the appendix.

6.3.2. Parametric Study

An investigation examining the effects of boundary conditions, the varying diameters, varying

D/t ratios and varying thickness vis a vis strength of the brace structure has been conducted and

is outlined below.

6.3.3. Effect of Boundary Conditions

2 sets of impact simulations, one with the brace connected to 2 chords on either side [chord

Free ends fixed] and a second simulation with just the brace member with fixed ends has been

carried out to examine the effects of boundary conditions. Only the OWT-A2 and OWT-F2

models is with a D/t ratio 23.7 and 54.4 has been considered for examining this effect.

In OWT-A2 (Figure 22), for a brace displacement of 40mm, the force required in case of fixed

brace is about 75KN, while to achieve the same displacement in axially flexible condition, the

force required is only about 40KN.

In OWT-F2 (Figure 23), for a brace displacement of 40mm, the force required in case of fixed

brace is about 67.5KN, while to achieve the same displacement in axially flexible condition,

the force required is only about 37.5KN.



Figure 22. OWT A2 force displacement curve

Figure 23.OWT F2 force displacement curve

The distinctive behaviour between the 2 configurations can be attributed to the development of

relatively big membrane forces in the brace (Refer Figure 24 & Figure 25. In case of fixed brace,

the development of large membrane forces resist further deformation. In the case where the

brace is connected to the chord, relatively smaller membrane forces are produced and hence

results in larger deformation. This is proved by the graph, comparing the membrane forces in

fixed brace and axially flexible brace.

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

0 0.02 0.04 0.06 0.08 0.1

Foce

[N

]

Displacement [m]

OWT A2 FORCE DISPLACEMENT CURVE

Poly. (AXIALY FLEXIBLE)

Poly. (FIXED BRACE)

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

0 0.02 0.04 0.06 0.08 0.1

Forc

e [N

]

Displacement [m]

OWT F2 FORCE DISPLACEMENT CURVE

Poly. (FIXED BRACE)

Poly. (AXIALLY FLEXIBLE)


41


Figure 24. Membrane Forces -OWT A2

Figure 25. Membrane Forces -OWT F2

The above stated graphs, help us to understand the importance of boundary conditions. For

realistic simulation results, the axial flexibility of the brace offered by the presence of the chord

has to be considered.

0

50000

100000

150000

200000

250000

0 0.005 0.01 0.015 0.02 0.025 0.03

FOR

CE

[N]

TIME [s]

MEMBRANE FORCES - OWT-A2

Poly. (AXIALY FLEXIBLE)

Poly. (FIXED BRACE)

0

50000

100000

150000

200000

250000

0 0.005 0.01 0.015 0.02 0.025 0.03

FOR

CE

[N]

Time

MEMBRANE FORCE - OWT-F2

Poly. (AXIALLY FLEXIBLE)

Poly. (FIXED BRACE)



6.3.4. Effect of brace thickness

Figure 26 presents the force-displacement relations for brace configurations of constant

diameter and varying thickness. The graph shows that, predictibly, with increasing brace

thickness we notice the strength increases.

Figure 26. Force-Displacement Curve for varying thickness- OWT F2

A consistent increase in strength is not noticed for a proportional increase in thickness. The

increase in thickness & strength for different braces at 0.01m and 0.02m displacement is shown

in figures & the tables indicate that in the case of an increase in thickness from 2.1mm to 3.1mm,

there is quite a significant strength increase. The increasing steepness of the graph braces at

small displacements can be seen in the graph. It signifies a significant increase in the brace

strength for small changes in structural configuration. The force displacement curves for

different thicknesses displays flattening behavior as the impact force increases. The results are

tabulated in Table 5 & Table 6.

0

50000

100000

150000

200000

250000

0 0.01 0.02 0.03 0.04 0.05 0.06

FOR

CE

[N]

DISPLACEMENT [m]

FORCE V/S DISPLACEMENT FOR VARYING THICKNESS - OWT F2

Poly. (t=2.1)

Poly. (t=3.1)

Poly. (t=4.1)

Poly. (t=5.1)

Poly. (t=6.1)

Poly. (t=7.1)

Poly. (t=8.1)


43


Table 5. OWT-F2-Strength Increase with Increasing Thickness. Displacement – 0.01m

Table 6. OWT-F2-Strength Increase with Increasing Thickness. Displacement – 0.02m

Brace Thickness

Increase in Thickness %

Force [KN] Strength Increase %

Strength Increase/Thickness Increase

0.0021 25

0.0031 47.62 51 104 2.18

0.0041 32.26 68 33 1.03

0.0051 24.39 95 40 1.62

0.0061 19.61 130 37 1.87

0.0071 16.39 170 31 1.87

0.0081 14.08 200 18 1.25

FOR DISPLACEMENT OF 0.02 m

Brace Thickness

[m]

Increase in Thickness %

Force [KN]

Strength Increase %

Strength Increase/Thickness

Increase

0.0021 19

0.0031 47.62 40 111 2.32

0.0041 32.26 50 25 0.77

0.0051 24.39 70 40 1.64

0.0061 19.61 90 29 1.45

0.0071 16.39 110 22 1.35

0.0081 14.08 132 20 1.42



45


Figure 27. Plastic Strain Plots for varying brace thicknesss

Below in Figure 28, the impact force has been plotted against local and global displacement

values in order to explain the overall brace deformation mechanism.

Figure 28. Force v/s Local/Global Displacement curve. Thickness =2.1mm

-10000

0

10000

20000

30000

40000

50000

60000

-0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

FOR

CE

[N]

DISPLACEMENT [m]

THICKNESS = 2.1mm

Poly. (LOCAL)

Poly. (GLOBAL)



Figure 29.Force v/s Local/Global Displacement curve. Thickness =4.1mm

In the initial stage of impact, the total deformaton of the brace is totally dependent on the local

indentation of the brace. A steep curve indicates greater resistance against local indentation.

Comparing the Figure 28 & Figure 29, it can be seen that the local indentation curve is lower for

the thickness of 2.1mm and higher for thickness of 4.1mm and hence the brace of thickness

4.1mm has higher resistance to local deformation.

As the striking mass penetrates further into the brace, the brace reaches its plastic strength value

and deforms globally, with the local deformation acting as a hinge[reducing strength] and hence

the force-displacement curves tend to flatten.

6.3.5. Effect of brace diameter

The effect of varying brace diameter are considered and 3 different H-brace configurations with

brace diameters of 76.3mm, 89.1mm and 114.3mm and constant thickness of 3.1mm. This

results in D/t ratios’s of 24.61, 28.74 and 36.87 respectively. The force displacement curves for

the same are shown below Figure 30.

-20000

0

20000

40000

60000

80000

100000

120000

-0.005 0 0.005 0.01 0.015 0.02 0.025 0.03

FOR

CE

[N]

DISPLACEMENT [m]

T=4.1mm

Poly. (LOCAL DEFORMATION)

Poly. (GLOBAL DEFORMATION)


47


Figure 30.Force v/s Displacement curve - Varying Diameter

The graphs show an increase in brace strength as the diameter is increased. The factors which

influence this increase in strength are as follows (Qvale, 2012):

Increasing elastic section modulus, W. This will in turn reduce the bending stresses in

the column according to equation 17:

Increasing plastic section modulus, Wp. This will increase the plastic moment capacity.

(Qvale, 2012).

Increasing contact area. The increasing column diameter will increase the contact area.

Hence, a larger impact force is required to produce the same contact pressure (Qvale,

2012).

0

10000

20000

30000

40000

50000

60000

70000

80000

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

FOR

CE

[N]

Displacement [m]

FORCE-DISPLACEMENT CURVE FOR VARYING DIAMETER, t=0.0031m

Poly. (DIAMETER=0.1143m) Poly. (DIAMETER=0.0891m) Poly. (DIAMETER = 0.0641m)



The Figure 30 indicates that through an impact-strength viewpoint, a bigger diameter brace is

ideal. Having said that, the graphs really do not provide a total picture of the impacts. The brace

deformation in the graph is the overall displacement. It will be furthermore intriguing to observe

exactly how the overall deformation is split among global and local column deformation. This

is shown in Figure 31 & Figure 32.

Figure 31. Force v/s Local Displacement curve. Thickness =3.1mm

From the graph above, it can be seen that the brace of diameter 64.1mm is stronger against local

deformation. On a closer look, it can be proved that the steepness of the D=64.1mm curve is

greatest and D=114.3mm curve is the least steep.

0

10000

20000

30000

40000

50000

60000

70000

80000

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

FOR

CE

[N]

LOCAL DISPLACEMENT [m]

FORCE-LOCAL DISPLACEMENT CURVE, t=0.0031m

Poly. (DIAMETER = 0.0641) Poly. (DIAMETER = 0.0891) Poly. (DIAMETER = 0.1143)


49


Figure 32. Force v/s Global Displacement curve. Thickness =3.1mm

In comparison, the behavior in global deformation is the exact opposite. The brace of diameter

114.3mm has the biggest resistance to global deformation. The brace of diameter 114.3mm is

steepest and the brace of 64.1mm is the least steep. It can be argued that the brace of diameter

64.1mm is influenced mainly by global deformation as opposed to brace of diameter 114.3mm,

which is mainly influenced by the local deformation.

-10000

0

10000

20000

30000

40000

50000

60000

70000

80000

-0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

FOR

CE

[N]

GLOBAL DISPLACEMENT [m]

FORCE-GLOBAL DISPLACEMENT CURVE, t=3.1mm

Poly. (DIAMETER = 0.1143m) Poly. (DIAMETER = 0.0891m) Poly. (DIAMETER = 0.0641m)



7. Jacket model

7.1. General

The jacket mesh was provided by STX FRANCE for the purpose of this LS-DYNA simulations

and hence no finite element creation had to be done for the same, the details of the jacket has

been portrayed in the figure below. The global mass of the Jacket structure is 540 Tonnes. The

transition piece is also modelled along with the jacket structure. The weight of the transition

piece is 65 tons.

7.2. FE Model


4-noded quadratic shell element have been employed for the brace and chord. The jacket was

meshed with 4-noded quadrilateral elements with element length = 100 mm. This results in Le/t

ratio between 1.67 & 2. Belytschko-Lin-Tsay shell element is used for all elements. This results

in 242903 elements. Refer Figure 33 & Figure 34.

Figure 33. FE mesh of Jacket Bottom


51


Figure 34. Jacket Model


The soil stiffness has not been modelled due to the non-availability of accurate soil stiffness

data and hence the nodes at the leg bottom at mud line has been assumed to be fixed. This could

be a conservative assumption as this could result in increased damage.




For the purpose of this simulation, the jacket members is modelled using material model -

piecewise linear plasticity as described in earlier section and allowed to deform. The material

properties are presented in Table 7. Cowper-Symonds strain rate model is used.

Table 7. Material Properties of Jacket

MODEL UNITS

Yield Strength 260 Mpa

Density 7850 kg/m3


Poisson's Ratio 0.3




53


8. OSV Bow Model

8.1. General

The OSV bow geometry has been created by the author based on structural detail provided by

Bureau Veritas. It was concluded in the initial CHARGEOL project meetings that an OSV of

3000 Tons would be considered for this collision scenario. 11 frames has been modelled which

is considered sufficient for the analysis. It has been modelled using the modelling software

Rhinoceros and meshed in PATRAN. Half of the OSV bow was created and after meshing, the

elements were mirrored to have a complete bow structure. The geometry is a simplified one in

the sense that small details [For Example brackets] have not been modelled. This reduced

modelling and computational time. However, during the meshing process, care was taken to

ensure connectivity between different structural members.

Figure 35. OSV Bow Geometry



Figure 36. OSV Bow FE Mesh

Table 8. Particulars of the Modelled OSV

Bow

Table 9. OSV Ship Particulars

SHIP PARTICULARS

Length 78m

Depth 13.8m

Breadth 17.6

Double Bottom Height 1.4m

Displacement 3000 T

MODELLED BOW PARTICULAR’S

Length 6.6

Breadth 12

Height 13.8

Frame Spacing 0.6

Double Bottom Height 1.4

Bottom Plating Thickness 12

Frames L 180*90*10

Shell Stringers T 300*100*10

Deck Girders T 450*150*15

Central Girder T 500*150*12.5

Bulkhead Stiffeners L 175*50*12


55


Figure 37. OSV Structural Configuration

8.2. FE Model


Half-model was created and mirrored in order to create a complete bow. An edge check has

been done to ensure that only the free edges are the free edges of the chord. No duplicates nodes

were found and interconnectivity between parts was ensured.


The bow model was meshed with 4-noded quad elements with element length = 100 mm. This

results in Le/t ratio between 6.667 & 10. Belytschko-Lin-Tsay shell element is used for all

elements. This results in 66451 elements. The element type has been described in detail in the

earlier section.




For the purpose of this simulation, the jacket members is modelled using material model -

piecewise linear plasticity as described in earlier section. The material properties is presented

in Table 10. Cowper-Symonds strain rate model is used.

Table 10. Material property of OSV Bow Structure

MODEL UNITS


Density 7850 kg/m3


Poisson's Ratio 0.3



8.2.4. Impact Location

The OSV impacts the jacket at 2 locations. STX has provided information that the tidal variation

in the location of the jacket is 11m. Hence, 2 impact locations have been considered as shown

below. Jacket leg impact is the considered scenario for both impact points. One impact location

is 43.2m above the mudline and the 2nd impact location is 32.2m above the mudline.

Figure 38. Impact Location 1 [Left] Impact Location 2 [Right]


57


8.3. FE Simulation Results – Impact Location 1

In the earlier section, we have examined the behaviour of an H-brace structure, which has

provided insights into the behaviour of a simple tubular structure. In this section, we shall

consider OSV bow collision with jacket structure. At the 1st point of contact, the jacket has a

leg diameter of 1.25m. 40mm, 50mm & 60 mm leg thickness has been taken into account.

8.3.1. Available Strain Energy

The total strain energy for collision is calculated:

Where, ms is the mass of the OSV, as is the added mass which has been considered and vs is

the velocity of the ship. The velocity is 2.675m/s. An added mass of 5% has been considered.

This results in a total strain energy of 11.2MJ.

8.3.2. Force-Deformation relationship

In the next page, one can find the force deformation relationship curves for the OSV Bow and

the 4-legged jacket. It can be clearly seen that the 4-legged jacket increases in strength with

increase in thickness of jacket leg. However, from the & Table 12, it is very interesting to

observe that the increase in strength is not consistently proportional to the increase in thickness.

When increasing the jacket leg thickness from 40mm to 50mm, we can observe a very

significant increase in strength of the leg. However when the thickness is increased from 50mm

to 60mm a similar significant increase in strength is not observed. In the next section titled

“effect of brace thickness”, we will discover that the significant increase in strength observed

when increasing the thickness from 40mm to 50mm is due to the substantial increase in the

resistance to local deformation. It is also important to observe that the curves as steeper, when

the jacket leg deformations are relatively small.

58

Figure 39. Force Deformation Characteristics : Varying Thickness

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-1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6

FOR

CE

[N]

DISPLACEMENT [m]

SHIP JACKET

Poly. (Thickness=50mm)


Poly. (D=60mm)

59

Table 11. Strength Increase vis a vis Thickness Increase. Displacement =0.05m

LEG THICKNESS [m] THICKNESS

INCREASE [%] FORCE [MN]

STRENGTH INCREASE [%]

0.04 2.5

0.05 25 4.6 84

0.06 20 6.4 39.1


Table 12. Strength Increase vis a vis Thickness Increase. Displacement =0.1m

LEG THICKNESS [m] THICKNESS INCREASE

[%] FORCE [MN]


0.04 4.1

0.05 25 10 143.9

0.06 20 12 20




Figure 40. Local Indentation. Thickness= 40mm [LEFT]

Thickness=60mm [RIGHT]


61


8.3.3. Effect of thickness

To examine the effect of leg thickness, 3 simulations with varying leg thicknesses of 40mm,

50mm and 60mm was carried out. The plots of the same has been shown below in Figure 41,

Figure 42 & Figure 43. The graphs follow an interesting pattern and provide further insights.

Figure 41. Force v/s Displacemet [Local/Global] . Thickness =60mm

Figure 42.Force v/s Displacemet [Local/Global] . Thickness =50mm

0

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0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

FOR

CE

[N]

DISPLACEMENT [m]

THICKNESS=60 mm

Poly. (LOCAL)

Poly. (GLOBAL)

0

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0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

FOR

CE

[N]

DISPLACEMENT [m]

THICKNESS=50mm

Poly. (LOCAL)

Poly. (GLOBAL)



Figure 43. Force v/s Displacemet [Local/Global] . Thickness =40mm

In the case of jacket leg with 60mm thickness, the resistance against local deformation is

considerably higher than its resistance to global deformation. The maximum local deformation

is 13.6mm while the maximum global deformation is 67.6mm.

In the case of jacket leg with 50mm thickness, the resistance against local deformation is more

or less similar to its resistance to global deformation. The maximum local deformation is

42.3mm while the maximum global deformation is 81.9mm.

In the case of jacket leg with 40mm thickness, the resistance against local deformation is much

lesser in comparison to its resistance to global deformation. The maximum local deformation

is 248mm while the maximum global deformation is 78mm.

The energy of the impact is the same for the 3 cases, however the jacket legs with 3 different

thicknesses display considerable different behaviour. While 40mm thickness jacket leg is more

susceptible to local deformation, the 60mm jacket leg is most susceptible to global deformation.

From a jacket design viewpoint, these results have some implications.

0

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0 0.05 0.1 0.15 0.2 0.25 0.3

FOR

CE

[N]

DISPLACEMENT [m]

THICKNESS=40mm

Poly. (LOCAL)

Poly. (GLOBAL)


63


The jacket leg with maximum susceptibility to local deformation, could reduce the overall

strength due to plastic hinge formation. Conversely, the jacket leg with maximum susceptibility

to global deformation will involve the surrounding members during the process of global

deformation.

Table 13. Displacement & Acceleration of the transition piece.

THICKNESS [m] TRANSITION PIECE DISPLACEMENT

[m] TRANSITION PIECE

ACCELERATION [m/s2]

0.04 0.040 11.1

0.06 0.042 12.4

Another observation is about the displacement and acceleration of the transition piece. The

same is shown in Table 13. Although the strength of the jacket increases with increase in leg

thickness, from a production point of view, higher thickness leg may lead to additional

challenges in welding. However, this is not within the purview of this thesis and is not dealt

with.

Figure 44. Plastic Strain Plot of Collision. Jacket Leg Thickness =40mm



8.3.4. Energy Dissipation Characteristics

The total available impact energy was calculated to be 11.2MJ. For the 40mm jacket leg the

impact energy is dissipated in about 1s. At this point in time, the entire jacket has dissipated

around 1.7MJ [0.57MJ is elastic] of energy and the ship 8.1MJ. The jacket has dissipated 16%

of the energy and the ship has dissipated around 74% of the energy. Around 9% of the energy

is dissipated by sliding energy. This energy dissipation characteristics indicate that this is a

shared energy design. Although inertia effects are taken into account, about 1% of the energy

is lost in motion of the ship/jacket.

The total available strain energy was calculated to be 11.2MJ. For the 50mm jacket leg the

impact energy is dissipated in about 0.96s. At this point in time, the entire jacket has dissipated

around 0.76MJ [0.54MJ is elastic] of energy and the ship 9.2MJ. The jacket has dissipated 7%

of the energy and the ship has dissipated 84%. Around 8% of the energy is dissipated by sliding

energy. This energy dissipation characteristics indicate that this is a shared energy design.

Although inertia effects are taken into account, about 1% of the energy is lost in motion of the

ship/jacket.

The total available strain energy was calculated to be 11.0MJ. For the 60mm jacket leg the

impact energy is dissipated when the time is about 0.96s. At this point in time, the entire jacket

has dissipated around 0.48 [0.45MJ is elastic] MJ of energy and the ship 9.58MJ. The jacket

has dissipated 4% of the energy and the ship has dissipated 87%. Around 8% of the energy is

dissipated by sliding energy. This energy dissipation characteristics indicate that this is a shared

energy design. However it is the closest to a strength design in comparison to thicknesses of

40mm and 50mm. Although inertia effects are taken into account, about 1% of the energy is

lost in motion of the ship/jacket.

As a general comment, it can be said that for the jacket structure, there is a component of elastic

energy that is present, which indicates that the jacket tries to go back to its original geometry,

while in the case of the OSV, there is no such rebound and the deformation is plastic in nature.


65


Figure 45. Energy v/s Deformation Curve. Thickness =40mm


-1000000

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0 0.2 0.4 0.6 0.8 1 1.2 1.4

ENR

GY

[J]

DISPLACEMENT [m]

THICKNESS = 40mm

SHIP JACKET

-2000000

0

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6000000

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10000000

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

ENER

GY

[J]

DISPLACEMENT [m]

THICKNESS = 50mm

SHIP JACKET




In the case of 40mm jacket leg, 77% of the total energy absorbed by the complete jacket is

absorbed by the impacted jacked leg itself. This corresponds to the earlier discussed relatively

high susceptibility to local deformation. The rest 33% is absorbed by rest of the jacket structure.


absorbed by the impacted jacked leg itself. The rest 42% is absorbed by rest of the jacket

structure.


absorbed by the impacted jacked leg itself. This corresponds to the earlier discussed relatively

high susceptibility to global deformation. The rest 50% is absorbed by rest of the jacket

structure.

-2000000

0

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4000000

6000000

8000000

10000000

12000000

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

ENER

GY

[J]

DISPLCAEMENT [m]

THICKNESS = 60mm

SHIP JACKET


67


Table 14. Energy Absorption Characteristics for OSV structural Members

STRUCTURAL MEMBER ENERGY ABSORBED %

DECK PLATES 30

DECK STIFFENERS 24.13

CENTER GIRDER 20.32

HULL SHELL 14.89

SHELL LONGITUDINALS 12.93

FRAMES 1.8

WEB FRAMES 0.65

A quick study of the energy distribution among ship structural members, provide information

as shown in the table below. However, one has to understand that this is valid only for this

particular collision scenario. Due to the nature of the OSV bow geometry, the first contact

Figure 48. Deformed Hull Shell



occurs between the hull shell and jacket leg at the level of forecastle deck. This results in the

deck plate and associated deck stiffeners playing a big role is dissipating the impact energy.

Figure 49. Deformed Deck Plate

Figure 50. Deformed Hull Shell Longitudinals


69


8.3.5. Resistance to Local Indentation

Resistance to local indentation is a critical parameter which should be considered because local

denting will reduce the strength of the jacket leg and hence the strength of the whole jacket

structure (NORSOK, 2004). NORSOK 004 provides information as to how the resistance to

local indentation should be assessed for unstiffened tubes (NORSOK, 2004).

LS-DYNA has been used to estimate the width of the contact area, which is one of the governing

parameters. At the first point of contact, the width is very small and is almost zero. The maximal

contact width, B, is estimated as 3.4m. This gives a B/D ratio of 2.72. Hence 2 NORSOK curves

with B/D=0 and B/D=2.72 has been plotted.

However, as it can be seen from figure Figure 51, the 40mm thickness leg follows the NORSOK

B=0 curve initially and then the strength increases. According to NORSOK ‘Often the stronger

of the ship and platform will experience less damage and the softer more damage than what is

predicted (NORSOK, 2004). As the softer structure deforms the impact force is distributed over

a larger contact area. Accordingly, the resistance of the strong structure increases. This may

be interpreted as an "upward" shift of the resistance curve for the stronger structure’

(NORSOK, 2004). This is clearly proved right from the graph.

However, it is interesting to note that only the resistance curve for 40mm thickness displays

some sort of consistency in comparison to the NORSOK curves. The resistance curves for

50mm and 60mm leg thickness indicate that they are stronger in comparison to the NORSOK

curves. The 2 50mm and 60mm resistance curves remain to be steep at the point where the

NORSOK curve for B=2.75 flatten out. This is an interesting observation which prompts us to

think weather the NORSOK curves display conservative tendencies, although the FEA results

need not be taken at face value, the trend of the 3 curves indicate that all three jacket legs have

higher resistance to local indentation than what is predicted by NORSOK.



Figure 51. . Comparison b/w NORSOK reistance curves against Numerical Simulation Resistance Curves

A possible reason for the NORSOK curves to be conservative, is that the NORSOK curves are

based on the supposition of a rigid ship (NORSOK, 2004). A section of the 40 mm and 60 mm

jacket cases, shown below, shows that in the 40 mm case, the deformation is significant while

the 60 mm jacket leg acts more like a rigid jacket leg. The ship tends to wrap round the jacket

leg in the case of 60mm jacket leg and when the ship deforms, the impact force is spread round

the column. As a result, as the leg thickness is increased and thereby increasing the leg strength,

the NORSOK calculation model becomes invalid.

-2

0

2

4

6

8

10

12

14

16

18

0 0.05 0.1 0.15 0.2 0.25

R/R

C

wd/D

RESISTANCE TO LOCAL INDENTATION - COMPARISON TO NORSOK CODE

NORSOK CURVE b/D=2.75

NORSOK CURVE b/D=0

Poly. (THICKNESS=40mm)



Figure 52. Deformed Leg Section. 40mm Thickness [left]

60mm Thickness [Right]


71


In an earlier section (Force Deformation Relationship), we had observed from the force

deformation curves and corresponding tables that the strength of the jacket leg increases

considerably when the thickness is increased from 40mm to 50mm. From the curves shown

above, it is clear that this can be attributed to the increase in resistance to local indentation.

72

8.4. FE Simulation Results – Impact Location 2

8.4.1. Force Deformation Relationship

Figure 53. Force Deformation Relationship Comparison b/w 2 impact locations

-2000000

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16000000

-1.5 -1 -0.5 0 0.5 1

FOR

CE

[N]

DISPLACEMENT [m]

SHIP JACKET




73

The force deformation relationship comparison between impact location 1 and impact location

2 is shown in Figure 53. The primary objective of the results of 2nd impact location, is to do a

comparison.

The dotted lines represent the results of impact location 2 and the solid lines represent results

of impact location 1.

Comparing the 2, it can be said that the jacket strength is slightly reduced, when the impact

location is closer to the jacket bottom. This is evident from the relative less steepness of the

jacket curves for impact location 2 [Dotted Lines on the right Side]. Conversely, the strength

of the ship seem to be higher [Dotted Lines on the left side], in case of the impact location 2.

The reason for the reduction in strength of the jacket could be the increased local denting which

occurs in impact location 2 [Refer Figure 54, Figure 55 & Figure 56], due to the relative proximity

to the bottom of the jacket leg which is considered fixed. Another reason could be that the

impact point 2 is relatively closer to a joint. This could also aid is higher local deformation.

Figure 54. Local Indentation Comparison b/w 2 impact locations, Thickness =40mm

0

50

100

150

200

250

300

350

0 0.2 0.4 0.6 0.8 1 1.2

IND

ENTA

TIO

N [

mm

]

TIME [S]

LOCAL INDENTATION COMPARISON. Thickness = 40mm

Poly. (IMPACT LOCATION 2) Poly. (IMPACT LOCATION 1)



Figure 55 Local Indentation Comparison b/w 2 impact locations, Thickness =50mm

Figure 56. Local Indentation Comparison b/w 2 impact locations, Thickness =60mm

0

10

20

30

40

50

60

70

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

IND

ENTA

TIO

N [

mm

]

TIME [s]

LOCAL INDENTATION COMPARISON - 50mm Thickness


0

2

4

6

8

10

12

14

16

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

IND

ENTA

TIO

N [

m]

TIME [s]

LOCAL INDENTATION COMPARISON . Thickness =60mm



75


9. Bulk Carrier Side Impact – 1 m/s

9.1. General

A Panamax Bulk Carrier Cargo Hold has been created by the author, as it was concluded in the

initial CHARGEOL project meetings that it could be interesting to consider a collision scenario

involving a Bulk Carrier and an offshore jacket, so as to have an understanding of the mechanics

of high energy ship collisions. 27 frames has been modelled which is considered sufficient for

the analysis. It has been modelled using the modelling software Rhinoceros and meshed in

PATRAN. Quarter of the Bulk Carrier Hold was created and after meshing, the elements were

mirrored to have half cargo hold. The geometry was simplified in the modelling process. Small

details (e.g. brackets) has been ignored. However, during the meshing process, care was taken

to ensure connectivity between different structural members. The vessel is classified ice class

1C.

Table 15. Bulk Carrier Particulars

SHIP PARTICULARS

Length, OA 224.9m

Depth, MLD 20m

Breadth, MLD 32.25m


Draft, Scantling 14.15m

Scantling Displacement 88000 T

Figure 57. Photo of Panamax Bulk Carrier



Figure 58. Bulk Carrier FEM Model

Figure 59. Double Bottom Structure


77


Figure 60. Web Frames & Topside & Hopper Longitudinals

Table 16. Particular's of the Model Bulk Carrier Cargo Hold

Length 25.65m

Breadth 32.25m

Height 20m

Frame Spacing 0.85m


Bottom Plating Thickness 0.02m

Frames T 550*225*15.5

Topside Tank Logitudinals T 450*180*12.5

Hopper Tank Longitudinals T 410*125*13, L 300*90*13, L350*100*13

Double Bottom Longitudinal Girder PL 15

Double Bottom Transverse Girder PL 13



9.2. FE Model


An edge check has been done to ensure that only the free edges are the free edges of the chord.

No duplicates nodes were found and interconnectivity between parts was ensured.


The model was meshed with 4-noded quadrilateral elements with element length = 200 mm.

This results in Le/t ratio between 10 & 16. Care was taken to ensure that the Le/t ratio at the

contact point of the cargo hold section is 10, which is the upper limit of the ratio to ensure a

good physical reproduction of the actual collision scenario. Belytschko-Lin-Tsay shell element

was is used for all elements. This results in 136451 elements.

Figure 61. FE Mesh of Bulk Carrier Hold


79


Figure 62. FE Mesh of Bulk Carrier Hold


The transverse edges are considered fixed to represent the rest of the bulk carrier structure

which would be present in the case we considered the whole bulk carrier model.


For the purpose of this simulation, the cargo hold members is modelled using material model-

piecewise linear plasticity as described in earlier section. The material properties is presented

inTable 17. Cowper-Symonds strain rate model is used.



Table 17. Material Properties of Bulk Carrier

MODEL UNITS


Density 7850 kg/m3


Poisson's Ratio 0.3



9.2.5. Impact Location

Only, 1 impact location have been considered for the bulk carrier impact simulation. The impact

location is 21.2m above the mudline.

Figure 63. Impact Location Bulk Carrier


81


9.3. FE Results – Impact Velocity 1 m/s

In the earlier section, we have examined the behaviour of an OSV bow collision. In this section,

we shall consider Bulk Carrier Side Collision with jacket structure. This will result in

simultaneous contact between the 2 jacket legs and the Bulk Carrier. At the 1st point of contact,

the jacket has a leg diameter of 1.25m. 40mm, 50mm & 60 mm leg thickness has been taken

into account.

9.3.1. Available Strain Energy

The total strain energy for collision is calculated using the earlier given equation. The mass of

the fully loaded bulk carrier is 88000 Tons, as is the added mass which has been considered and

vs is the velocity of the ship which is 1m/s. An added mass of 40% has been considered. This

results in a total strain energy of 61.6MJ.

9.3.2. Force Deformation Curves

The force deformation curves for the bulk carrier side impact with 3 different leg thickness are

given in the next page. A similar pattern to the one we have observed in OSV simulations are

simulations can be seen from the force deformation plots. When the thickness of thickness of

the impacted leg is increased, the strength of the jacket increases and conversely the strength of

the ship decreases. However, a bigger increase in strength is noted when the thickness is

increased from 50mm to 60mm.

82

Figure 64. Force-Displacement Curve -Bulk Carrier Side Impact 1m/s

-10000000

0

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20000000

30000000

40000000

50000000

60000000

70000000

-1 -0.5 0 0.5 1 1.5 2 2.5

FOR

CE

[N]

DISPLACEMENT [m]

SHIP JACKET

THICKNESS = 60mm THICKNESS = 50mm THICKNESS = 40mm

83

Table 18. Strength Increase Comparison for displacement 0.5m

LEG THICKNESS [m] THICKNESS

INCREASE [%] FORCE [MN]


0.04 28

0.05 25 34 22

0.06 20 47.5 40


Table 19.Strength Increase Comparison for displacement 1m

LEG THICKNESS [m] THICKNESS INCREASE

[%] FORCE [MN]


0.04 34.3

0.05 25 44.6 30

0.06 20 57.3 29

FOR DISPLACEMENT OF 1 m



Figure 65. Plastic Strain Plot of one impacted Leg. 60mm Thickness [LEFT] & Thickness 40mm

[RIGHT]


85


9.3.3. Effect of Leg Thickness

In the case of jacket leg with 60mm thickness, the resistance against local deformation is

considerably higher than its resistance to global deformation. The maximum local deformation

is 0.3m, while the maximum global deformation is 0.88m.

In the case of jacket leg with 50mm thickness, the resistance against local deformation is more

or less similar to its resistance to global deformation. The maximum local deformation is 0.52m

while the maximum global deformation is 1.02m.

In the case of jacket leg with 40mm thickness, the resistance against local deformation is much

lesser in comparison to its resistance to global deformation. The maximum local deformation

is 0.68m while the maximum global deformation is 1.41m.

Similar to the results from OSV Bow collisions, 40mm thickness jacket leg is more susceptible

to local deformation, the 60mm jacket leg is most susceptible to global deformation. This has

important consequences.

The jacket leg with maximum susceptibility to local deformation, will reduce the overall

strength due to plastic hinge formation. Conversely, the jacket leg with maximum susceptibility

to global deformation will involve the surrounding members during the process of global

deformation.

Table 20. Displacement and Accelerations of Transition Piece

THICKNESS [m]

TRANSITION PIECE DISPLACEMENT [m]

TRANSITION PIECE

ACCELERATION [m/s2]

0.04 1.07 6

0.06 0.6 5.2

Another observation is about the displacement and acceleration of the transition piece. The

results of the same are shown in the Table 20 above.



Figure 66. Local/Global Deformation Comparision. Thickness =40mm


0

5000000

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15000000

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25000000

30000000

35000000

40000000

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

FOR

CE

[N]

DISPLACEMENT [m]

40mm

Poly. (LOCAL) Poly. (GLOBAL)

0

10000000

20000000

30000000

40000000

50000000

60000000

0 0.2 0.4 0.6 0.8 1 1.2

FOR

CE

[N]

DISPLACEMENT [m]

50mm



87



9.3.4. Energy Dissipation Characteristics

The overall behaviour is such that a majority of the collision strain energy is absorbed by the

jacket. The bulk carrier is capable of carrying 75000 Tons of cargo [88000 is total displacement]

and hence has quite strong scantlings. This relatively high strength of the ship is the reason,

why a majority of the energy is absorbed by the jacket in comparison to the OSV bow collisions,

where, it was seen that the colliding OSV absorbed the majority of the impact energy.



around 56MJ of energy and the ship 3MJ. The jacket has dissipated 90% of the energy and the

ship has dissipated 5% of the energy. Around 5% of the energy is dissipated by means sliding

energy. This can be stated as being ductile design, since a huge majority of the energy is

dissipated by the jacket.

0

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50000000

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70000000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

FOR

CE

[N]

DISPLACEMENT [m]

60 mm






around 53.6MJ of energy and the ship 5.6MJ. The jacket has dissipated 87% of the energy and

the ship has dissipated 9% of the energy. Around 4% of the energy is dissipated by means

sliding energy. This can be stated as being shared design, although it is quite close to ductile

design.



around 49.8MJ of energy and the ship 9.5MJ. The jacket has dissipated 80% of the energy and

the ship has dissipated 14% of the energy. Around 6% of the energy is dissipated by means

sliding energy. This can be stated as being shared design.

Figure 69. Energy Displacement Curve . Thickness = 40mm

-1E+10

0

1E+10

2E+10

3E+10

4E+10

5E+10

6E+10

-0.5 0 0.5 1 1.5 2 2.5

ENER

GY

[J]

DISPLACEMENT [m]

THICKNESS = 40mm

SHIP Poly. (JACKET)


89






structure.

-1E+10

0

1E+10

2E+10

3E+10

4E+10

5E+10

6E+10

-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

ENER

GY

[J]

DISPLACEMENT [m]

THICKNESS = 50mm

SHIP JACKET

-1E+10

0

1E+10

2E+10

3E+10

4E+10

5E+10

6E+10

0 0.2 0.4 0.6 0.8 1 1.2

ENER

GY

[J]

DISPLACEMENT [m]

THICKNESS = 60mm

SHIP JACKET



In the case of 50mm jacket leg, 60.8% of the total energy absorbed by the complete jacket is


structure.



structure.

Figure 72. Plastic Strain Plot of Jacket with leg Thickness=40mm, Post Collision


91


Figure 73. Top view of Jacket Leg with 40mm Leg Thickness, Post Collision

Figure 74. Strain Plot of Ship & Jacket. Isometric View



Figure 75. Strain Plot of Ship Structural Members

A quick study of the energy distribution among ship structural members, provide information

as shown in the table below. The first contact point is at the hull shell plate outside the hopper

tank. Hence we also notice that the hull shell plate absorbs 44% of the energy, followed by the

hopper tank longitudinal stiffeners, which absorb 30% of the energy absorbed by the ship

followed by the web frames.

Table 21. Energy Dissipation Characteristics - Ship Structural Members

STRUCTURAL MEMBER ENERGY ABSORBED %

HULL SHELL 44

HOPPER TANK LONGITUDINALS 30

WEB FRAMES 24

OTHER STRUCTURAL MEMBERS 2


93


9.4. FE Results – Impact Velocity 2 m/s

9.4.1. Force Displacement Relationship

The force displacement curve for the jacket impacted by a bulk carrier at 2m/s has been given

in the next page. Although the relative strength of the jacket increases with increasing thickness,

it has not been designed to withstand such a load. The impacted leg is totally damaged. The

dent to diameter ratios are 0.73, 0.58, 0.38 for jacket leg thicknesses of 40mm, 50mm and 60

mm respectively. From the literature, it was seen that beyond a dent to diameter ratio of 0.6, the

leg may be considered to be failed. Going by the same logic, the 2 impacted legs of the jacket

leg of thickness 40mm has failed. The dent to diameter ratio for 50m thickness and 60mm

thickness is less than the 0.6 critical value. However there is extensive damage in the structure,

including extremely high shear stress at the leg bottom. The jacket absorbs the majority of the

energy, due to the relatively higher strength of the ship structure. The total energy was 251 MJ.

Figure 76. Plastic Strain Plot. Thickness = 40mm. Time = 1s. [LEFT] Time= 2s [RIGHT]



Figure 76. Plastic Strain Plot. Thickness = 40mm. Time = 3s. [LEFT] Time= 4s [RIGHT]

Figure 77.Figure 76. Plastic Strain Plot. Thickness = 40mm. Time = 5s

95

Figure 77. Force Deformation Curves-Bulk Carrier Impact- 2m/s

0

10000000

20000000

30000000

40000000

50000000

60000000

70000000

-1 0 1 2 3 4 5 6 7

FOR

CE

[N]

DISPLACEMENT [m]

SHIP JACKET

Poly. (Thickness =60 mm) Poly. (Thickness =50mm) Poly. (Thcikness=40mm)

96

10. DISCUSSIONS & CONCLUSIONS

In this thesis, analysis of a simple H-brace structure subjected to rigid striker model and 4-

legged jacket platform subjected OSV bow collisions and Bulk Carrier side collisions have been

carried out. 2 impact locations have been considered for OSV and one for the bulk carrier.

The author first examined the effect of boundary conditions on the H-Brace structure. 2

conditions were considered: axially fixed condition and axially flexible [With surrounding

Chords] condition. We have found evidence that in the case of axially fixed boundary condition,

large membrane forces are produced in the brace, which enable it to resist the crushing forces

and as a result, there is less local indentation. However, there is a significant difference between

axially flexible & axially fixed condition and hence for realistic simulations we have to consider

the presence of the surrounding brace and the axial flexibility it offers.

The second parametric study was conducted by the author by varying the thickness and diameter

of the brace structure. The results showed that there was an increase in brace strength with

increasing thickness. A substantial increase was noticed when the thickness was increased from

2.1mm to 3.1mm. This is largely attributed to the substantial increase in resistance to local

indentation. However it was interesting to notice that the increase in strength was not

consistently proportional to the increase in thickness. From a point of view of force-global

deformation plots, by varying the diameter, there was evidence that larger diameter meant more

strength. However, after examination of the percentages of distribution the total deformation

between local and global deformation, it was found that large diameter braces were more

susceptible to local deformation, whilst the smaller diameter braces were more susceptible to

global deformation. This is an important finding as braces which are more susceptible to local

denting could pose a bigger threat to the overall structure as it will effectively reduce the

maximum strength of the overall structure by acting as hinge.

The following simulation concerned impact of the 4-legged jacket structure with OSV Bow.

The results showed that the strength of the jacket increases with increase in leg thickness. By

varying the thickness of the 4-jacket legs, we verified that the behaviour which was earlier seen

on H-brace in terms of the changing strength in local/global deformation cases with respect to

change in thickness. The jacket leg with 40mm thickness had relatively lesser strength against


97


local deformation, while the jacket leg with thickness 60mm was more prone to global

deformation. The energy dissipation characteristics of the OSV bow collision scenario was also

looked into and it was found that in the case of OSV bow collisions, the ship absorbed a majority

of the energy in all 3 cases. Increasing the leg thickness would bring the jacket close to strength

design against this particular OSV configuration. Since the first point of impact, was the deck,

the deck plate, associated stiffener’s and the central girder dissipated a majority of the strain

energy. From the energy dissipation characteristics, it is clear that considering a deformable

model is important in the case of OSV Bow collision, to have an accurate picture of the collision

damage. An assumption of rigid ship would be conservative. A comparison was done between

impact location 1 and impact location 2 in terms of the force displacement characteristics. The

jacket strength reduced when the point of impact was closer to the leg bottom. It was concluded

that this behaviour is due to the increased local denting in the jacket leg in case of impact

location 2.

In the case of Bulk carrier side impact at 1 m/s, the results showed that the strength of the jacket

increases with increase in leg thickness. By varying the thickness of the 4-jacket legs, we

verified that the behaviour which was earlier seen on H-brace and OSV bow collision in terms

of the changing strength in local/global deformation cases with respect to change in thickness.

The jacket leg with 40mm thickness had relatively lesser strength against local deformation,

while the jacket leg with thickness 60mm was more prone to global deformation. The energy

dissipation characteristics of the Bulk carrier side impact scenario was also looked into and it

was found that in the case of Bulk carrier side impact, the jacket absorbed a majority of the

energy in all 3 cases. At 40mm jacket leg thickness, it was close to ductility design and in case

of 50mm and 60mm thickness, it was a shared energy design. Since the first point of impact,

was the hull shell plate outside the hopper tank, a majority of the energy was absorbed by the

hull shell plate, the hopper longitudinal stiffeners and web frames. From these results, it can be

said that a simplification considering a rigid bulk carrier model will not be too conservative as

for jacket leg thicknesses of 40mm and 50mm, the design is close to ductility design. In the

case of collision at 2 m/s collision, there was extensive damage to the jacket structure From

dent to diameter ratio’s a , we can come to a basic conclusion that 40mm jacket legs have failed.

The 50mm thickness leg is very close to failure and dent-diameter ratio for 60mm thickness is

considerably lower than 0.6. However, high shear stress were observed in the jacket bottom. If

not for the clamped leg bottom condition, the jacket could have very likely tipped over.



11. FURTHER WORK

1. The author has only dealt with damage analysis of the 4-legged jacket structure. The

effects of the weight and inertia of the wind turbine, wave loads etc has not been

considered. Hence, post collision, by initializing the stresses and strains present in the

jacket, it would be advisable to conduct an analysis to verify whether the damaged jacket

can withstand the the global loads.

2. An analysis which includes the soil stiffness would provide further more accurate

insights into the overall jacket behavior.

3. Windfarm support vessels constantly service the windfarm and a collission analysis of

the same would also be advisable.

4. Radical new design’s for OSV are available in the offshore market today, which

includes the X-BOW concept, which may have a distinct collision behavior. It would

be advisable to verify the impact of collision by an X-BOW.

5. Offshore windfarm installation vessels and installation barges may also pose a

significant threat to the jacket structure, since it functions in close proximity to jacket

strucures, a collision analysis could be relevant.


99


12. ACKNOWLEDGEMENTS

The thesis has been an extremely challenging assignment for the author. Modelling and meshing

a total of around 10 geometric models, which included relatively simple 8 H-Brace

configurations along with challenging OSV Bow model and Bulk Carrier Model was a

herculian task as far as the author is concerned. However, a lot was learnt about the intricacies

of modelling and meshing throughout the course of the thesis.

A combined total of 24 FE simulations has been carried performed with an accumulated CPU

Clock time of roughly 400 hours, in the course of which a good understanding about the

capabilities of LS-DYNA was comprehended.

I would like to first thank my supervisor – Prof.Herve Lesourve, for all the support and guidance

extended thoughout the thesis. One could not have asked for a better supervisor.

Secondly, I would like to thank Mr.Matthieu Gelbart of STX France & Mr.Stephane Paboeuf,

Bureau Veritas for all the information and insights they have provided in the course of the

project.

My collegue and friend Mr.Michael O’Connor and Mr.Andres Barrera have been there for any

help or support and their companionship will always be remembered.

I would like to thank my parents, who have always stood like a rock in suporting me, whatever

my needs.

Last, but not the least, I thank god almighty for his abundant grace.

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



13. REFERENCES

Breu, F., Guggenbichler, S., & Wollmann, J. (2008). DIRECTIVE OF THE EUROPEAN

PARLIAMENT AND OF THE COUNCIL. Vasa (Vol. 0016, pp. 1–61). Retrieved from

http://medcontent.metapress.com/index/A65RM03P4874243N.pdf

Buldgen, L., Le Sourne, H., Besnard, N., & Rigo, P. (2012). Extension of the super-elements

method to the analysis of oblique collision between two ships. Marine Structures, 29(1),

22–57. doi:10.1016/j.marstruc.2012.08.002

Buldgen, L., Le Sourne, H., & Rigo, P. (2013a). A simplified analytical method for estimating

the crushing resistance of an inclined ship side. Marine Structures, 33, 265–296.

doi:10.1016/j.marstruc.2013.06.005

Buldgen, L., Le Sourne, H., & Rigo, P. (2013b). Fast strength assessment of mitre gates to ship

impact. International Journal of Crashworthiness, 18(5), 423–443.

doi:10.1080/13588265.2013.802146

Cho, S. R., Seo, B. S., Cerik, B. C., & Shin, H. K. (2013). Experimental and numerical

investigations on the collision between offshore wind turbine support structures and

service vessels, 281–287.

Haris, S., & Amdahl, J. (2013). Analysis of ship–ship collision damage accounting for bow and

side deformation interaction. Marine Structures, 32, 18–48.

doi:10.1016/j.marstruc.2013.02.002

Herndon, V. (2008). Cape Wind final environmental impact statement.

Hong, L., & Amdahl, J. (2008). Crushing resistance of web girders in ship collision and

grounding. Marine Structures, 21(4), 374–401. doi:10.1016/j.marstruc.2008.02.001

Le Sourne, H., Besnard, N., Cheylan, C., & Buannic, N. (2012). A Ship Collision Analysis

Program Based on Upper Bound Solutions and Coupled with a Large Rotational Ship

Movement Analysis Tool. Journal of Applied Mathematics, 2012, 1–27.

doi:10.1155/2012/375686

Livermore Technology Corporation. (2006). LS-DYNA Theory Manual (pp. 15–573).

Livermore Technology Corporation. (2014). LSTC Website.

Lutzen, M., Simonsen, B. C., & Pedersen, P. T. (2000). Rapid Prediction of Damage to Struck

and Striking Vessels in a Collision Event. Proceedings of the International Conference of

Ship Structures for the New Millenium: Supporting Quality in Shipbuilding.

Minorsky, V. (1959). An Analysis of Ship Collisions with Reference to Protection of Nuclear

Power Plants. Journal of Ship Research.

NORSOK. (2004). NORSOK STANDARD N-004, (October).


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Norsok, T., Federation, T., & Industry, N. (2007). ACTIONS AND ACTION EFFECTS,

(September).

Ohtsubo, H., & Wang, G. (1995). An upper-bound solution to the problem of plate tearing.

Journal of Marine Science and Technology, 1(1), 46–51. doi:10.1007/BF01240012

Qvale, K. H. (2012). Analysis and Design of Columns in Offshore Structures subjected to

Supply Vessel Beam Collisions Kjetil Hatlestad Qvale, (June).

Skallerud & Amdahl. (2002). Nonlinear Analysis of Offshore Structures. Research Studies

Press Ltd, England.

Soreide, T. H. (1985). Ultimate Load Analysis Of Marine Structures. TAPIR, (2006), 2011–

2012.

Wierzbicki, T. (1995). Concertina tearing of metal plates. International Journal of Solids and

Structures, 32(19), 2923–2943. doi:10.1016/0020-7683(94)00237-Q

Zhang, S. (2002). Plate tearing and bottom damage in ship grounding. Marine Structures, 15(2),

101–117. doi:10.1016/S0951-8339(01)00021-1



14. APPENDIX

FORCE DEFORMATION PLOTS & ENERGY DEFORMATION PLOTS

Figure 78. Energy -Displcement Graph - 15 Degrees

Figure 79. Force-Diplacement Graph - 15 Degrees

0.00E+00

5.00E+02

1.00E+03

1.50E+03

2.00E+03

2.50E+03

0.00E+00 5.00E+00 1.00E+01 1.50E+01 2.00E+01 2.50E+01 3.00E+01

Ener

gy (

J)

DISPLACEMENT (mm)

ENERGY-DISPLACEMENT GRAPH - 15 DEGREES

0.00E+00

1.00E+01

2.00E+01

3.00E+01

4.00E+01

5.00E+01

6.00E+01

0.00E+00 5.00E+00 1.00E+01 1.50E+01 2.00E+01 2.50E+01 3.00E+01

FOR

CE .

(KN

)

DISPLACEMENT (mm)

FORCE DISPLACEMENT GRAPH -15 DEGREES


103


Figure 80. Energy -Displacement Graph - 30 Degrees

Figure 81. Force-Displacement Graph - 30 Degrees

-5.00E+02

0.00E+00

5.00E+02

1.00E+03

1.50E+03

2.00E+03

2.50E+03

0.00E+00 5.00E+00 1.00E+01 1.50E+01 2.00E+01 2.50E+01

I En

ergy

(J)

Displacement (mm)

ENERGY DISPLACEMENT GRAPH - 30 DEGREES

0.00E+00

1.00E+01

2.00E+01

3.00E+01

4.00E+01

5.00E+01

6.00E+01

7.00E+01

0.00E+00 5.00E+00 1.00E+01 1.50E+01 2.00E+01 2.50E+01

FOR

CE .

(KN

)

DISPLACEMENT (mm)

FORCE-DISPLACEMENT GRAPH -30 DEGREES



Figure 82. Energy-Displacement Graph -45 Degrees


0.00E+00

2.00E+02

4.00E+02

6.00E+02

8.00E+02

1.00E+03

1.20E+03

1.40E+03

1.60E+03

1.80E+03

0.00E+00 2.00E+00 4.00E+00 6.00E+00 8.00E+00 1.00E+01 1.20E+01 1.40E+01 1.60E+01 1.80E+01

Ener

gy -

(J)

DISPLACEMENT(mm)

ENERGY-DISPLACEMENT GRAPH - 45 DEGREES

0.00E+00

1.00E+01

2.00E+01

3.00E+01

4.00E+01

5.00E+01

6.00E+01

0.00E+00 2.00E+00 4.00E+00 6.00E+00 8.00E+00 1.00E+01 1.20E+01 1.40E+01 1.60E+01 1.80E+01

FOR

CE.

(K

N)

DISPLACEMENT (mm)

FORCE-DISPLACEMENT GRAPH - 45 DEGREES.


105


Figure 84. Energy-Displacement Graph - 60 Degrees


0.00E+00

2.00E+02

4.00E+02

6.00E+02

8.00E+02

1.00E+03

1.20E+03

1.40E+03

0.00E+00 1.00E+00 2.00E+00 3.00E+00 4.00E+00 5.00E+00 6.00E+00 7.00E+00 8.00E+00 9.00E+00 1.00E+01

Ener

gy (

J)

DISPLACEMENT (mm)

ENERGY DISPLACEMENT GRAPH - 60 DEGREES

0.00E+00

5.00E+00

1.00E+01

1.50E+01

2.00E+01

2.50E+01

3.00E+01

3.50E+01

4.00E+01

4.50E+01

5.00E+01

0.00E+00 1.00E+00 2.00E+00 3.00E+00 4.00E+00 5.00E+00 6.00E+00 7.00E+00 8.00E+00 9.00E+00 1.00E+01

FOR

CE

(KN

)

DISPLACEMENT (mm)

FORCE DISPLACEMENT GRAPH - 60 DEGREES

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