1 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
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1
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.
P 4 Jose Babu Maliakel
Master Thesis developed at ICAM-Nantes, France
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.
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
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
2.1. General ....................................................................................................................................... 18
2.2. Energy perspective ..................................................................................................................... 18
2.3. Force – deformation relationships .............................................................................................. 19
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
6.3.2. 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
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
7.1. General ....................................................................................................................................... 50
7.2. FE Model .................................................................................................................................... 50
7.2.1. Mesh and Elements .............................................................................................................. 50
7.2.3. Material Properties ............................................................................................................. 52
8. OSV Bow Model ............................................................................................................................... 53
8.1. General ....................................................................................................................................... 53
8.2. FE Model .................................................................................................................................... 55
8.2.1. Model Verification ............................................................................................................... 55
8.2.3. Material Properties ............................................................................................................. 56
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
Figure 6. Components of a Monopile Foundation ................................................................... 17 Figure 7. Gravity foundations (Source Luc van Braekel ) ....................................................... 17
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 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
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
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
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
P 12 Jose Babu Maliakel
Master Thesis developed at ICAM-Nantes, France
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)
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
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.
P 14 Jose Babu Maliakel
Master Thesis developed at ICAM-Nantes, France
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.
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
Figure 4. Tripod Foundation (Source Alpha Ventus)
P 16 Jose Babu Maliakel
Master Thesis developed at ICAM-Nantes, France
Figure 5. A jacket foundation.( Source Alpha Ventus)
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
Figure 6. Components of a Monopile Foundation
Figure 7. Gravity foundations (Source Luc van Braekel )
P 18 Jose Babu Maliakel
Master Thesis developed at ICAM-Nantes, France
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.
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
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:
P 20 Jose Babu Maliakel
Master Thesis developed at ICAM-Nantes, France
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
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
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
P 22 Jose Babu Maliakel
Master Thesis developed at ICAM-Nantes, France
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.
.
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
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).
P 24 Jose Babu Maliakel
Master Thesis developed at ICAM-Nantes, France
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)
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
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.
P 26 Jose Babu Maliakel
Master Thesis developed at ICAM-Nantes, France
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:
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
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
P 28 Jose Babu Maliakel
Master Thesis developed at ICAM-Nantes, France
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