FI
u
FINITE ELEMENT ANALYSIS OF SHIP-ICE COLLISION USING LS-DYNA
By
©Rui Zong
Athesis submitte d tothe Schoo lof Grad ua teStudies in pa rti al fulfi llme ntofthereq uirem ent sforthedegr ee of
Masterof Enginee ring
Facultyof EngineeringandApplie dScie nce Memoria lUniversityof Newfou nd la nd
July2012
St.John ' s Newfound la nd
ABSTRA CT
Theenergy indu stry ' sincreasin ginterest in the Arcticregion dem and smore andstro nge r polar shi ps. lACShasreleased a setofdocum entstitled Unifie d Requir em ents for Polar Ships(UR[)toharmoni ze diffe rent icc classifi ca tio nspecificatio ns.This thesisdefin es a procedu refo r evaluatingan"lACS Polar Class"ship undericeimpact susin gLS-DY NA.
anex plici t finiteclem ent ana lysis tool. The finalprodu ctincludes anumericalmodelthat is capableof evaluating thegloba l motion sof the shipand icc.theship-icc cont actfor ce.
and thelocal structural respon se of the ship.Afe w iccmateri almod elswhosepressure - arearelations hips complywith theURI arc proposed aswell. Restorin gforces arc mod eledusin guser-d efin ed-cur ve-functions.Thisinnovat ive approac hsigni fi cantly reduc esthecomput at ion cost by excl udi ng thewater dom ainfromthe ana lys is.The Arbi trary Lagran gian- Eulerianmeth odinLS-DYNA isdiscussed and employedto estimate necessary inp utsfortheuser-defined-cu rve-fu nct ion s,Severalship-iccim pac t scenariosaremodel ed inLS-DY A and cont act forcesarccompa red with the estimatio ns byDDeP S. a sim pleana lytica lsolutio nthat is consis tentwith the URI.[nthelastpart of thisthesis.the shi p fromthepreviou sanalysisisicc-st ren gth ened withinterna lstructures inaccorda ncewith the URIand theDNV specific atio ns.Local structural respon se ofthis ship undericeimpact sis assessed.
ACKNOWL EDGEMENTS
Tobeg in with thisthesis ,Iwould liketo express my since res tappre c iatio ntomy supervisor Dr. Claude Dal eyforhis exce lle ntsuppo rt, directi on , andguida nce. Iamalso than kfulto STEPS2 andNSERCCREATE programfo rthe ir gene ro us financi al suppo rt.
This thesis would beimpossiblewithoutthehe lp andsuppo rtfromafe w grea t peopl e.I wouldalso liketo sta te my greatgratitude tothefoll owin g:
Dr.Wei Qiu, profe sso r atMUN, for brin ging metothis outsta nd ing univers ity.
Dr.Bruce Colbo urne, pro fe ssor atMUN,for allthe ins ightfu land inspi ringdiscu ssion s thro ug ho ut myresea rch .
Mr. Bruce Qui nto n,afell o w grad uatestude ntat my office , fo r your wond erfulhelp and pati en ce.
Dr. .Junyon g Wangand Dr.Rob er Gagno natNRC - lOT , fo r yourrema rka b le help.
Lastly, Iwou ld liketothankmy fami lyand my girl friend fo r your uncondit ion al support.
This thesi sisdedi catedto you.
iii
Tabl eof Contents
ABSTRACT .
ACKNO WLE DGE ME TS....
Tableof Co ntents
...ii
...iii
...iv ListofTab les
Listof Figures
...xi ... xiv
List ofNomencla ture orAbbreviatio ns xviii
ListofAppe nd ices...
Chapte r 1 Introdu cti on I
1.1ScopeandObjective s
1.2 ThesisOrganizati on ..
1.3LS-DyNA ..
1.3 .1General Inform ation ..
1.3 .2TimeSte pControlandTotalTimeCost 1.3.3 TheArbitra ry Lagran gian-Eulerian (ALE)Metho d...
...5 ...5
...7 ...9
1.3.4Contac t Model... . 12
1.3.5User DefinedCurveFunction 1.3.6Presentation of Nume rica l Mod el s..
.15 ..16
Chapter 2 Litera ture Review ..
iv
.. 17
2.1. Unified lACSPolarRules 2.1.1Originof thelACSPolarRules ...
2.1.2LoadDesign Scenario...
...17
...17
...20
2.2Ship Icc Contactand Pressure-Area Curves .. 2.2.1TheShip-IccContact Mechanism.. ...23
. 23 2.2.2Spatial PressureDistribution 24 2.2.3 ProcessDistribution... 2.2.4 Spatial vs. Process ...26
...27
2.3Studies using finiteElementAnalysis Programs 29 2.3.1StudiesUsingDYNA.... ...29
2.3.2 Studies using otherFEAPrograms... 2.4 Summaryof Literature Review Chapter 3 Ice MaterialModel... 3.1SimulationSetup 3.1.1Geometric Model .. ...31
...32
... 35
...35
. 35 3.1.2MaterialModels. .. 38
3. 1.3ElementChoices .40 3.1.4 Boundaryand InitialConditions... 3.1.5OtherInputs . .40 ...41
3.1.6 Mesh Converge nceStudy... .. .41
3.1.7Nom inal Contac tArea.. . 42
3.2IceMateri alModelsBasedon the Crus hable FoamMateri al... .45
3.2.1Gagnon'sCrus ha bleFoam IceModel.. . .45
3.2.2IceModel A.. . 47
3.2.3IceModelB... . .49
3.2.4 IceModel C... . 51
3.3IceMater ialModel sBased on the Elas tic- Plastic Materi al ... ...53 3.3.1 IceMod elD ..
3.3.2Icc ModcIE...
3.4Summa ry...
Cha pter4 ALEMeth od..
4.1Simulatio nsforEvaluatingtheComputationCost 4.1.1Geome tric Model
4.1.2 Materi alModels...
. 53
. 54
. 56
. 59
...59 ...59
. 62
4.1.3ElementChoices ..
4.1.4Bound ar y and Initial Conditio ns...
4. 1.5 Other Inputs ..
4.1.6 MeshConve rgence ...
vi
. 63
....64
. 66
.. 66
4.1.7Evaluatio nof theComputatio nCost., . 4.2OscillatoryAnalysisvs.TransientAnalysis .
4.2.1GeometricModel . 4.2.2MaterialModels 4.2.3ElementCho ices
. 69
. 70
. 71
...73
...73
4.2.4Bound ar y and Initial Conditions 73
4.2.5LoadingCond itio ns . . 75
4.2.6Added Massusin gthe Osci lla to ryAna lys is 75
4.2.7 Adde dMass using the Transie ntAna lysis 76
4.2.8Comparison .
4.3 Estimationor Adde dMass andDamp ingCoefficient....
4.3.1Geometric Model . 4.3 .2Material Models . 4.3.3ElementCho ices . 4.3.4 Bound a ry and In itial Cond it ions.
. 79
. 80
. 80
. 82
. 82
. 82
4.3.5 Loadi ngCond itions 83
4.3.6 Ship'sAdde d Mass and Dampin g Terms ... ...84
4.3.7Ice Adde d Massand Damp ing Terms 88
4.3.8Comparison 90
vii
4.4 Summa ry...
Cha pter5 Ship lee Collisio nForce ...
5.1 Defin ed- Cu rve- Functi on s..
5.1.1 Restorin g Forces..
5.1.21mpleme ntatio n.... 5.1.3 Drag andAddedMass.
5.2MassReducti on Coeffic ient....
5.2. 1Sim ulationSetup...
5.2.2 Result s 5.3SimulationSetup ...
5.3. 1Geometric Mod el..
5.3.2MaterialMod els...
5.3.3ElementChoices .
5.3.4 Bound ar y and initial conditions...
.. 91
.. 94
. 94
.. 94
.. 96
.. 100
.. 101
. 102
...104
. 107
.. 107
.. 107
. 107
.. 107
5.3.5LoadingCondi tio nsand Dampin g...
5.3.6Mesh Conve rge nce ..
5.4 Ship-leeContactForce..
. 108
. 108
. 111
5.4. 1"Dry" Collis ionCases 111
5.4.2"Wet"CollisionCases.. . 113
viii
5.4.3"Dry't vs. ""WeC .
5.5Summary .
Chapter 6 ShipsStructural Response .
...115
. 119
. 121
6.1ShipStructuralDesign. . .
6.1.1MainFrames ....
... 121 ...122
6.1.2Load CarryingStringers .
6.1.3DeepWeb Frames
6.1.4Bulkheads .
6.1.5Summary .
6.2SimulationSetup . 6.2.1GeometricModel . 6.2.2MaterialModel....
6.2.3 Element Choices 6.2.4Boundary andinitialconditions...
6.2.5LoadingConditions and Damping
. 124
...125 ...126
. 127
. 129
...129 ...130 ....131
. 132
...132
6.3ShipStructural Response 133
6.3.1Contact Forceand Pressure ...
6.3.2Von Mises Stress .
. 133
...135
6.3.3 Pressure-Deflection Curve 138
ix
6.4Summary .
Chapter 7 ConclusionsandRecommendations.
7.1Conclusions . 7.2Recommendations...
Chapter 8 Bibliography .
...140
...142
... 142
...143
....148
Appendices 156 AppendixA: STePS2 Cluster Specifications ...157 AppendixB:DYNA'sKeywordFileof theFinalModel 159
Listof Table s
Table 2- 1: Polar Classesin lACSUnified PolarRules....
Table2-2:Ice StrengthTerms in theURI Table3- 1:Geometryof the Shipand Ice ..
Table 3-2:Mate rial Propert ies of the Ship Model Table3-3: Mate rial Properties oftheIceModel. . Table3-4:ElementCho ices for Ship and Ice . Table3-5:SurgeDistan cexand Nomin al ContactAreaAnominal.
.20
.. 38
..38 ..39 ....40 ....44
Table3-6:Materi alPropertiesofGagnon' s IccModel 46
Table3-7: Stress -Strain Relationshipin Gagnon'sIceModel .46
Table3-8:Materi alPropertiesof IceModel A .48
Table3-9:Stress-VolumetricStrain Relationshipin Icc Mode lA .48 Table3- 10:Stress-VolumetricStrain Relationsh ipin Ice Model 13 .50 Table3-1I:Strcss-VolumetricStra in Relationsh ip in Icc Mode lC ...51 Table3- 12:Mate rial Propert ies of Icc Mode l D .
Table3- 13:Material Properties of Ice Mode lE .
...53
.55 Table3-14:Stress-VolumetricStra in Relati onshipin IccModel E 55
Table3- 15:Summaryof ProposedIccMaterialModels 56
Table 4-1:ElementChoices fortheALE Simulations ...63
Table 4-3:Dimensions of the ALE Domain ..
Tabl e4-2:Summary of theMesh ConvergenceStudy 68
..72
Table4-4:Influenceof theMagnitud e of the Force on theHea ve Added Mass 77 xi
Table4-5:Heave Added Mass CoefficientsatVery-LowFrequenciesandVery-High
FrequenciesontheUnit Hemisphere . . 79
Table 4-6:Boundary Conditionson the Shipand Ice..
Table4-7:ValuesofAppliedLoads
. 83
...84
Table4-8:AddedMass and Damping Termsofthe Ship 87
Table4-9:Added Mass and Damping TermsoftheIcc . 90
Table4- 10:Added Mass CoefficientsCalculated byDDePS (1967)and PresentWork..91 Table5-1:LoadDefinitionforRestoring Forces.... . 99 Table5-2:Radiiof Gyration Estimated byDYNA and DDePS 105 Table5-3: MassReduction CoefficientsCo .
Table5-4: LoadDefinitions ontheShipand Icc .
. 106
. 108
Table5-5:ComputationTimeofSimulations using VariousElementSizes 109 Table5-6:MaximumContactForce (Finite Ice.Dry Collision) .
Table5-7:MaximumContactForce (Infinit eIcc.DryCollision).
. 112
. 112
Table5-8:MaximumContactForce(Finite Ice.Wet Collision) 114 Table5-9:MaximumContactForce(Infi nite Icc. WetCollision) .. . 114 Table5-10: Dryvs.Wet-Maximum ContactForce.Finite Icc 116 Table5- 11: Dry vs. Wet-Maximum Contact Force.InfiniteIcc..
Table6-1:HullAreaExtents (lACS 2010)
Table6-2:ScantlingsofStructural Members in the BowRegion...
. 116
...122 ....128 Table 6-3: MaterialParametersforthe Non-Rigid Part of the Ship 130 Table6-4: MaterialParameters ofthe RigidPart of theIcc...
xii
. 130
Table6-5:ElementChoices ..
Table6-6:LoadDefinition on the Ship...
xiii
.. 132
.. 133
Listof Figures
Figure I-I: Com par iso n of Lagrangian , Eule rianandALE (LSTc' 20 I0) 10 figure 1-2:Coupling in the ALE meth od...
Figure 1-3:Com pariso nofSOF TOptions..
...12
. 14
Figure 1-4:Contac t Mod elwithSOFT=2... . 15
Figure2- 1:Mapofthe Arctic Ice-CoveredWaterDefin edbyIMO 19 Figure2-2:SketchofIce Contact witha Structure(Daley2004) 24 figure2-3 :Spat ial Pressur e- AreaRelat ion ship (Da ley2004). .. ...25 Fig ure2-4 :Nominal, trueand measured areas(Daley2004) 25 figure2-5: ProcessPressur e-Ar eaRelat ion ship (Da ley2004) .. . 26 Figure2-6:Link bet weenProcess andSpat ial Distr ibuti on s (Daley2004) 28 figure3-1:Geome tric Mod els of the Shipand Ice in Rhinoceros® 36 Figure3-2 :theIceBlock with Round ed Edges...
figure3-3:Ship Bow...
. 36
....37
Figure3-4:Sepa ration betw eenthe Ship and Ice (To pView) 37 Figure3-5:Stress-Volum et ric Strai nCurveof theIccModelinConve rge nceStudy..39 Figure3-6:Boundar y Condition on theInfinit eIce.... . .41
Figure3-7:Mesh Conve rge nce . ...42
figure3-8: Intersect ion ofthe Shipand Ice ...43 figure3-9:Stress -Vo lume tricStra in Relation sh ipinGagno n's IceModel .46 Figure3- 10:ProcessPressur e-A rea CurveofGagno n'sCrusa bleFoam IceMod el .47 fig ure3- 11:Stress-Volum et ric Strai nCurvein IceMod el A .48
xiv
Figure3- 12:Pressure -AreaCurveof IceModel A...
Figure3- 13: Stress-Volumetric StrainCurvein IceModelB..
. .49
. 50
Figure3-14: Pressure-AreaCurveofIce ModelB 51
Figure3-15:Stress-VolumetricStrainCurve of IceModelC.. . 52
Figure3- 16:Pressure-AreaCurve of IceModelC... . 52
Figure3-17: Pressure-AreaCurve of IceModelD... . 54
Figure 3- 18: Pressure-AreaCurve of IceModelE... . 55 Figure3- 19:Pressure-AreaCurve of Ice ModelC(All DataIncluded)... . 58 Figure 4-1:Top Viewof the Geometric Modelin Rhinoceros®... . 61 Figure4-2: 3DModelin DYNA...
Figure4-3:the ALEDomainincluding Ambient Layers...
Figure 4-4: Convergence of theIce SurgeMotion ..
Figure4-5:Convergence of SwayMotionof Ice..
Figure4-6: Convergence oftheIccHeave Motion Figure 4-7: 3DModelin DYNA ...
. 62
. 65
. 67
. 67
...68
. 72
Figure 4-8: PrescribedHeaveMotion oftheSpherein the OscillatoryAnalysis 74 Figure 4-9:HeaveMotion of the Semi-SubmergedSphere... . 76 Figure4- 10:TimeHistory of theSemi-SubmergedSphere'sHeavemotion 78 Figure4- 11:Influenceof theMagnitude ofthe Forceon theHeave AddedMass 78 Figure 4-12:3D ModelforEstimatingthe AddedMass CoefficientsontheShip... . 81 Figure 4-13:3D ModelforEstimatingthe Added MassCoefficienton theIce 81 Figure4-14: Time Historyof the Ship HeaveMotion ... . 85
Figure4-15:rime Historyofthe Ship Roll Motion Figure4- 16:rimeHistoryoftheShip Pitch Motion Figure4-17:Time History of the leeHeave Motion ..
Figure4-18:rime HistoryoftheIceRoll Motion...
Figure 4-19:rimeHistoryof theIcePitch Motion..
Figure 5- 1:CreatingaRigidPart .
...86 .. ...87 ...88
. 89
. 89
. 98
Figure 5-2: Creatingthe LocalCoordinateSystem.. . 98
Figure5-3:NormalDirectionoftheContactSurface... . 103
Figure5-4: ContactLocationon theIce ... . 103
Figure5-5:MeshConvergence-ShipGlancingwithFinite Ice 110 Figure 5-6:MeshConvergence-ShipGlancing with InfiniteIce 110 Figure5-7:Comparisonof the ContactForce-Dry vs.Wet (Finite Ice) . 118 Figure5-8:Comparisonofthe ContactForce-DryvsWet (Infinite lee)... . 118 Figure 6- 1: HullArea Extents(lACS 2010)....
Figure6-2:MainFrames and theHull...
. 123
...124
Figure6-3: Load Carrying Stringers and theHull 125
Figure6-4:Deep WebFramesandthe Hull..
Figure 6-5: Bulkheadsincluding Stiffeners. andthe Hull..
...126
. 127
Figure6-6:BowRegion with Internal StructuralMembers 129
Figure 6-7: Rigid andNon-RigidShipand Ice... . 131
Figure 6-8:Comparisonof theContactForce:Rigid ShipvsNon-RigidShip 134 Figure6-9:Time History ofthe AveragePressure...
xvi
. 134
Figure6- 10:ATypical VonMisesStress Distribution on the MainFrame ...136
Figure6- 11:A TypicalVon MisesStressDistribution on theDeepWebFrame 136 Figure6-12:TimeHistory oftheEffective Stress . . 137 Figure6- 13:Time HistoryoftheEffectivePlastic Strain 137 Figure6- 14:Pressure-DeflectionCurveof theMain Frame Member..
xvii
. 139
Listof NomenclatureorAbbrev iations
ID One Dimensional
2D TwoDimensional
3D ThreeDimensional
ABS AmericanBureau of Shipping classification society ALE the Arbitrary- Lagrangian-Eulerian method
CAC Canadianarctic class
CAD Computer-aided design
Card Aunitwhere users giveinputsintoDYNA
CFD Computational fluiddynamics
CG Centerofgravity
Computationcost/time Lengthof time requiredforthe solver torun thenumeric al model
ComputerCluster
DDcPS DOF DNV DYNA FE FEA GL
Acollectionofnetworkedcomputers thatfunction as asingle computer
Thesoftware DirectDesignforPolar Ships Degree of'frccdom
DetNo rskeVeritas class iticationsoce ity
Refer sto eitherLS-DYNAorMPI'-DYNAinterchangeabl y Finiteelement
Finiteelementanalysis
GermanischerLloyd classi ficationsociety xviii
lACS IMO LSTC LR Part Rhinoceros®
Simulation time URI
International Associationof ClassificationSocieties International MaritimeOrganization LivermoreSoftwareTechnologyCorporation LloydsRegisterclass ifica tio nsociety
A collectionofelementsin DYNAwith similar properties A CADsoftwaredevelopedbyMcNeel NorthAmerica Lengthof timeexplicitly simulatedwithin thenumerical model Unified Requirementsfor PolarShips publishedbylACS
xix
ListofAppendices
AppendixA: STePS2 ClusterSpeficica tio ns . Appendix B:DYNA' sKeyword Fileofthe Fina lMode l
... 157
...159
Chapter I Introduction
TheArctic regionisbelie vedtohou se oneof the world's lar gest oilandgasresourc es. A UnitedStatesGeolog ica lSurveyestima tes that 530 billionbarr els ofpoten tialpet roleum arclocated beneat h this area.Theice-infestedsea waterandothe r harsh env iro nme nta l condi tions havebeen cha lle nging theindustr y eversince thefirstope rat ionin the Arctic.
Howeve r,the increas ing dem andfromthe globa leconomy, isdrivin gthe oilandgas ind ustry tobemo re and more active in the Arctic region .
Shipsopera ted in the Arcticareacanbedivided into twomain catego ries: icc-br eakin g vesselsand ice-str en gth ened ships.Ice-br eakin g vesselsarcusedto suppor tother operating units andactivities .The irstro ng hullstructuresena ble themtotake on hea vy tasks suchasiccbreakin g,maneu verin gin icc andicc mana gem ent.Icc-st ren gth ened ships,whose hulls arerelative ly weakerthanice-b reakers, arc designedto withstand possibl e expos ure to a certain level of iccload .depend ing on theiriccclass.They ha ve lim ited abilityin breakin g ice and maneu ver ingin icc coveredwater. Com mo n ice- strengthe nedships intheArcticare vesselssuchas cargo ships, tank er s. andsupplyships.
Historic all y.iceclassifi cation s governi ng polar shipsarc regulated by various classificatio nsocieties. In2006.theIntern ational Associatio nof ClassiiicationSocieties (lACS)released a setof docume ntstitledUni fie d Requir em ent s for Polar Ships(URI) to harm on izediffer ent iceclassifi cation speci fica tions . Moreicc- str en gthen ed shi ps com plyingwith the URIare expecte d in thenearfuture.
Extensivestudiesconce rning icc-b reakin g vessels havebeen carr iedout tounderstandthe mechanism of the hull breakin g ice and thephysics ofthebroken icc actingagainst the hull.Research and experienceon theicc-stren gth ened vesselsarc relative ly limited.The presentthesisisprimarily conce rnedwith ice-stren gthened shi psunderthenew URI.It presentsastudyusing thestate-o f-art finiteeleme ntana lysis(FEA)program LS-D YNA to investigatethegloba l mot ion and localstructuralresponseofanicc-strengthenedship unde r icc impac tscenarios.
1.1Scope and Objective s
Thisthesisdeta ilsa procedurefor analyzing ship-ice collisions usin gthe commercia l FEAprogramLS-DYNA.Thefi na lprod uct is a FEAmodel ingtempl ateto evaluate the glo balmotion.and the globa land local structura lresponseof an iccstrengthene dship under variousiceimp actscenarios. Thisstudy iscom posedoffoursubto pics:
• Developanice materia l model whose pressu re-area relatio nshi pcomp lies withtheURI.
• Estimate theaddedmassanddam pingcoeffi cien tsoftheship andicc usingthe Arbitrary -Lagra ngian-Euler ian(ALE)method.
• Modelvariousship -icccollisio nscenar iosandcomparethe result s with calculationsusin g the Popovmodel thatis consis tentwiththeURI.
• Co mbineresults frompreviou s subtop icsto generatea solutionfor evaluatingaship'sstruct ura lresponse undericc impacts fo ranice- strengthened ship.
1.2 ThesisOrganization
This thesis conta inssix chap ters.Thischa pter presen ts thebackgro und.objectivesand outlineofthisthesis. and introdu ces readers tothe comme rcial finite eleme ntana lysis programLS- DYNA.Itsdetailed theory manu al (Hallq uist.2006) and usermanual (LSTC.
2007a. 2007b)are availableonline . However .back groundkno wled ge of com putatio n timecost.the ALEmeth od . and implem ent ation of the user-defin ed -cur ve- funct ion s are briefl ypresent edhereto support discussion s in later chapters.The use of user-d efned- curve - functio ns is an inno vat ive approac h forthis applica tion de velopedin thisthesisto simulate thewater dom ainwherethe ship-icecollision take splace.
Cha pter2is thelitera ture review. General inform ati on on previou s workon the URI incl udinga shortintro ductio n todesign scenarios ispresent edfirst.foll owedby the develop me ntofbasicknowled ge ofthemechani sm s ofship/structure- iceinterac tio n. the icepressure-arearelati on shi ps.andadiscu ssion of exis tingstudiesonship-icecollision usin g FEAprogram s includingLS-DYNA.A sum maryof the literatu re review ex plains themotivationand methodologyfor this thesis.
EachofChapter3 to Cha pter6 add ressesoneofthe subto pics listedin thepreviou s sectio n.Chapter3fo cu ses on developinga propericematerialmodelthatfitsthepurpose of thisthesis.Icemater ialpropertie s and itsfailuremechani cs are themostimportant facto rs in determinin gthe ship-ice contact forc e. The pressur e-arearelati on shipisthe most direc t indicati on ofice strength.The pressu re-area curvespecifie d in the URIis
considered asthebenchmark.Variousice materialmodels areevaluated by simulatinga simpleship-iceglancing impact scenario.Oneicematerialmodelis chosen based on closest compliancewith the URI.
Chapter 4explores thepossibility of implementing the ALEmethod.ALE simulationsin LS-DYNA havebeensuccessfullyimplementedto simulate thelluiddomaininmany studiesonship-ice collision.Sonaturallyit is selectedas atoolforthisthesis.However.
existingstudies usingALE areallconcerned with theglobal motion offloatingbodies andtheglobalcontactforces.Thisthesisaimsatevaluatingtheship-ice collisionin both the globalandlocalcontexts.A discussioninthischapterwillshowthattheALEmethod isnot anefficientapproachdue tothehighcomputation cost.Analternativesolution featuring user-defin ed-curve-functionsis then proposed and discussedinChapter5.
Ratherthan simulatingthewhole lluid domain.theALEmethod is employed to estimate added mass and damping coeffic ientswhichcan beinput intouser-defined-curve- functions.Simulationsoftransient andoscillatoryanalysesare conductedto estimate those coefficientsandresultsarecomparedwith literature.
Chapter5 explainsmodelingthe global contactforce of a ship-ice collision.Theship is simplifiedasrigidand theiceismodeled usingthematerialmodeldevelopedinChapter 3.Hydrodynamicforces aremodeledusinguser-defined-curve-functionswithoutactually simulating water. Simulationsofvariousship-ice collisionscenariosare performedand
resultsare com pare d to calculat ions usin g the Pop ovmodel whichis cons istentwith the URI.
In Chapter6. theship used in previou s sections isice stre ngt he nedinaccordancewith the URI.Th isstructuredanddeforma bleship isthenput in the collis io n modelsdevelopedin Cha pter5 in lieu of therigid one.The ship'sgloba l motion . and its globa land local structura l resp on sesunderice im pactsare ana lyze d.The final FEAmodel can beused as atemp late for analyzi ngothership-icecollision probl em s.
Cha pter7 concludes the completestudyandrecomme ndsfuturework.
1.3LS-DVNA
Thecommerc ial finit e eleme nt programLS-D YNA istheprim arynumericaltoolforthis research.Thissection introdu cesreade rsto itsgenera lcharacte ristics,as well as someof itsbackg rou ndtheori esthat are releva ntto this thesis.
1.3.1General Information
LS-DYNAis a genera l-purpose finite eleme ntprogram develop edbythe Livermo re SoftwareTechno logyCorpora tio n(LSTC)andwide ly usedby theautomo bile.
constr uct io n, military,aerospace. manu fact ur ing. andbioe ngineeringind ustr ies.Its core- compe tency ishighl ynonlin eartransientdynami cfinite eleme ntana lys is using explicit timeintegratio n."Transientdyna mic" impliesthe analysisofhigh- speed . short-d uratio n
eventswhere inerti al forces domi nate.Ship-icccollisioncould be a typica l tran sient dynamic problem."Explicit"meanssolvingequat io ns that invo lvetimeand time- dependent variables (velocity. acceleration.andinertial.etc.)to accuratelycapturethe dynam ic effects.A "nonlinear"proble mis generallycharacte rized byat least oneofthe follow ingcom plica tions:
• Bo undar ynonlin ea rity---Contact bet weenpart s orobjec ts changesover time orrestr aintson partsaretime depend en t.
• Geomet rica l nonline arity--- Largedeform at ion s occ ur. thusrequirin gnew eq uilibriumeq uations basedon the deforming geo metry.
• Materialnonlin earity--- Materi alsdonot exhibit ideall yelasticbehavio r and thisleadsto changesin the stress-strai nrelatio nship.
Obvio usly.a ship -icccollision problem fitsinallthree criteriaofnon linearity.This makesLS- DY Athe bestavailable tool lorthisresearch.Thedetailedtheory manual (Hallquist. 2006) of LS- DYNAis ava ilable onLSTC"swebs ite.Someim portan t theor ies relatedtothisthesiswillbepresent edinthechap ter.
Thisthesisutilizestwo versionsof LS-D YNA. The first one runs ononeor mo reparallel processorsina sing le comput er. Thisversion isusedmainlyto runsma llandsim ple simulatio ns.Anothervers ion isMPP-DYNA.which runs on aco mpute r clusterthat workslikeasuper comput erby connectinga groupof indep end entcompute rs.The cluste r used in thisthesishas128 coresand isverypow erfulinsolving largemodelsthat contain
elabora tegeo me try .very relin edmesh. com plex materi almodels.lon ge r simulatio n time.
complica tedboundarycond itionsor com binations thereo f.Thisefficiencyis achieve dvia modeldecomp osition that dissectsthe who lemode linto parts.Thereare three dceom posin gmeth ods (LSTC 2007a):the automa tic Recur s ive Coordi nate Bisect ion (RC B) meth od,the simpleheuri sti cmeth od (GREE D Y).and thcmanu almethod.In almos tall cases,theRCBisthe superior meth od for its robustness.
MPP-DYNAisthetoolfor mostof the simulatio ns presentedin thisthesis. Since LS- DYNAandMPP-DYNAessentiallysharethesame theo riesandcodes,theywill beboth referred asLS-DYNAfrom Chapter 4onwa rdsunless otherwisespec ified.
1.3.2 TimeSte pContro land Total TimeCost
Thegoalofthisthesisistoprodu ce apract icalsolution fo rrcalworld ship-icecollisio n prob le ms. Aspart ofthis. comp utationcost mustbetaken into con siderati on.During the solution. LS-DY NAloopsthro ughallthe possible eleme nts toupdatethe stressand the righ thandsideforcevector.The newtime ste p isdeterm inedbythcminimum valueof all the critical time ste psoverallclements.Genera llyspea king. the ship is ana lyze d usin g shellelement swhileicc.water. andairare modeled using solidcleme nts.
Forshe llelements. thecritical time stepcanbe com putedfrom:
Mc = ~
Eq ua t io n I>twhereLsisthe charac teristic lengthof a shelleleme ntandcis thespeedofsound:
Eq ua t io n 1-2
whereEisthe Young's modulu s,pisthematerialdensit y andvisthePoisson's ratio.
Thedefaultequation fo r calculatingLsis:
Equation l-d
whereL,isthelength of sideioftheclem ent ,f3equa ls Ifor triangle and 0 for quad rilateral elemen ts,andAsisthe sur faceareaof theeleme nt.
Thecritica l time ste pforsolidelementsis comp uted ina similar mann er:
Eq ua t io n I-u
whereLeis charac teristic len gth .Qis a functionofbulkviscos ityandc isthe adia batic speedof sound.Eq uatio nsforcalculatingQandc arc verycomplica tedand unnecessar y to bepresent edhe re.
As show nin the eq uationsabove,eleme ntsizes and materialprop erti estogeth er deter mine the criticaltimeste p.Note that in LS-DYNA. rigid clemen tsarc not conside red in the com putationof time step.Users sho uld defin e aprope rtime ste pvaluewhenthe model onlycontainsrigidcleme nts.
Besid esthe critica l time ste p, thetotal computationcostalsodependson thenumber of clements. boun darycon di tions, and the ana lys ismeth od . MoreDO F.more comp lica ted
loadin g conditions,and the ALE analysisgenera lly requir elonger com putation time.This is amajor cons ide ration in thisthesis andisfurtherdiscussedinChapter 4.
1.3.3The Arbitrary Lagrangian-Eulerian (ALE) Method
TheALEmeth odiscurrentl ythe only method for simulating water in DYNA.Ithasbeen usedinseveralstudies . Itsfull detailedtheor ycanbefoun d in DYNA ' stheo rymanu al (Ha llq uist,2006).Thissectiononly introdu ces readers tothebasicknowled ge ofthe ALE meth od.Implem ent ati on isdiscu ssedinCha pter 4.
Figure I-Iillustratesthediffer ence oftheLagran gian . Eulerian.and the ALEmeth odin ana lyz inga solidpieceof material (red) moving and deformin g.IntheLag ran gian simulatio n, themeshde form swiththematerial.In the Euleriansolution. themate rial flow sthrou ghthefixedmesh. TheALEmeth odis a combinationofthesetwo.The mesh is attac hed tothematerial (Lagrang ian)and passesthrough the fixedback ground refer encemesh (Eule rian) .Inother word s.thematerialdefo rm s ina Lagrangia n formul ation at thefirst step.Theseco ndste pisthe advec tio n.which mean sthatclem ent statevariablesin the deforme dcleme nts(redones inFigure I-I) arerema pped back onto the Eulerianrefere nce mesh .
Figu rc I-I:Compa r ison of Lagrangian, Euler ia n and ALE(LST C,2010)
Fluid -str uct ure inte racti on ana lys is usin gthe ALEmeth odrequi resthree addi tiona l com putations besid esthe Lagra ngia nste p.The first one isthe advec tio n men tion ed earl ier.Itcontro ls theflowin g orfluxing ofmateri al sin thetot al ALEdom a in.The secondcalculation isinter facerecon st ruc tion which defin esmulti-mat eri al co-exis te nce inoneeleme nt.The last one isthe coup ling betw eenLagran gian cleme ntsandALEpart s (fluid-s truct ure in thisthesis). Setupofadvec tio nand inter fac e recons truct io nis very sta ndar dandstra ightfor war d in the ALE sim ulations,while couplingreq uires user's de fin edinputs.Note thattheclem ent sizeof Lagra ng ian part s sho uld be sim ilar tothat of the ALEpartsforthe ALE algo rithm tofuncti on accura te ly.
Thecoup lingcalcu latio nin the ALEmeth odispen alt ybased and isdem on strat edin Figure 1-2.In the le ftpart ofFig ure 1-2,there isnocoupling forcesince the she ll str ucture(gree n) isnotincontactwith the water(Eu lerian materi alin red ). Once pen et rati on occurs,itismeasur edto compute thecou plin g force as a springsyste m.The
10
springstiffness depends on thematerialproperties of all bodiesinvolved. The penalty factor namedPFAC. a scale fa ctor of scaling the estimatedstiffnessisrequiredfor calculating thecoupling force.This PFAe. whose default value is 0.1. isrecommendedto be redefined bytheuser.Its valuecan be eithera constantorafunction of penetrating depth. Notethat its value isdifferentineachanalysis.Evenin the sameanalysis. if the elementsizeor the geometric model ismodified.its value needstobere-calibrated.Prior toconducting adetailed ALEsimulation.severalexperimentalsimulationsare generally neededtodeterminea proper value.In eachALEsimulation presentedin thisthesis.the PFACisset toavalue so thatthefloatingbody'sneutral buoyancyin the simulation is the sameasthat determinedby a simple hydrostatic calculation basedon its geometry.
However,thefloatingbody stilloscillatesaround theneutralpositionwithverysmall amplitude.It is almost impossibletodeterminethe optimal PFAC value tocompletely eliminatethis smalloscillation. Manyhours were spenton calibratingthePFAC value duringthisresearchtominimizethenoiseitmayintroducetothe solution.
11
(note:MMG=AMMG) ALE material interface
(fromIR)
Fpena'ty- kspring
. dx" .
Moving Lagrangian "/ Penetration shell structure Spring
stretch
Figurc1-2: Coupling inthcALEmet hod
1.3.4Contact Model
Therearctwotypes ofcontac talgo rithms in LS-DY NA.The first one is"on e-w ay contac t".Itonlychecks theuser-specified slave nodesforpen etration of themaster segme nts.Itthe n tran sfe rscompr essionload sbetw eenthe slave nod esand themaster segme nts.When contac t frictionisacti ve.tang enti alload s arealso tran smitt edifrelativ e sliding happ en s.A Coulomb frictionformulationisusedwithanexponentialinterpo lation functio ntotran siti on fromstatic to dynami c friction.Thistransiti onrequires adecay coefficie nt.Itonly workswhenthestatic frictioncoeffi cientislargerthan thedynami c friction coeffic ient. One-way contacts maybe appro priate when themasterpart isrigid.It may also beused for deform abl ebodieswhenthemasterparthas a coarse mesh and the
12
slavepart has a relative lyfine mesh.Othe rcommo napplica tio nsare contactsofbeam-to- surfaceor she ll-e dge -to-s urface .
The othe r typeis the"two-way contac t" .Itfunctions essentially inthe sameway asthe
"one-waycontact".except that thesubro uti neschec king the slaves nod esforpen et rat ion are calleda second timeto chec k themaste rnodesfo r penetra tion throu gh theslave segments.Inotherwords. thetreatm ent is symme tricand thedefin ition of the slave surfaceand master sur faceis arbitrary.This meth od results in highe r com puta tioncost due to the extra subrout inecalls.
Theauto matic -si ng le-s urface -co ntac tis a"two-wa y contact "and is recomme ndedasthe supe rioralgorit hm byDYNA. Thesoftconstraintoption(SOFT) can be added intothe contactstiffnesscalculatio n by the user.When SOFTis setat I. thecontac talgo rithm adoptsthe soft constrai nt fo rmul ation .Itis effectivefor contac tsinvo lv ing dissim ilar mesh sizes and dissim ilarmaterialprope rties. The pinball segme nt based contac t is activa ted by settingSOFT at 2.Itisthe recommende doptio nfortreatin g contac tatshar p corners.Simulatio nsof a ship impactin g an ice bloc kwithroundededgeswerecarriedout to exami ne thei rdiffe rence. Theshipandicehaddram at icall ydiffe ren tma te rial prop erties.Ineachsimulatio n.adiffe rent SOFT option is chose n.Result ant contac t fo rces arecompare dinFigure 1-3. Time histo ries of the contac tforcesusingdiffer ent SOFT optio nsare simi larto eachotherandroughly havethe same peak value .Measuri ng the distance betwee n the shi pand iceindicates thatthe contac tshouldstartsat about1.1
13
seconds.Inallsimulations. DYNA detec tsa contactbeforethebodie s areactually in contact. Thisismarked asthe vertical line(purple)in thefigur e.Howeve r.in thecase where SOFT=2.the cont act occurs muchearlierthan other cases.Figure 1-4 is a sna pshot from the simulation whereSOFT=2.Theship isin redandtheiceblockisin blue.Itshows that theice (blue) is already deform edbeforethegeo metriesare in contact.
This phenomen on alsoexists in the casewhere SOFT=1. but ismuchless seve re.This
"ea rlycontac t" affectstheanalysisof thenomina lcontactarea andhencetheice pressure- area relatio nshi p.Itisdiscussed inChapter3.Theauto matic- single-surface -co ntac tis usedforallsimulations inthis study.Thevalueof SOFT is setat 1inalmos t all simulations.
E
1.4I - - - -I -+ - -- - I - -+ - - - -H - - - - --~1.2I---I~-_,~-+__-_H,_---
~1.0I - - - ,...- -- I - - - -- + - -- \ -l - - - -
~0.8I - - - --+--J---., - - -- + - - -,;\ - - - -
Cl0.6I - - - , _f - -- f -- - I - - - - -- - t - - -t - t - - - - -
0.4I - -- - +- --t-I -- - ---+- - - \ + - - - - -
0.01....-~_~~l---'---~_ ___'_::l2oo.__ __ _ '
1.0
Timc (s) - No SOFTOption
figllrc l-3 :Compa r isono fS OfTO plio ns
Notc:Thevert ica l purplelinemark s thetime instan twhenthe contac tsho uldinit iate.
14
Figure1-4:Contac t ModelwithSO FT=2
1.3.5User DefinedCurv e Function
InDYNA.the *DEF INE_CURVE_FUNCTIONcard defin es acurvewher ethe absc issa istime. and the ordinateis expresse d by a fu nctionofothercurve de fin ition .for ces.
kinem ati calquant ities.intrinsicfunction s.interp olatin gpol yn omi al s. andcom binatio ns ther eo f Forinstan ce.thedispl acem ent curvefu nctio nrepo rts thedispl acem ent (ordina te) over thetime (abs cissa) .The nanexte rna l load can bedefin ed asthedispla cem ent multipliedby a coeffic ie nt.A fu ll list of the *DE FINE_CURVE_FUNCT ION is available in DYNA ' sKeyw ord User'sManu al(2007) .Func tions that giveva luesofz-translationa l displ acem ent (heave).y-rotatio naldisplacem ent (pi tc h).andx-rotationa l displ acem ent (roll)arc used in thisthesis.Detail ed im pleme ntationis addressed inChapter 5.
15
1.3.6PresentationofNumerical Models
Anumericalmodel is constructed in DYNAby enter ing inputsin"cards" . eachof whic h is fora specific purpose.When asimulationispresen ted . only important inputs is selec ted andorga nizedinto thefoll o win gcategories:
• Geome tric model:This catego rygivesthedetailed informa tionon the dimen sion s of the geome tric model. Geometric models can be generated in DYNA or otherCAD program s.Rhinoceros®(McNeel NorthAmer ica) is used inthisthesis for produ cin g geometr ic models .
• Materialmodels:Thissection discussesmater ialtypes and their param eters.
• Elementcho ices:This categor ypresent s choi cesofeleme nt types (so lids.
shells.ctc.)aswellas eleme nt parame ters suchas theshellthickn ess.
cleme nt formulation s. ambie nt types.andinteg ratio nalgor ithms.
• Bound ar y conditions and initialconditi ons:In DYNA.the bound ar y conditions defin ethe con fi neme ntonobje ctsand theirprescribedmoti ons.
Theinitialconditions includeinitial veloc ities. initial strains.theinitial hydr ostaticpressuredistr ibu tion . and theinitial volume fracti on . etc.
• Othersettings: The sectio ncovers the loaddefiniti on .the co ntac t model.
dampin gdefin ition .userdefin edfunction s.etc.
• Mesh conve rge nce: The approp riate elementsizeisdetermin ed viathe meshconv ergence study .
• Resultsdecl aration : This partpresent sand discussesthe results.
16
Cha pter 2 Liter a tureReview
Studiesonicebrea kingvesselsarcmostl yconc ern ed with thelevelicc failure mechani sm.
the globa liccresistance on the ship.and themo vem ent of broken icefloes around the hul l. Thesetop ics are not coveredin thisliterat urereview. This literatur ereview exam ines thetop ics of shi pim pactingice floes.ber gybits. and icebergs.The rev iew focu ses on afewareas:originand theorie s in theURI. mech ani sm s of the ship-icccontact.
iccpressure- are arelation ship s.and thefinite eleme nt analysisof ship-icc interacti on.
Specialattentionisdevotedtostudies usingDYNA sinceit istheprimarytoolforthe presentthesis. Eachtopicwillbe discussedin ase pa ratesectio n followedby abrief summa ry.
2.1.UnifiedlACS Polar Rules
Thissection presen ts theoriginof theURIandadiscu ssion ofdesign scena riowhich is impo rtantto the finiteclem en tmodelin ginlate r cha pters.
2.1.1Origi nof the lACSPolarRules
The rearc severa l majorpolar shipclassifica tio ns developedby variouscountries to protecttheir arctic wate rs and interests.They arc:
• Canad ianASPPR/CAC( 9 Classes)
• RussianMRS/N SR(9Classes. 4Icebreaker)
• Finnish/Swedish(Baltic) (5 Classes)
• ABS(USCG) (5Polar Classes .5Balti c Classes) 17
• DNV (3Icebr eake r. 3Polar. 5Balt ic Classes)
• LR(5Polar. 5Baltic Classes)
A "class"refe rsto the iceclass assigned to a ship by aclassificati on society.Eachice classwill haveits own requ irem ent sregard ing hull thickn ess. structura lscantlings.
rudders. prop ellers.mechani cal systems.and heat ing systems.
In recentyea rs.theincreasin gly globa lizedind ustry hasdem and ed aharm oni zed setof classificatio nsfor shipsoperating in the Arcticwaters(see Fig ure2- 1).In2006. lACS released a setof Unified Requir ementforPolar ClassShips(URI) to com pleme nt the Guide linesfor ShipsOpera tinginArctic Ice Covered Waterspublishedby theIMO.The IMO class ific atio ns provid e a frame wo rk forthedesign andoperationofpolarshipsand thelACS givesspecific requir em ent sonstructuresand machin ery.Table2- 1 listsa genera l descripti on of lACS polar classes.Back groundtheor ies ofthe URIcan befound in Daley (1999.2000.2002) . Kend rick etal.(2000a.2000b.2009).
18
Figure 2-1:Map of the ArcticIcc-Cov er edWater DefinedbyIMO
19
Polar Class IceDescription (basedon WMO Sea ice Nomenclature) PCI Year-round operation inall Polarwaters
PC 2 Year-round operation in moderatemulti-year ice conditions Year-roundoperation insecond-yearicewhich may include multi-year PC 3
ice inclusions
Year-roundoperationin thickfirst-yearice which mayinclude old ice PC4
inclusions
Year-round operationin medium first-year ice which mayinclude old PC5
ice inclusions
Summer/autumnoperation in mediumfirst-yearice which mayinclude PC6
old ice inclusions
Summer/autumnoperation inthin first-year ice which mayinclude old PC 7
ice inclusions
2.1.2Load DesignScenario
Theenergy method (Popovetal..1967)solves themaximum ship-icecontact forceby equatingthe normalkinetic energywith the ice crushingenergy.Afurtherdeveloped version usingtheprocesspressure-areaice crushing modelcanbe foundin Daley (1999.
2000.200I.2002). andKendricket.al,(2000b).andis adopted in theURI.The balance of effectivekineticenergyKEeand theice crushingenergyIEis expressedas (Daley.
1999.and Kendrick et.al,2000b):
20
where
KEz=IE Eq ua t lon z-I
Eq uatiol12-2
WhereVnisthenorm al veloc ityandMeis theeffective mass and is give nas:
M=-M
e Co Eq ua tion z-J
whe reCoisthemassredu ction coefficie nt. Itsdetailedderivation can befound in Popo v etal.(1967). Itwill bediscussedinSection 5.3.
Thisappro ae hrationa lly linkstheiceload tothedesign scenarioofanang ulariceedge (theedge of afloe ora channel)glanc ing the sho ulde rof thebow.Theshi p is assumed to surgeforwar dat thedesi gn spee d. hit and penet ratetheice.and thenrebound away.The ice crushingforce mustbe sma ller thantheminimumbendin gfo rcecau sin giceflexu ral failure.Class depend ent factorssuchasicethickn ess.ice stre ngth,shipspee d.andthe bo wshape are all includ edin thederi vation.The norm al contac t for ceFnat bo wis give n
{ [
¢
] 1+eX}3+~ex
Z+Zex_ tan (Z ) 1 Z
3 +Z e x
Fll- Posin(If')cos( fJ')Z [zMeVn (3
+
2ex] Eq ua tio n z-uwhere¢.fJ'arethe icewedgeang le and norm alhullframeangle resp ecti vel y.ThePoand exarefrom theproc essicepressur e-a rearelat ionship:
Equation z-S
21
wherePisthetotalpressur e.Aisthenom inal contac tarea.Poistheice strengthterm correspo nding tothe pressureon1m2no min alloadin g area.existhe expo nen tia lterm whichvariesoverdifferentprocesspressur e-area relationships.In the URI.exis spec ified as -0.1andPoisclassdepe ndent (see Table2-2).The irvaluesare care fu llychose n to ens urethat resul tinglocalloads are compatiblewit h boththeWestern and Russian approac hes.The pressur e-area relationship in the URI is give ninEq uatio n2-6 .The concep tofpressure-a reacurveis explained inthe next sectio n.
Eq ua tio n 2-6
Table2-2:Ice St r en gt h Term sin the UR I
Iceloads on non- bow areas(bow -inter med iate.mid. stern.and bott om ) areconve rted fromthe load onthebowbymultipl ying em pirica larea factors.The designload is considered as theaveragepressur e overa rectang ular load patch.Itis statica llyapplied to the shipstructuretodeterm inetheminimumscantlings.A com plete derivat ion ofthe designloadand framing designis given byDaley (1999.2000).Daley etal.(2009a.
200%. 20I0). and Kend ric k et al.(2000a. 2000b.2009).
22
2.2 ShipIcc Contact and Pressure-Area Curves 2.2.1The Ship-Icc Contact Mechanism
In the earliest iceloadmodel s,the totaleon taet foreewastheprimary conce rn.Itwas usually estimatedwithanassumptio nofuniformpressuredistr ibuti onwithin thecont act region. After 1980 .morefieldtrials and measu rement swith evolving techn olo gies sugges ted thatthepressur esactually varyover man y ordersof magnitud ewithinthe contac tregion.This mech ani sm is idealized inFigure2-2(Daley2004).Extruded rubble, spa lls, internalcrack s, andextrus ioncan be observ ed inall ice-structu recontact scenarios.
Flexu ral crack smaynotbepresentunlessllexuralfailure tak esplace.Direct so lid contact will exert thehighe stpressure on the structureand damage theice. However.the confine ment inthe directcontactregionmakesit capable ofsustaining veryhigh pressur es. Extruded rubble and crushedicewill resultin verylow pressure at the edge of thecontact region .Thiseffectcanbereprese nted using apressure- areaplot wherethe area istheindepend ent variable.Ice strength, thickness, andvelocitygenerallyvary in a much smaller rangethancontactareaand havelessinfluence on pressur e.Nowadays.the pressure-area relationship hasbecom ethemostpopularpresent ationof icepressur edata.
Itis also usedtodeterminebothglobaland localiceloads onstructuresandships. There are twodistin cttypesof pressur e-arearelationship s (Frcderking 1998.1999;Daley1985, 2004.2007 ): theprocesspressure- arearelation ship and the spatial pressure- area relationship.
23
extruded rubble
';~p aIlS - -
lfr-- internal crack
~
~l comminution/
~· ~ xt!!J_sion
I flexural
i crack
Fi/:lIre2-2: Skctchoflcc Contactwitha Strllctllre([)alcy2004)
2.2.2 Spatial Pressure Distribution
Figure2-3explains the spatial pressur edistributi onwhichdescrib estheva riation or local peakpressur e on local areas withinaglob al contac tarea.Atanyinstant timetor an ice co ntactevent.a verysma ll areaAl and its corres po nding peaklocal averagepressu rePI can beplott ed asthepoint(AI'PI)'Alarger areaAz will necessaril yresult ina sma lle r averagepressu repz.So another point(Az,Pz)can belocated on theplot. Simi larly. the averagepressur eP,of thewholecontact area At can be plotted asthe point (At,Pt ). The spatial pressur e-area curve isusefulin dete rm iningthe designload on local structures.It can be expressedas:
Eqllation2-7
whereCvar ies fro m0.5 to5MPAande variesfrom -0.7to-0.25 in most cases.No te that the areadiscu ssedhereis thenominal contactarea.There are twoothe rareaterm s:true areaand measu red area.Their differ enc eisdemonstratedinFig ure2-4.
24
Localdistribution of pressure(ideal) allal lime-(
Spatial PressureArea Plot
1',
A:A: AT
Figu re2-3:Spa t ial Pressu re-Ar eaRclati ouship ([)alc y2004 )
_force
,_ . ..tndenter
__force
f
.&extrusionspalhng __.force, .oaneuorces
:/prossuropanels .J •l..,:
rA
nominal pressure lrue pressure disrnhutinn
measurecpressures Figurc2-4:Nomina l, tr uca nd measur ed areas(Da ley2004)
25
2.2.3ProcessDistribution
Theprocess pressure-areais ofte n usedtodet ermin ethe contac t for ce.Itgivesthe relations hi pofthe averagepressur e and thetotal contac tarea (sec Figure2-5).At the instant timetl•thetota lcontac tareaAl•and its correspo nd ingaveragepressur eP,canbe plotted asthe po int(Al,Pd.Asthe contac tevent progressesto theinstant timetz.the ave ragepressurePzoverthetotalcontac tareaAzcanbeplott ed as the point(Az•Pz).
Sim ilarly.at the ins ta nt timetN'thepo int(AN.PN)can beplotted. In thisthesi s.the discu ssion oftheprocesspressu re-ar ea curveisbased on thenomin alcontac tarea.
atiime
=
l, attime=I: at time=
t-;'\
I ~i~.-l
1',:
II: :1_,I
I[A'
Pro ces s
l~_~
Pressur e AreaPlot /1. •
P: .--.-- A,A· :I..
Figllre2-S:ProcessPressure-AreaRelations h ip(Daley2004)
26
2.2.4 Spa tialvs.Process
Figure2-6showstheconnec tio n bet weenthe processand the spatialpressure-areacurves.
Basic ally.atanyinsta nt time of a contactevent. thereisacom pletespatial pressur e-area curvebutonlyone po int ontheprocess-area curve .Astheimpact event develops. there willbe asetofspatial pressu re-area curves.Joinin gthe endsofthem willgenera tea comp lete processpressu re-area curveofthe contactevent.Theconnec tionof the two ind ica testhatgreatertotal contactarea and total contac tforcestend to yield higher pressures.Thespatialcurveinev itab ly hasatren d of falling.while theprocess curve may riseor fallasthe totalarea increases(Da ley200 4.Frede rking 1998).
Both spatialand process curvesare concep ts in the contextof a sing le ice contac tevent.
Mostexistingpressure-areaana lysesare based onanassemblageof data and measu rement s ofmultiple events therefor e cannotbe sim plycatego rizedas eitherspatial orprocessrelatio nshi ps.Thoserelatio nshipsare genera lly present ed in theform:
Eq ua t io n z-S
wherekis thepressure over1m2load ing area;Aistheloaded area andnis a constant lessthanI(Maste rsonetaI2 007).For examp le. thepressur e-area curve inCSA S47 1and API RP2NisP=S.lA-u,s(derived by Masterso nandFreder king 1993).Afew other relatio nship sinthisformcan be found in Mastersonetal.(2007).The pressur e-a rea curve specif iedbytheURIisaprocessdistribu tion.Itisinthe formof P=PoA-u,!as menti oned earlier(seeEquation2-6andTable2-2)
27
.=CI\'g ll/lA, at time
=
I,A,
Process Pressure Area Plot to gether with corresponding Spatial Pressure AreaPlots
at time
=
t.'\
/
~ P/"
> -'; r : : p/a Area
at time
=
I, 111'."~I, ur l'd I'andprl''''ur\.',P,
j
3,
I p,=CI\'g ll/l.'"
1'.:
: - r
- !
A:I P:=CI\'g ll/l A:
F=P, I,xA ,
j
P" A,I I'.
Figure 2-6: Link betw eenProcess and Sp atiall)istributi on s ([)al ey 2004 )
28
As state dea rlie r. the goalof thisthesisisto inves tigateicc-stre ngthe nedshipsregulated bythe URI.There fore.develop ingan icemateri almodel whose pressur e-area relationshi p comp lieswith the URI has the utmost im por tance.Itisthe corners toneof this studyandis addresse d inCha pter3.
2.3 StudiesusingFinite Element AnalysisPrograms
Thissectio n reviews stud iesofthe ship-iceinterac tio n probl emusin gfinite eleme nt ana lysis.A sub-sec tio n isdedi catedto studies usingLS-DY NA since it istheprimar ytool forthis research.Itincl udesstudies usin g theALEmeth od.Inadd itio n.a few stud ies usin g otherFEAprog ram swill bepresent ed as well.
2.3.1StudiesUsing DYNA
Gagno net al. (200 4) publish ed apaper ona series ofmodeltests of atran sitin gtank er passin gbyfloatin giccfloes. Gagnonetal.(2006)report ed anALE simulatio nof oneof themodel tests.The nume rical solutio nshowe dgoodagreeme ntwiththe physicaltestin termsof swaymoti on.In the same paper , Gagnon proposed a crus ha ble foammaterial modelfor simulatingshi pcolliding withabergybit in DYNA.This inno vativemateri al mod el was validate dagainst data fromactua l measur em ent s.Note that allsimulatio ns in this studyonlyallowe d the ship tomovefo rwa rd and rest rained itinallotherDOf' .
Wangctal. (201Oa)pro posed a studyof iceresistan ce on the Canad ianicebrea ke rTerry Foxin levelice.The ice failureenve lop developed byDer radj i-Aou at (2003)was ado pted
29
and mod ified tomodellevel ice.The fluid dom ain wasmod eledusin gthe ALE meth od.
Theship wasfi xedinallDOrexceptthesurge moti on. Simulations includ ing water.and not incl udi ngwater.werecomparedwithfu ll-sca le measur em en ts.Water was proven im por tant in numeri cal ana lysisofship break inglevel ice.
Wanget al.(2010b)further investi gatedmodel ingfluidstructuralinterac tion using DYNA . A wavemak er was simulated usin gthe ALEmeth od.The wavelen gth andwave heigh t fromthe numerical simulatio nwere inreasonab leagree me ntwiththeexperime nta l results .AnALE simulationofathinicepiecefloat ing in water was alsoperforme d.and showedgood resul ts ofthebuoyan cy forceon the ice anditsvertical displacem ent. Late r in thepaper.simu lationsofthe Terry Foxmo vingthrou gh watercoveredbyicepieces wereconductedandgloba l icefor ces on the shipwererecorded. Inthestudy.theshipwas modeled as a rigidbodyandfreetomo ve only in the surgediree tion.Icepieces were treatedas rigid bod ies with uniform sha peandsize.Meshdepend ency wasnot invest igated.
Extra attentio nwasdevotedtoreviewin gliteratur e onship local structura lrespo nse under iceloadsusing DYNA.Unfort unately,onlya few studieswere found.The first one was theMaster'sthesisbyMyh re (2010)at thc NorwegianUnivers ityof Scienceand Techno logy.Inhisanal ysis of an ice collisio nwitha sectio nof themid-ship structure. the par t of the icethatcould possiblybe affecte d bythe contactwasmodeledusin gtheice modeldevelo ped by Liuetal.(2009). Thisis amaterialmodelbased on the Tsai-W u
30
failurecriterio n.The restof thehalf spherical icewastreated asrigidtosave comput ati on cost. Thiswas a veryefficientapproac h. Liu' sicemodelisdiscu ssedin the nextsub- section.
Theother two studies usin gDYNAwere verysimi lar to eachother.Lee etal.(2007) exploredthe possib ility of globa l20 modelin g of ship-ice interacti onusin gDYNA. The ship-icecontac t forc ewasdetermin ed viaa globa lanalysis.and then a sectio nof LNG sidestructurewas analyzedinalocal FEA.Kimetal.(20 II)foll ow edthe sim ila r approach.They first estima ted theloadby globa lanalysis.andthenappliedit to a sectio n ofa cargo shi p todeterm inethelocal structura lstrength.
2.3.2Studies using other FEA Programs
Kwak etal,(2006)analyzed a sectio nofthebowstructure ofanArctic tank erunderice load s.Icemodels with differ ent elastic modulu s, failurestresses,andyieldstresses were testedinsimulatio nsofcollision betw eentherigidbow and deform abl e ice.Oneice model gavethe contact fo rcethatcompl ies with the URI. Thenthisicemod elwasusedto collidewith theflexibl ebowtoevaluate the shipstruc tura lstre ngth.Water and hyd rod ynam ic effects werenotincluded in theanal ysis. The meth odol ogy ofadj usting ice materialprope rtiesin this study isusefultothepresentwork.
Wang et al.(2008a)evaluated the struct ura linteg rityofan LNG ship underaship-ice collision.They used a combinationofgloba land localfinite elementanalysis modelin g.
31
Theglobalsimu latio ntreated the shi p as elastic- plas ticand ice as crus ha b lefoamwith a mate rial failurecrite rio n.Itestima ted the sh ip-icecontac tforce,contac tarea, materi al de form ation , andmat erial failure.In theloc alfinite eleme ntana lysis model,theiceload was appliedstatica lly to a sectio nofthemid-sh ip str ucture todete rmin ethe critica l load . Th isworkde fin ed a procedure fo r evalua ting hullstruc tureinLNG shi ps under iceload s.
Following this proced ure. Wang ctal. (2008b) invest igated ano the rcargosh ip'sstruct ura l respon seunde rice im pac t. Differ entfromtheir prev iouswork. they ado pte dthe UR I to dete rmi ne the valuesof iceload and loadin g area rathe r than a globa lsimu lation.Theice patchload s fromsixdiffer ent collis ionscena rioswerethen appliedto alocalmod el of the mid-shipto assessits stre ngth.
Liu etal.(2009)prop osed an icemate rialmod elbased on the Tsai-W u failure criter ion.
whichassociatesdamage withplasti c strai n.for ana lyz inga collisio n between a bergy bit anda sectio nofmid-ship struc ture .The pressu re- ar ea curveP= 7.4A-o.7defi ned byISO (2008)wasthe benc hmar kforLiu'sicemod el. Com pare d tothe pressure -a rea relations hipspecifiedin the UR I.Liu'ssolutio noverestima ted pressur e whe n the contac t areawas small,i.e .. a shipim pac tinga sma llicefloe.
2.4Summaryof Literature Review
A few conclusio nscan bedrawn from thelite ratur ereview.There is aneedfo ran ice mat erialmod elthat is show n to com p lywith the UR Ifor ship-icecollis io nana lyses usin g
32
DYNA.Itisnecessar yto verify ifthe crus hab le foammod el (Gagno netal.2006)could be usedinthisstudy.Ifnot ,developin g a suita ble icemodelwillbe apriorit y.
Existing finit e eleme ntsolutio nsfor ship-icecollision probl em s canbe catego rizedas foll ows:
• Mode lingice im pac tinga sectio nofthe shipstruct ure: Kwak etal.(2006).
andMyhre(2010).
• Modelin gthelocal shipstructure under staticiceloads ratherthan simulatingtheimpac t:Wangetal.(2008b)
• Usinga sim plifiedgloba lship-icecollision mod eltodete rmin ethe contac t forceand then applyi ngthat fo rce statica llytothe shipstructureina separa teana lysisofthelocal shipstructure:Wangetal.(200 8a).Lee etal.
(2007). Kimetal.(2011).
• Ana lyzi ngship-icecontac t us ing globa l mod el ing where hyd rod ynami csis includ edbutthe shipstructura lresponseisnot:Wang etal.(2010a)and Wangetal.(20 10b).
Eachoftheirmeth od shas pros andcons.Thefirst typedoesnotinclud e globa l moti on or hyd rodynam icfor ces.Thesecondone doesnot considergloba l mot ion.hyd rod ynam ic forces.ice strength.or thedynami c effec toficeload.How ever. bothof the mare very quicksolut ions.The third one ismore compre hensive thanthepreviou stwo but the procedu reis complicated.Cond uct ingtwoseparateana lysescould be timeconsuming.
33
Although thelast category isthe onlyone thatmodelshydrodynamic effects, it is only concernedwith the globalcontactand motion.Itmaynotbe a cost-effec tivesolutiononce theshipstructural responseisinvolved. An ideal solution would combine hydrodynamic forces,the global motions of the shipand ice,the contact force,icefailure. and theship structuralresponseinoneefticientanalysis.This isthe goalof the present thesis.
34
Figure 3-1: Geometric Modelsof theShip and IceinRhinocero s®
Figure3-2: the IceBlock with RoundedEdges
36
Figllre3-3:Sh ip How
Figllr e3-4:Sep ar ationhetwccnthc ShipalldIcc (Top View)
37
Table3-I : C eomet ry ofthe Ship andlee
Ship Ice OverallLeng th 66.0m 8.494m Leng thatWate rline 61.8m 8.494m
Beam 12.0m 15.154m
Ile igh t 7.20m 4.00m
Dra ft 4.80m 3.510m
Corner Rad ius N/A 1.0m
Wate rlineAng lec 300 N/A
SheerAng ley 600 N/A
FrameAng le~ 450 N/A
WaterplaneCoeffic ient 0.75 1.0 Block Coefficient 0.79 1.0
3.1.2Materhll Models
Theshipis always treated as a rig id bod y for the workcovered in this cha pter . Itsmaterial prop erties arelisted inTable3-2.
Table3-2:Materiall' rope rti esofth e Sh ipM odel
Card ID MAT_R IG ID(MA'r_020)
Materia lType Den sit y IYoun g's ModulusIPoi sson 'sRatio
Rigid 7850kg/ m31207GPa
1
0.3
38
Eachsimulatio ninvestiga tedadifferenticemateri almodel.Thosethat showed thebest result s are presentedinthis chapter. An icemodelbased on the crushablefoam materialis used in themesh conve rgencestudy.Itsparameters and the stress -stra in relati onship are show n inTable3-3and Figur e 3-5. Thoseparametershaveminorinfluence on themesh converge nce.
Table3-3:Mat erialPropertiesof the Ice Model
Card ID MAT_CR USHA LBEJ OAM (MAT_063)
Mate rialType Density
IE IPoisson'sRati oITensileStressCutoff Elastic-Plastic 900 kg / m319 GPaI 0.003
I 800M Pa
Figure 3-5: St ress-VolumctrtcStrainCu rve of the lee Model inConvergenceStudy
39
3.1.3 ElementChoices
Automaticmeshing isusedto createtheshi pandicemeshmod els.Therigidship is meshedusin g shel leleme ntsand theice bloc kismesh ed withsolideleme nts. Inform ation on the eleme ntformulatio nandeleme nt type arelistedin Table3-4.Thefu llyintegra ted formul ation isa very fast algorit hmand it is chose nfor the rigid she lleleme nts.If she ll eleme ntsare used to meshanon-r igidbod y.theBelytschk o-Tsay form ulationwill bethe bestchoice.Itis therecomme ndedoptio n formost structura lanalys is(Qui nton.2009). Thedefaultsolidclemen t(Ipoint solid) is chose n forice for itssuper io rrobustness. Otherfully- integratedsolidsare less sta blewhenthe defo rmat ionislargebecause oneof theintegrationpointsmayhave anegative jacobia nwhile the who leeleme nt maint ain s a positivevolume.Theconve rge ncestudy that determi nesthe proper eleme ntsize is presentedin Section3.1.6.
Tablc3-4:Eleme ntCho ices forShipand Icc Part Eleme ntType FormulationOption Ambie ntType Ship Shel l 16 (Fully Integrated ) N/A
Ice Solid I(Defa ult) 0
3.1.4 Boundarylind InitialCond itions
Ineachsimulatio n. two faces of theiceblock are fixed(sec Figure3-6).Theshipisfree tomo ve inthe longitud inaldirection . butconfi ned inallother5Oa F.Itstarts mo vin g forward towardstheicc atan initial speedof 3m/s .Aftermovin g for about4.02m. the shi p bo w beginsim pacting the iceblock at the roundedcorne r.Theice isthen grad ua lly
40
crushedand deforming asthe collision proceeds. At the same time.the shipslows down until the endofthesim ulation.
Figllre3-6:Boundary Co ndi tio non the Infinite Ice
3.1.5 Other Inputs
Therecommendedautomatic-s ingle-surface -co ntact isused . Asdiscussed inSection 1.3.4 . its SOFT optionis setat1sincethe mater ialpropert ies of the shipand ice are dramati call ydifferen t. There isno gravityor anyotherexterna l load.Nodamp ing is adde d tothe system.
3.1.6 Mesh ConvergenceSt udy
Ameshcon version study is cond ucted by comparing the time histories ofthe contact for ces. Figure3-7 shows that conve rgence is reachedwhen the clementsize is smaller
41
than 0.35m.Forsubse q uentsimulatio ns, 0.24m isthen cons idere d as anappro pria te cleme ntsize for subse que ntsimulatio ns.
Z6.0
~
5.0~4.0
~3.0 U2.0
f---~~ /
Timc(s) Elem entSize:
Figurc3-7:Mcsh Collvcrgcllcc
3.1.7NominalContact Area
Aftereachsimulatio n is co mpleted. thetimehistor y ofthecont actfor ceisdirectl y obtai nedfromthesimulation'soutputs.Thetime histo ry ofthe nom inal contac tarea couldnotbe accuratelygiven byDYNAduetothe coarsemesh, soit isderi vedusingthe CADprogram Rhinoce ros®. The procedur ecanbeillustratedinFig ure3-8.After the ship ismoved forward fo r adistan cexfrom itsinitialpositi onA tothenewlocationB, an inte rsect ion ofthe shipand icc can becreated asthe yellow curve.Thesurfaceareaofthe yellowcurveis conside redas the nomin al contactarea corres po nd ing tothe surge distance x .
42
Figure3-8: Intersecti onof theShip and Icc
Valuesofthe shipsurge distances andcorres pon di ng nomin al contac tareasare listedin Table3-5 . The rel ati on shipbetweenxandAn omi n al ,as obta ined bytheline ofbesttit, is show n inEquation3- 1.Itis app lica ble fo r allsim ulatio ns present edin this chapte r. In eachsim ulat ion. the time hist ory ofthe shipsurge distan ceis provide d byDYN A.Itis then subst ituted into Equat ion3- 1 to yie ld thetimehistor y ofthenomin al contac tareafor that sim ulation.The processpressur e- ar ea curveofthe ice isthen genera te d by ana lyz ing the timehisto ryofthe contac tforce and thetimehisto ry ofthenom inal contac tarea
43
Table3-5:Surge Distan cexandNomi na lContac tAreaAllom/lIl1l
x(m) Anominal x(m) Anominal
4.530 0.000 4.999 1.045 4.549 0.042 5.000 1.048 4.569 0.089 5.500 2.200 4.609 0.182 6.000 3.541 4.649 0.273 6.500 5.101 4.709 0.408 7.000 6.881 4.749 0.496 7.500 8.882 4.789 0.583 8.000 11.103 4.849 0.715 8.500 13.545 4.889 0.802 9.000 16.207 4.939 0.913 9.500 19.089 4.969 0.979 10.000 22.193
{
0, X<4.53
Anominal
=
2.2207x -10.054, 4.53<X<5 0.0016x3+OA014x2- 2.0801x+1.21 7 1, x2:5Eq uat ionJvl
Recallthe discussio n inSection 1.3.4 andFigure1-4. whichshowthatDYNA detectsa contac tbefore thegeometriesare actuallyin contact.Thisphenome non means that the nomina lcontact area derivedin Rhinoceros®isdifferentfromthat inDYNA. Although setting SOFT=1 helps minimizethisdiscrepancy.itstill makesthe analysisof the
44
pressure -a rearelatio ns hip less accura te,especia llywhe n the contactarea is sma ll.
The refo re,ana lys is in this chapterdoes not inc ludedatafromcontac tswherethe nom inal contactareais lesstha nOAm2.
3.2Icc Material ModelsBasedon theCrushable Foam Material
Thissectionpresen tsthe resultsof modelingiceusing thecrus hab le fo ammaterialmodel available inDYNA.Differentmode lsaredevelope d by changingthe param et ers in the crushab lefoam mode l.More than 30model s wereevaluatedandseveralofthemhave showedthe desir ed results . In addi tion,aprev io usmodel (Gagno netal.2006) is introducedinthissectio n.
3.2.1Gagnon' s Crushable Foam Icc Model
Gagnon'sice model(Gagnonetal.2006) wasin itiall ydeve lo ped toreprodu cethe spatia l pressu re-ar ea curve withahigh centra lpeak load.It isnecessary to deter mi neifit titsthe purposesof thisstudy.Gagno n's mod elis basedon the crus ha blefoammaterial model where the deformationis mostly unrecoverable.Its key parame tersare listedinTable 3-6.
Thesma llPoisson'sratio limitsthematerial'sdefo rmation in directi on s other thanthe load ing directio n.Therelations hipof stress andvolume tricstra inis show ninTable3-6 andFigure3-9. Notethat inthecrus hab lefoammaterialmodel,thematerial'sbeh av ior followsthestress-stra inrelatio ns hipratherthan the Young's modulu s.
45
Table3-6: Mal eri al I'ro pe rliesofGag no n'sIceMod el Card ID MAT_CR USHALB EJ OAM (MAT_063) Density Young' sModulusIPo isson'sRatioITen sile StressCutoff 900kgjm3 9GPa
1
0.003
1
8MPa
Table3-7: Stress-Slrain Relali onshipinGa gnon'sIceModel
Figure3-9: Sl ress-VolumetricStra in Re lalions hip inGagnon'sIceModel
46
Aprocess pressure -areacurveofGagnon's icemod elis show ninFigure3- 10.Thiscurve doesnotfi tthe formofP = PoA-O.1
•In later sections theprop erti es are mod ifiedto de velo pmodel s with thedes iredpressure-area relatio nship to serve thepurposes of this study.
~8f - - - -f - - - --
~
I'
f - - - -- r - - - -Nomina lConta ct Area (m"2)
Figure3-10: ProcessPressur e-Area Curve of Gagnon 'sCrusa ble Foam IceModel
3.2.2Icc ModelA
The ten sile stresscuto ff(TSC) valueinGagnon'smodelis8M Pa.Icemodels with significa ntly diff erent TSC valueswere tried and they all displ ayedunsuit abl ebehavior.
TheYoung'sMod ulus has amino r impac ton thepressu re-area curveaslon g asits value isinthe real istic range.The stress-volumet ricstrai n relat ion sh ip isthe dominantfactor in the formofthepressu re-area curve.Materialdens ity and Poisson' s ratioarenot alte red.
47
Table3-9 andFigure3- 11showstheredefin ed stress -strain relationsh ipin themodifi ed crushablefoamicemodel- A. Other parameters are listedin Tabl e3-8.
Table 3-8: Material Propertiesof lee ModelA CardII) MAT_CR USII ALBEJOAM (MAT_063) Density Young' sModulusIPoisson' sRatioITensileStress Cutoff 900kg/m3 5GPa
1
0.003 18.00 M Pa
Ta ble 3-9:St ress-Volumetric StrainRelationshipin Icc ModelA
Figure 3-11:St ress-VolumetricStr a inCu rve in IccModelA 48
