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Doctoral Theses at NTNU, 2008-149Paul E. ThomassenMethods for Dynamic ResponseAnalysis and Fatigue Life Estimationof Floating Fish CagesISBN 978-82-471-9063-0 (printed ver.)ISBN 978-82-471-9077-7 (electronic ver.)ISSN 1503-8181NTNUNorwegian University ofScience and TechnologyThesis for the degree ofphilosophiae doctorFaculty of Engineering Science and TechnologyDepartment of Marine TechnologyTheses at NTNU, 2008-149Paul E. ThomassenPaul E. ThomassenMethods for Dynamic ResponseAnalysis and Fatigue LifeEstimation of Floating Fish CagesThesis for the degree of philosophiae doctorTrondheim, May 2008Norwegian University ofScience and TechnologyFaculty of Engineering Science and TechnologyDepartment of Marine TechnologyNTNUNorwegian University of Science and TechnologyThesis for the degree of philosophiae doctorFaculty of Engineering Science and TechnologyDepartment of Marine TechnologyPaul E. ThomassenISBN 978-82-471-9063-0 (printed ver.)ISBN 978-82-471-9077-7 (electronic ver.)ISSN 1503-8181Theses at NTNU, 2008-149Printed by Tapir UttrykkABSTRACTThepresentthesisis aneorttointroducestate-of-the artmethodsforanalysisof marinestructuresinrelationtofatiguedesignofoatingshcagesmadeofsteel whentheyareexposedtowaveloading.Structuralfatigueproblemshavebeenidentiedasalikelyfrequentcauseforthecol-lapseofoatingshfarmsmadeofsteel bypreviousauthors. Theprincipal objectiveofthisthesisistoimprovethecapabilitiesoffatigueanalysisofoatingshfarmsexposedtowavesthroughthreesteps:Development of ahydrodynamic andstructural model appropriate for structuralanalysiswithinanengineeringcontext.Development of a prototype software tool based onthe Finite Element Method(FEM).Toperformaparameterstudyemployingthedevelopedtool.AllthepresentedanalysisresultsarerelatedtoaBaseCaseStructure(BCS).Thisisasimpliedoatingshfarmconsistingofonlyonecage. Thecageis30 mby30 mandismadeofsteelpipeswith1 mdiameter. Eachcornerhasahorizontal,linearmooringineach perpendiculardirection. The netpenis representedas lineardamping horizontallyandvertically.A set of four typical regular waves(TRW) haverst been denedcorrespondingto thewaveclassesgiveninNS9415. Thewaveheightvariesfrom1 mto5.7 mandthewaveperiodfrom2.5 sto6.7 s. TheTRWareappliedforrepresentationof thewaveclimatebased on regular waves. The hydrodynamic load model is a combination of linear potentialtheory and horizontal drag for the oater and horizontal and vertical drag damping for thenetpen. It has been shown that the vertical wave force can be conservatively approximatedas the product of water plane stiness andwave surface elevation: Fvert=kw. Thepotential damping is quite high, typically between 15 and 20%. The total damping level isupto30%horizontallyand40%vertically. Forthenonlinearanalysis, theinstantaneouswaterplanestinessistakenintoaccount.The rigid body natural periods have values between 1.7 s and 2.4 s. The highest exuralnaturalperiodisapproximately0.6 s.Thediscretizationof thestructureisbasedontheFEMandthetimeintegrationisbasedontheNewmark-methodwith=0.25and=0.5, i.e. constantaverageac-celeration. Thismethodisunconditionallystableforalinear system. Linear3Dbeamielementswereusedtomodeltheoaterandlinearspringswereusedtomodelthemoor-ingandthe buoyancy. Inthe nonlinear analysis the buoyancysprings were nonlinear.Thestructuralandaddedmassaswell asthehydrodynamicdampingwerelumped. ThestructuraldampingwasmodeledusingRayleighdamping.Comparisonoflinearandnonlinearanalysisinregularwavesshowsthatthenonlineareectsincreasewithwaveheight. Typically, whenthecrosssectionisfullysubmergedordry in the nonlinear analysis the bending moments about the horizontal axis do not exceedcertainlimitingvalues.ThefatigueanalysisforirregularwaveswerebasedonSNcurves,theMiner-Palmgrenrule, andrainowcounting. ThesoftwarelibraryWAFOwasused. SNcurvesC2andFwerechosentobeusedintheparameterstudy. Further, theparameterstudywasbasedonwaveclassC. ThewavescatterdiagramwasgeneratedfromaWeibull distributionofthemeanwindspeed. AJONSWAPwavespectrumwasusedwithapeakednessfactorof3.3. Allwavesareassumedtobelong-crestedandperpendiculartotheBCS.Thecriticaldetailsareassumedtobelocatedatthetopofthemid-sectionsforbothaperpendicularandaparallel cylinder, i.e. thebendingmomentaboutthehorizontal axisisappliedforcomputationofthestressrange.Fatigueanalysisbasedonregularwavesshowedthattheresultsareverysensitivetothewaveperiod. Regular waves arethereforenot recommendedtobeusedfor fatigueanalysis. ThisrecommendationalsoappliestotheUltimateLimitState.For irregular waves, thenonlinear analysis gaveapproximatelytwicethefatiguelifefound from linear analysis. The dierence between fatigue damage increases with signicantwaveheight. Thisimpliesthatthelineardamagewillbedominatedbyhighersignicantwaveheightsthanforthenonlinearanalysis.Thelowlevel of themaximumstressrangeleadstotheassumptionthatthefatiguelimitstatewill bedecisivefordesign. Additionally, thestressrangeinterval dominatingthefatiguedamagewill beinthedomaingovernedbym=5(lowstressrangeandhighnumberofcycles)inthetwo-slopeSNcurves, i.e. thefatiguedamageisverysensitivetothestressrange.Fitting a two parameter Weibull distribution to short-term and long-term stress rangesshowedthat asimpliedmethodbasedonalong-termWeibull distributioncannot berecommended.iiAcknowledgmentThe PhD-studyresultinginthis dissertationwas supervisedandinspiredbyProfessorBerntJ.Leira,DepartmentofMarineTechnology,NTNU.Iamgratefulforhisguidance,patience, and friendship through the ups and downs of this doctoral journey. I hope we cancontinueourcooperationinthefuture. Myco-supervisorwasAssociateProfessorLudvigKarlsen, Department of Marine Technology. His practical knowledge and understanding oftheNorwegianshfarmingindustryhasbeenmostvaluable. ProfessorOddM.Faltinsenand ProfessorDag Myrhauggave valuable suggestionsregarding the hydrodynamicmodelandthewavemodel,respectively.I want to thank the members of my committee Professor Gregory R. Miller (UniversityofWashington),Dr. DanielN.Karunakaran(Subsea7),andProfessorBjrnarPettersen(NTNU)fortheirparticipationandvaluablecomments.Thesoftwaredevelopedasapartofthisdissertationwasbasedontheniteelementframework developed by Dr. Jae Won Jang and Professor Gregory R. Miller, University ofWashington. Iwanttoexpressmysincereappreciationtothemforsharingtheirwork.Many membersof various branchesof the sh farming industryhave been forthcomingand helpful. In particular, I wantto thank Ketil Roaldsnes (Noomas SertiseringAS) andAlfE.Lnning(BmloConstructionAS).Mymanyvisits tothelibraryfor marinetechnologyat Tyholt have always beenapleasant anduplifting experience due tothe friendlyandhelpful sta. The stahaschanged, but thefriendliness has beenconsistent. I want tothankall thelibrarystamembersoverthelastveyearsforhelpingmeoutandputtingmeinagoodmood.MystudieswerefundedbyascholarshipfromthestrategicprogramMarineandMar-itimeTechnologyatNTNU.AdditionalfundingwereprovidedbytheDepartmentofMa-rineTechnology. Finally,monetary(andmoral)supportwereprovidedatatimewhenitwasmostneededbytheEliogJensEggvinsfondtilfremmeavnorskhavforskningattheInstituteofMarineResearch,Bergen.Theworkwiththisdissertationhasbeenalongjourneyformeandthoseclosesttome. It has mostly been a pleasantone at least looking back. My wife Elin has been mygreatest fan and has made it all possible. She gave birth to Birk, Alvar, and Nora overthecourseofthisworkandtheyhaveallbeenaconstantreminderthatgettingaPhDisnottheonlyimportantthinginlife... ThisdissertationisdedicatedtoElinandourchildren.iiiivNomenclatureLatinsymbolsSymbol DescriptionAiiAddedmassindirectioniAw,buoyWaterplaneareaofmooringbuoyusedinBCSAsteelSteelareaofcrosssection(pipe)usedinBCSAbuoyBuoyancyareaofcrosssection(pipe)usedinBCSAsubSubmergedareaofpipeAwWaterplaneareaaiUndisturbedwaterparticleacc. componentatz= 0inthedir. ia1UndisturbedhorizontaluidparticleaccelerationD OuterdiameterofthepipeusedintheBCSBdistrDistributedbuoyancyofthepipeusedintheBCSBbuoyBuoyancyofmooringbuoyusedintheBCSCDDragcoecientofMorisonsequationCD,yDragcoecientofyarnCMMasscoecientsofMorisonsequationCmDiractionpartofCMCm,eq,iEquivalentaddedmasscoecientindirectioniD Accumulatedfatiguedamage. OrouterdiameterofpipeusedinBCS(i.e. Dpipe)Dsc,1yFatigue damage for 1 year assuming only one wave height/waveperiodcombination(forregularwaves)Dsc,tFatiguedamageforadurationtassumingonlyoneseastateDL0FatiguedamagecorrespondingtoL0DN=1FatiguedamageforonestresscycleDbuoyDiameterofmooringbuoyusedinBCSDpipeOuterdiameterofpipeusedinBCSDyDiameterofyarnDAF DynamicamplicationfactorContinuedonnextpagevSymbol DescriptionDAFmMaximumdynamicamplicationfactord DraftofthepipeusedintheBCSE ModulusofelasticityforsteelF FetchFdiff,iAmplitudeofdiractionforceindirectioniFdrag,aAmplitudeofdragloadFelElasticaxialforcecapacityFmassMassforceFmass,aAmplitudeofmassforceFFK,xFroude-KriloforceinhorizontaldirectionFFK,zFroude-KriloforceinverticaldirectionFprePretensioninginmooringlinesusedintheBCSfyYieldstressforsteelG Shearmodulusforsteelg AccelerationofgravityH WaveheightofregularwaveHmaxMaximumwaveheightofregularwaveHsSignicantwaveheightH1/7Waveheightcorrespondingtomaximumwavesteepnessh Shapeparameterofa2-parameterWeibulldistributionhbuoyHeightofmooringbuoyusedinBCSI 2.momentofinertiaITSt. VenantstorsionconstantIpPolarmomentofinertiaIwWarpingconstantKC Keulegan-CarpenternumberkmoorStinessofmooringlineusedinBCSkmoorStinessofmooringlineusedinBCSatfullsubmergencekwWaterplanestinesskw,maxMaximumwaterplanestinessL FatiguelifeL0DesignfatiguelifeLpipeLengthofpipesusedinBCSLscFatiguelifeassumingonlyoneseastate(irregularwaves)oronewaveheight/waveperiodcombination(regularwaves)lwWaterplanelengthMaMomentamplitudeContinuedonnextpageviSymbol DescriptionMelElasticbendingmomentcapacityMplPlasticbendingmomentcapacityMTElastictorsionalmomentcapacitym NegativeinverseslopeofSNcurvemcageMassofBCS(fourpipes)mdistrDistributedmassofpipeusedinBCSmpipeMassofonepipeusedinBCSN PredictednumberofcyclesfortofailureforstressrangepscPercentageofoccurrenceoftheseastatescpDDynamicpressureq Scaleparame

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