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The Effects of Stochastic Characteristics of Materials on the Reliability of a Composite Ship Hull

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The Effects of Stochastic Characteristics of Materials on the Reliability of a Composite Ship Hull

    The Effects of Stochastic Characteristics of

    Materials on the Reliability of a

    Composite Ship Hull

    J.MarineSci.App1.r201l11O:1-6

    DOI:10.1007/sl1804.0l11034.9

    TheEffectsofStochasticCharacteristicsofMaterials

    ontheReliabilityofaCompositeShipHull

    WeiZhang,WenyongTang,NianzhongChenandShengkunZhang

    StateKeyLaboratoryofOceanEngineering,ShanghaiJiao

    University,Shanghai200240,China

    Abstract:Theeffectsofstochasticcharacteristicsofmaterialsonthereliabilityofshiphullsmadeof

    compositematerialsunderlongitudinalmomentwereextensivelystudiedusingreliabilityandsensitivity

    calculationsofacompositeshiphullwhichwassagging.Thereliabilityindicesandfailureprobabilitiesofthe

    shipinthreekindsoffailuremodes(buckling,materialfailure,andultimatecollapse)werecalculatedbythe

    surfaceresponsemethodandJCmethod.Theimportancefactorsofrandomvariablesinstochasticmodels.

    suchasthemodelerrorsinpredictingtheultimatelongitudinalstrengthofshipandthelongitudinalbending

    momentthattheshipwithstands,aswellasthestochasticcharacteristicsofmaterialsinthemodelsused.were

    calculated.Then,theeffectsoftheserandomvariables,includingthestochasticcharacteristicsofmaterialson

thereliabilityindexandthefailureprobabilityofshipswhichweresagging,werediscussedwi

    ththeir

    importancefactors.Theresultsshowthattheeffectsofstochasticcharacteristicsofmaterialso

    nthereliability

    ofshiphullsmadeofcompositematerialsshouldbeconsideredduringthereliabilityassessme

    ntofcomposite

    ships.Finally,someconclusionsandrecommendationsweregivenforhigh

    speedshipdesignandsafety

    assessment.

    Keywords:compositematerial;reliabilityanalysis;response

    surfacemethod;sensitivityanalysis

    ArticleID:1671-9433f2011)01000106

    1IntrOductiOn

    Compositematerialshavebeenwidelyusedinthemodem shipbuildingindustry,especiallyinthefieldofhighspeed craftduetotheirhighspecificstrength,highspecific stiffness,lightweight,corrosionresistance,design flexibilityandmanyotheradvantages.Underextemal impactloadings,compositeshiphulls'longitudinalultimate strengthwillreduce.whichmayleadtothefinalfailureof theentireship.Withtheincreaseofthesizesofshiphulls madeofcompositematerials,theresearchesonlongitudinal ultimatestrengthandthesafetyassessmentoflongitudinal ultimatestrengthbecomemoreandmoreimportant.

    Mansoureta1.(1997)hadusedtheprimary,secondary, tertiaryandfatigue1imitstatefortheanalysisofthesurface effectonshipstructuralreliabilitybasedontheinitiallimit stateandtheinitialyieldlimitstatereductionoftheinitia1 moment'slimitstate.Kameta1.f1993)useda

    phenomenologicalfailurecriteriontoestablishthelimitstate

equationoflaminatedcompositeplatesforthefirstply

    failurereliabilityassessment.GuedesSoaresf1997) discussedthereliabilityanalysisofthecompositeplate. IbnabdeljalilandCurtinf1997)consideredthestrengthof compositesandtheirsizedependencewith1oca1lpad sharingfLLS)usingaMonteCadosimulationmodelbased onthe3-DlatticeGreen'sfunctiontechnique.Ananalytical Receiveddate:2O10.10.15.

    CorrespondingauthorEmail:wytang@sjtu.edu.cn HarbinEngineeringUniversityandSpringer-VerlagBerlinHeidelberg2011

    formulationwasderivedanddemonstrated,mappingthe reliabilityofasmallcompositestructureunderLLStoa largestructurewhosestrengthwasgovernedbyitsweakest bundleoffibers.Lineta1.f1998)usedstochasticfinite elementanalysisandsecond.orderperturbIationtechniques toderivethestrengthoflaminateunderin.planeloadsbased onfirst.plyfailureusingtheTsaiWucriterionandbuckling.

    SutherlandandGuedesSparesf1997),Yushanovand Bogdanovichf19981reviewedthestateoftheartin reliabili?predictionmethodsforcompositestructureand proposedananalyticreliabilitypredictionmethodologyand exampleapplicationforlaminatesunderinplanelpads.but

    theyhadnotresearchedthereliabilityofshiphullsmadeof compositematerials.Zhueta1.f19961haddonea

    preliminarystudyonthereliabilityofshiphul1madeof compositematerialsbasedonthesimplebeamtheoryof shiphul1.Suneta1.(2002)hadcombinedtheresponse surfacemethodandJCmethodtoreliabilityanalysisand sensitivityanalysisforcompositeshiphullgirder.However. currentresearchonreliabilityanalysisforcompositeship

    hullsrarelyconsidersmateria1stochastics.Actually,dueto therandomnessofthecompositematerials'mechanical properties.itisnecessarytoconsiderthestochastic characteristicsofcompositematerialsduringthereliability assessmentofcompositeships.

    Theeffe:ctsofthestochasticcharacteristicsofmaterialsonthe reliabilityofshiphullsmadeofcompositematerialsunder longitudinalmomentwereextensivelystudiedbyreliability andsensitivitycalculationofashiphullsmadeofcomposite materialsundersagging.Thereliabilityindicesandfailure 2WeiZhang,elalTheEffectsofStochasticCharacteristicsoJ'MaterialsoHtheReliabilityofa

    CompositeShipHull

    probat)ilitiesoftheshipunderthreekindsoffailuremodes: buckling.materia1failureandultimatecollapsewere calculatedusingresponsesurfacemethodandJCmethod. Then.theefrectsofvariabilityofstochasticcharacteristicsof materialsonthereliabilityindexandfailureprobabilityof shipundersaggingwerediscussedwiththeirimportance factors.Theresultsshowedthattheeffectsofstochastic characteristicsofmaterialsonthereliabilityofshiphulls madeofcompositematerialsshouldbeconsideredduringthe reliabilityassessmentofcompositeships.

    2Bucklinglongitudinalstrengthofcomposite

    shiphullsundersaggingmoments

    whentheshiphullisundersaggingmoment.thedeckis undercompressionandtheshipbottomisundertension. Whentheshiphul1isunderhoggingmoment.thedeckis undertensionandtheshipbottomisundercompression. Generallythethicknessofthedeckofthecompositeshipis farlessthanthebottom,andthecompressivestrengthof

    compositematerialplateissmallerthanthetensilestrength. theultimatestrengthfailureofthecompositeshipgenerally occursundersaggingmoments.Thusonlythereliabilityof shiphullsmadeofcompositematerialsunder1ongitudinal saggingmomentisconsideredinthispaper.

    ThecompositeshiphullisassumedtobeanEulerNavier

    beam.Thetransversecrosssectionsofshipremainplane

    whenit'ssubjectedtobendingmomentsandtheeffectof transverserestraintonlongitudinalstressisnegligible.Thus thecrosssectionofthecriticalsegmentofshiphullremains planeduetohullgirderflexureandthenormalstainvaries linearlyacrosstheperpendiculardirectionofthe cross.section.Thatis

    f=z1z=Z-Z~

    (1)

    whereZNAistheinstantaneouselasticneutralaxisofthe crosssection,zthedistancefromZNA,Zthevertical coordinateofcrosssection,andthecurvatureof

    crosssection.whichareshowninFig.1.

    0,,

    Fig.1Thecrosssectionofship

    Thebucklingstrengthoftheshiphullundersagging momentsiscalculatedasfollows:

    Thefirststepistocalculatethebucklingstrainofeach stiffenedpanelinthecriticalsegmentofthehullusingthe progressivefailuremethod,thesevaluesarethencompared andtheminimumisfoundout.

    ) Emin=(

    whereNpstandsfortotalnumberofstiffenedpanelsinthe

crosssection.

    Then,basedonEq.(1),thebucklingstrengthoftheshiphull isdefinedas

    Mu=D(p

    whereDrepresentstheflexuralstiffnessofthehull whereEiistheYoung'smodulusoftheithelement,Athe

    sectionarea,ZftheverticalcoordinateofelementIand cross

    themomentofinertiaofthelement.

    3Limitstatefunctionandresponsesurface

    functionofcompositeshiphullsunder

    saggingmoments

    Thelimitstatefunctionofshiphullsmadeofcomposite materialsundersaggingmomentsisdefinedasfollows: Z(El,G12,Gz,G3,,)一叩Mg

    whereat.isthelongitudinalbucklingstrengthoftheship hull,whichisafunctionofE1,Gl2,G23,Gl3and;r/isthe

    modeluncertaintyofthelongitudinalstrengthofshiphull; rigisthemodeluncertainty;isthedesignsagging moment;andEJ,GI2,3,Gl3arestochasticcharacteristics ofmaterials,whichareshowninTable1.

    Apolynomialtyperesponsesurfacefunctionincluding squaredtermsisusedtoreplacetheoriginalimplicitlimit statefunction:

    +?c

    whereaisaregressioncoefficientandb.andcirepresentthe regressioncoefficientscorrespondingtoithvariablex Thereliabilityindicesandfailureprobabilitiesoftheship arecalculatedbyresponsesurfacemethodandJCmethod. Theprecisionofthismethodcanmeetthecomputational requirements.

,

    +

    2

    Z

    4

    ,L

    ?

    =

    D

    ^?

    +

    

    ll

    g

    JournalofMarineScienceandApplication(2011)10:1-6 Table1ParametersofmaterialandcharacteristicsOf randomvariables

    4Procedureofreliabilityanalysisofcomposite shiphullsundersaggingmoments

    1)Assumethattherandomparametersoftheinitialiteration

    pointcanbeexpressedas:X=(","

    (generallytakingthemeanofthesevariables); 2)Get2n+lsamplingpoints

    functiong(,,,...,)andg(xl",

    wherefisarandomnumber.

    Of

    ...,

    gfromthe

    ?l,...,"),

    3)Substitutethe2n+lsamplingpointsintoEq.(6)andthe

    polynomiallimitstatefunctionwhichisconstructedbythe linearregressionmethod.Updatethelimitstatefunctionby aniterativeprocedure.

    GetthecheckingpointKandreliabilityindexby theJCmethod,wheresuperscriptKrepresentstheKthstep iterative.

    5)Comparetheindex.fl'-fl1withtheaccuracy gives.IfI'一』<,thenthefinalsafetyindex

    andthefailureprobabilitycanbeobtainedby=(f1),

    where(.)representsthestandardnormalcumulative distributi.nfunction;if'-flI>,then

    '()+()('i,returnto2).

    5Reliabilityanalysisofanallcomposite

    hullundersaggingmoments

    ship

    with

    considerationofthestochastic

    characteristicsofthematerial

    5.1Bucklinglongitudinalstrengthofanall-composite shiphullundersaggingmoments

    Theshiphul1iSalongitudinallyframedstructure.Halfof themidshipcrosssectioniSshowninFig.2.Themoulded breadthiS9mandthemouldeddepthiS6m.The

    thicknessesoftheplatesare4.1mmforthedeckandsides and7.2mmforthebilge.Thegeometriesofthestifiened compositepanelsatthemidshipcrosssectionareshownin Fig.3.Thedimensionsofthestiffenedpanelsinthedeck, sides,andbilgeareshowninTable2.Themateria1 propertiesareshowninTable3.

    Fig.2Crossmid-sectionofship(unit:mm)

    '—————————一D—————————————' +

    ]://

    Il//+l:——_J{1LVV——J,

    ,

    4+I

    Fig.3Geometryofhatstiffenedpanels 4WeiZhang,eta1.TheEffectsofStochasticCharacteristicsofMaterialsontheReliabilityofa

    CompositeshipHull

    Table2Sizeofhat-stiffenedpanelsmill

    Table3Parametersofmaterial ParametersandsymbolValue Elasticmodulusin1principal materialdirectionEI/(N'm Elasticmodulusin2principal materialdirectionEJ(N'm) Poisson'sratiov

    Shearmodulusin2-3principal materialplaneG23/(N'm) Shearmodulusin1-3principal materialplaneGI3/(N.m) Shearmodulusin1-2principaI materialplaneGI2/(Nm1

    Tensilestrengthin1principal materialdirection(N?m0) Compressivestrengthin1principal materia1directionXc/(N?m, Tensilestrengthin2principal materialdirectiony/(N?m1

    Compressivestrengthin2principal

materialdirectionyr/(N?m)

    Shearstrengthin2-3principal

    materialplaneR/(N?m,

    Shearstrengthin13principal

    materialplaneS/(N?m,

    Shearstrengthin12principal

    materia1plane7"/fN?m-2)

    15.7x10

    14.8×10

    0.127

    3.4×10

    3.4×10

    3.4×10

    2.38×10

    2.04×10

    2.1×10

    2.24×10

    2-35×10

    2-35×10

    1.04×10

    Thebucklinglongitudinalstrengthoftheallcompositeship

    hullundersaggingmomentsMuisobtainedtobe 3.4551xl07N.m.

    5.2Sensitivityanalysis

    Sensitivityanalysisisanimportantpartofstructural reliabilityassessment.0nebenefitistoidentifythe parametersthathavethemostimportanteffectonthe estimatedreliabilityorsafetyindex.theotherbenefitisto identif3,thoseparametersthatcanbetakenasfixedvalues andneednottobeconsideredasrandomvariablesin

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