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    论文翻译案例(部分):论文翻译案例(部分)MechanicalResponseofSteelWireWoundReinforcedRubberFlexiblePipeunderInternalPressureAbstract:Steelwirewoundreinforcedflexiblepipeinthisstudymainlyconsistsofmultipleanisotropicsteelwirewoundreinforcementlayersandmultipleisotropicrubberlayers.Basedon3Danisotropicelastictheory,theanalyticsolutionsofstressesandelasticdeformationsofsteelwirewoundreinforcedrubberflexiblepipeunderinternalpressurearepresented.Astheadjacentreinforcementlayerswithwoundanglehavedifferentradii,thesinglereinforcementlayershowstheeffectoftensile-shearcoupling.Moreover,thestaticloadingtestresultsofsteelwirewoundreinforcedrubberflexiblepipeunderinternalpressurearebasicallycoincidedwiththecalculatedvaluesbypresentmethod.KeyWords:steelwirewoundreinforcedrubberflexiblepipe,anisotropicelastictheory,tensile-shearcouplingCLCnumber:O343.8,TB333,TE832Documentcode:A
    IntroductionSteelwirewoundreinforcedflexiblepipeisclassifiedintotwotypes:rubberflexiblepipe,polymericflexiblepipe.Beingsuperiortotraditionalpipeinmanycharacteristicssuchasgoodcorrosionresistance,thermalinsulation,bendingproperties,dynamiccharacteristicsaswellashighspecificstrength,easylayingandquickconnection,steelwirewoundreinforcedrubber
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    flexiblepipe(hereinaftercalledflexiblepipe)hasbeenincreasinglywidelyappliedinthefieldsofpetroleumindustry,constructionmachineryandagriculturalmachinery.Domesticandoverseasscholarshavesuccessivelycarriedoutstudyonmechanicalresponsecharacteristicsandfailuremechanismoffilamentwoundreinforcedpipeundervariousformsofload.Rosenow[1]usedclassicallaminatetheoryforpredictingthestress-strainresponseofthinwalledfiberwoundreinforcedplasticpipeunderinternalpressure.Barton[2]solvedthemechanicalresponseofisotropiccylindricalshellunderuniforminternalpressurebasedonaPapkovich-Neubersolution.Fuetal[3]performedrelevantresearchonthebucklingbehaviorofthepolarandrectilinearlyorthotropicpipeunderuniforminternalorexternalpressuresbyusingtheRayleigh-Ritzmethod.BasedonLekhnitskiisolution,Wild&;Vichers[4]presentedasolvingprocessaboutanisotropiccylindershellundercombinedactionofcentrifugalpressureandaxialload.Xiaetal[5]putforwardtheelasticsolutionofstressandelasticdeformationoffilamentwoundcompositepipeunderinternalpressurebyusing3Danisotropicelastictheory.Chouchaouietal[6,7]andTarnetal[8]deemedthatcompositepipewithmultilayerstructurewaslaminatedofsingleanisotropicplate,andperformedstressanalysisonthecompositepipewithmultilayerstructureundercomplexloadssuchasinternalorexternalpressure,tension,twistandbend.Flexiblepipeconsistsofmultiplereinforcementlayersandmultiplerubberlayers.Theadjacentreinforcementlayerswithwoundangle±φwereusuallyregardedasanorthotropicunity,andthenwereanalyzedbyusinglaminatetheory.Bythisapproach,thedifferenceinradiusoftheadjacentreinforcementlayerswithwoundangle±φwasneglectedbesidestheeffectofrubberlayer(flexwear).BasedonXia[5]analyticsolution,reinforcementlayerbeingasanisotropicmaterialandrubberlayerbeingasisotropicmaterial,mechanicalresponseofflexiblepipeunderinternalpressurewasanalyzedunderthepreconditionofcompatibledeformationbetweenreinforcementlayerandrubberlayerbyusing3Danisotropicelastictheory.1ConstitutiveequationofflexiblepipeFlexiblepipegenerallyconsistsofoilresistanceflexliner(NBRB6240),flexbarrier,flexwear(NBRB6240),
    Receiveddate:2009-06-04Foundationitem:theNationalNaturalScienceFoundationofChina(No.50439010)*E-mail:guzhaozheng@yeah.net
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    two-to-foursteelwirewoundreinforcementlayer(flextensile)andflexshield,asshowninFig.1.Fig.1Schematicofflexiblepipe
    StructuralcylindricalcoordinatesrθzofflexiblepipewasestablishedasshowninFig.2.Theconstitutiveequationofreinforcementlayerasthekthlayerinstructuralcylindricalcoordinatesis
    (1)Fig.2Cylindricalcoordinatesofflexiblepipewhere,,,,andarestresscomponentsofthekthlayer,,,,,andarestraincomponentsofthekthlayer,arestiffnesscoefficientsofthekthlayer,uppercone(k)representsthekthlayer.Rubberlayerusesisotropicmaterial,andtheconstitutiveequationofrubberlayerasthekthlayerinstructuralcylindricalcoordinatesis:(2)withrelation:.2Theoreticanalysis2.1Reliefofpartialrigid-bodydisplacementUndersmalldeformation,localrigid-bodyrotationdisplacementisusuallyneglected,sodisplacementisdeemedtoonlyconsistofrigid-bodytranslationdisplacement,integralrigid-bodyrotationdisplacementanddeformationdisplacement.Inrectangularcoordinates,rigid-bodydisplacementcomponentsareasfollows:,(3)wherearerespectivelyrigid-bodytranslationdisplacementcomponentsalongx-axis,y-axisandz-axis;ωx,ωyandωzarerespectivelyintegralrigid-bodyrotationangledisplacementcomponentsaroundx-axis,y-axisandz-axis.Therelationshipbetweenrigid-bodydisplacementcomponentsincylindricalcoordinatesandthoseinrectangularcoordinatesis:(4)
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    Rigid-bodydisplacementshouldhavenoinfluenceonstrain,butEq.(4)showsthatrigid-bodydisplacementcomponents,ωxandωyinrectangularcoordinatesmakerigid-bodydisplacementcomponentsincylindricalcoordinatesbecomethefunctionsofcoordinateθ.Whendisplacementmethodisadopted,unknownfundamentalquantitieswillbecomethefunctionsofthreeindependentcoordinatesr,θandz,whichwillbringdifficultytothesolutionofdeterminedpartialdifferentialequations.Meanwhile,thestaticproblemofflexiblepipeunderinternalpressuredoesnotrelatetoinertiaforcecausedbyacceleration,andrigid-bodydisplacementonlyhasinfluenceonacceleration.Thenthefollowingfirstlyrelievestherigid-bodydisplacementcomponents,,ωxandωy,thatis,thefollowingdisplacementonlycontainstherigid-bodytranslationdisplacementcomponentalongz-axis,theintegralrigid-bodyrotationangledisplacementcomponentωzaroundz-axisandthedeformationdisplacementthatcausesstrain.2.2DisplacementanalysisDuetoaxialasymmetryofconstitutiveequation,thedeformationdisplacement,stressandstrainofflexiblepipeunderinternalpressurearenotaxiallysymmetric.AsshowninFig.2,isolatorPABCistakenfromarbitrarypointPofflexiblepipe,wherePA,PBandPCrepresentradiallength,circumferentiallengthandaxiallength,respectively.Similarly,thesameisolatoristakenfrompointP?andpointP??,andpointPandpointP?havethesameaxialcoordinatezandradialcoordinater,andpointPandpointP??havethesamecircumferentialcoordinateθandradialcoordinater.Supposeflexiblepipeisinfinite.Thesethreeisolatorsofflexiblepipeunderinternalpressurehavethesamestressdistributionandstraindistribution.Therefore,itisassumedthatthestraincomponentsandstresscomponentsofflexiblepipeunderinternalpressureareareonlythefunctionsofradialcoordinater.Meanwhile,basedonactualdeformationofflexiblepipe,itisassumedthatallthedisplacementcomponentsatarbitrarypointofflexiblepipeareirrelevanttocircumferentialcoordinateθ.Basedontheaboveassumption,andaccordingtogeometricequationof3Delasticproblem,thedisplacementcomponentsatarbitrarypointofflexiblepipeareanalyzedasfollows.(1)Suppose:(5)whereistheundeterminedfunctionofradialcoordinater,sameasbelow.Throughintegration,itcanbeobtainedas,(6)whereistheundeterminedfunctionofradialcoordinater,sameasbelow.(2)Suppose:(7)
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    throughintegration,itcanbeobtained,(8)wheredoesnotcontainintegralconstant,sameasbelow.(3)Suppose:(9)substitutingEq.(8)intoEq.(9),throughintegrationandarrangementitcanbeobtainedas,whereistheundeterminedfunctionofaxialcoordinatez,radialcoordinaterandaxialcoordinatez,sameasbelow.istheundeterminedfunctionof
    Sincetheleftsideoftheaboveformulaisirrelevanttoθ,soitcanbeobtainedas,(10),(11)substitutingEq.(10)intoEq.(8),weget.(12)(4)Suppose:(13)substitutingEqs.(6)and(12)intoEq.(13),itcanbeobtainedas.(14)SincetherightsideofEq.(14)doesnotcontainindependentvariablez,itcanbeknownthatf1(r)shouldbeaconstant.Suppose,whereisaundeterminedconstant,Eqs.(5)and(6)canberewrittenas,(15)
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    .(16)(5)Suppose:(17)substitutingEqs.(12)and(16)intoEq.(17),andthroughintegration,itcanbeobtained,(18)substitutingEq.(18)intoEq.(11),weget.(19)(6)Suppose:,(20)substitutingEqs.(12)and(19)intoEq.(20),itcanbeobtainedas.(21)SincetherightsideofEq.(21)isonlythefunctionofindependentvariabler,soweget,(22)throughintegration,weget,suppose,whereisaundeterminedconstant,itcanbeobtainedas,(23)substitutingEq.(23)intoEq.(19),weget.(24)Throughtheaboveanalysis,fromEqs.(12),(16)and(24),thedisplacementcomponentsatthekthlayerofflexiblepipeunderinternalpressurearedescribedas,(25)
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    where,,,and
    areonlythefunctionsofr.
    2.3SolutionofgoverningequationsSubstitutingEq.(25)intogeometricequationof3Delasticproblem,thegeometricequationofthekthlayerofflexiblepipeunderinternalpressurecanbesimplifiedas(26)Asmentionedpreviously,thestresscomponentsofflexiblepipeunderinternalpressureareonlythefunctionsofradialcoordinater.Therefore,the3Delasticequilibriumdifferentialequationsofflexiblepipeinstructuralcylindricalcoordinatescanbesimplifiedas,(27),(28).(29)ThroughintegrationofEqs.(28)and(29),itcanbeobtainedas
    (30)whereA(k)andB(k)areunknownintegralconstants.2.3.1SolutionofgoverningequationsofreinforcementlayerAccordingtogeometricEq.(26),substitutingconstitutiveEq.(1)ofreinforcementlayerintoEqs.(27)and(30),differentialequationscanbeobtainedasfollows:,(31),(32).(33)
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    Itisassumedthatreinforcementlayermaterialisnotsoftened,thatis,and,supposingthat,thesolutionofsecond-orderlinearnonhomogeneousdifferentialEq.(31)is,(34)andthesolutionoffirst-orderlinearnonhomogeneousdifferentialEqs.(32)and(33)is,(35),(36)whereA(k),B(k),D(k),E(k),F(k)andG(k)areunknownintegralconstants,andthecoefficientsare(37)SubstitutingEqs.(25)and(34)–(36)intogeometricEq.(26),thematrixrepresentationoftheequationforthestraincomponentsofthekthreinforcementlayerofflexiblepipeunderinternalpressure,containingunknownintegralconstantsA(k)–E(k),canbeobtainedas.(38)
    SubstitutingEq.(38)intoconstitutiveEq.(1),thematrixrepresentationoftheequationforthestresscomponents,containingunknownintegralconstantsA(k)–E(k),canbeobtainedas(39)
    2.3.2SolutionofgoverningequationsofrubberlayerThroughcomparisonbetweentheconstitutiveEq.(1)ofreinforcementlayerandtheconstitutiveEq.(2)ofrubberlayer,itcanbeknownthatthestiffnesscoefficientsofrubberlayerincylindricalcoordinateshavethefollowingrelations:(40)Eq.(40)intoEq.(37),thecoefficientsofrubberlayerasthekthlayerofflexiblepipeunderinternalpressurecanbegottenas
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    (41)Eqs.(41)and(34)–(36)intoEq.(25),Eq.(41)intoEqs.(38)and(39),thedisplacementcomponents,straincomponentsandstresscomponentsofrubberlayerasthekthlayerofflexiblepipeunderinternalpressurecanbeobtainedas
    (42),.2.4BoundaryconditionItisassumedthatflexiblepipeconsistsofnsinglelayers(includingreinforcementlayerandrubberlayer),andeachsinglelayercontains8unknownintegralconstantsA(k)–G(k),and.Therefore,thereare8nunknownintegralconstants.Itisassumedthatinterlaminarbondingisgood,andboundaryconditionareasfollows.(1)Thestressboundaryconditionofinnermostlayer:(44)(43)
    (45)(2)Thestressboundaryconditionofoutermostlayer:
    (46)(3)Theinterlaminardisplacementcontinuousconditions:
    (47)(4)Theinterlaminarstresscontinuousconditions:
    (48)
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    r0isinnerradiusofflexiblepipe,routisouterradiusofflexiblepipe,rkisouterradiusofthekthlayerandisalsotheinnerradiusofthe(k+1)thlayer,andp0isinternalpressure.AccordingtoEqs.(39)and(44),fromthelatter2equationsofEq.(45)andthelatter2equationsofEq.(46),itcanbeobtainedthat,andthensubstitutingitintothelatter2equationsofEq.(48),itcanbeobtainedas.(49)Eq.(49)intoEqs.(25)and(32)–(36),itcanbeknownthattheaxialdisplacement,circumferentialdisplacementofreinforcementlayerorrubberlayerasthekthlayerare.(50)Eq.(50)intothelatter2equationsofEq.(47),itcanbeobtainedas,.Astherightsideoftheaboveformulasisconstant,andtheleftsideisthefunctionofz,therefore,weget
    (51)Eq.(51)showsthatunknownintegralconstantGistherigid-bodytranslationdisplacementalongz-axisatdifferentlayersofflexiblepipe,andunknownintegralconstantFistheintegralrigid-bodyrotationangledisplacementaroundz-axisatdifferentlayersofflexiblepipe.Throughtheaboveanalysis,eachsinglelayer(includingreinforcementlayerandrubberlayer)contains2unknownintegralconstantsD(k)andE(k),aswellastwounknownconstantsε0andγ0.Therefore,thereare2n+2unknownintegralconstants,whichcanbedeterminedbythefollowingboundaryconditions:
    (52)Eq.(52)contains2nequations.Basedondifferentterminalsupportconditionsofflexiblepipe,2correspondingboundaryconditionsarecomplemented.Forexample,theaxialstressσzofflexiblepipewithfreeendonbothterminalsshouldsatisfyaxialequilibriumconditions:
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    (53)theresultanttorqueofterminalshearstressτzθshouldbezero,thatis
    (54)Anotherexample:theflexiblepipewithfixedendonbothterminalsshouldsatisfydisplacementboundarycondition,fromEqs.(48)–(50),wegetε0=0,γ0=0.(55)Displacementboundaryconditionusuallycannotbefullysatisfied.AccordingtoSt.Venanttheorem,itcanbeknownthatthishaslittleinfluenceontheflexiblepipefarawayfromterminals.2.5BriefsummaryTherigid-bodytranslationdisplacementGalongz-axisandtheintegralrigid-bodyrotationangledisplacementFaroundz-axisatdifferentlayersofflexiblepipehavenoinfluenceonstraindistributionandstressdistribution.Meanwhile,itcanbeknownthatA(k)=B(k)=0fromEq.(49),therefore,thedisplacementcomponentsofrubberlayerandreinforcementlayerasthekthlayerrespectivelyare,(56).(57)Thestraincomponentsofrubberlayerandreinforcementlayerasthekthlayerarerespectively,(58)
    (59)Thestresscomponentsofrubberlayerandreinforcementlayerasthekthlayerarerespectively,(60)
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    (61)
    Eqs.(56),(57),(60)and(61)intoboundaryconditionEq.(52)aswellascomplementaryboundaryconditionEqs.(53)and(54)orcomplementaryboundaryconditionEqs.(55),2n+2unknownintegralconstantsD(k),E(k),ε0andγ0canbeobtained,theobtainedunknownintegralconstantsintoEqs.(56)–(61),thedisplacementdistribution,straindistributionandstressdistributionfarawayfromterminalsofflexiblepipeunderinternalpressurecanbeobtained.3Caseanalysis3.1TestspecimenThetestspecimenadoptsthesubmarineoilpipewiththeinnerdiameterof10inchmanufacturedbyHebeiOuyaSpecialFlexiblePipeCo.Ltd.,asshowninFig.3.Thecomponentsoftestspecimeninclude:(1)Theflexlinerwiththethicknessof4mm,thematerialofNBR(NitrileRubber)B6240,themooneyviscosityof41(ML1+4,100℃),thedensityof0.99g/cm3,thePoissonratioof0.499,thestressatdefiniteelongation100%of3.1–3.3Mpa,thetensilestrengthof20.1–21.0Mpa(50min),andthehardnessof70(JISA).(2)Theflexbarrier,thegummingmeshclothlayerwiththethicknessof1mm.(3)Theflexwearwiththethicknessof1mm,thematerialofNBRB6240,therubberadhesiveofAS-88,theadhesivestrengthof8kN/50mm,and3layers.(4)Theflexshieldwiththethicknessof5mm,thematerialofCR(ChloropreneRubber)321,themooneyviscosityof50(ML1+4,100℃),thedensityof1.23g/cm3,thePoissonratioof0.499,andthetensilestrengthofgreaterthan26Mpa(50min).(5)ThereinforcementlayerwoundwithΦ2.0mmbrassplatedsteelwire,withthetensilestrengthof4200N/pieceor2450Mpa,thepoisson’sratioof0.26,theYoungmodulusof2.07×105Mpa,andtheshearmodulusof8.21×104Mpa.(6)Theflexiblepipe,withroundsteelorhexagonalsteeljoint,thetensilestrengthof445Mpa,inaccordancewithFig.3SchematicdiagramoftestspecimenGB/T14292-93standard.TheengineeringelasticconstantsforcomponentsoftestspecimenareshowninTable1.
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    Table1Engineeringelasticconstantsforcomponentsofspecimen
    Elasticmodulus
    E(MPa)Shearmodulus
    G(MPa)PoissonratioνTensilestrength
    σb
    (MPa)
    Steelwire2.07×1058.21×1040.2612450NBRorCR3.01.00.499
    TheflexlinerandflexwearmaterialoftestspecimenisNBR,andtheflexshieldmaterialisCR.Thereisnoorthereisverylimitedlinearpartinrubberstress-straincurve.Therefore,Youngelasticmodulusdoesnotexist.Thispaperusestheso-called“elasticmodulus”calculatedbyrubberstressatdefiniteelongation100%aselasticmodulusofrubber.Althoughtheobtained“elasticmodulus”ofrubberdoesnotcoincidewiththedefinitionofYoungelasticmodulus,flexiblepipebearsexternalloadsmainlythroughreinforcementlayer,sothisapproachhaslittleinfluenceonthecalculatedvaluesofstraindistributionandstressdistribution.
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    Testspecimenconsistsof5rubberlayersand4reinforcementlayers.Theinnerradiusoftestspecimenr0=0.127m,theouterradiusrout=0.148m,thesteelvolumefractionofreinforcementlayerVf=0.785andthesteelwirewoundangleφ=±32.74°.Testspecimenisregardedasbalancedcross-plylaminatedcompositestructure.AccordingtoChineseengineeringempiricalformula[9],thepredictedvaluesofengineeringelasticconstantsforreinforcementlayeroftestspecimeninmaterialcoordinatesareshowninTable2.
    Table2EngineeringelasticconstantsforreinforcementlayeroftestspecimeninmaterialcoordinatesParameterLongitudinalelasticmodulusE1LatitudinalelasticmodulusE2
    Cross-sectionelasticmodulusE3In-planeshearmodulusG12
    In-planeshearmodulusG13Cross-sectionshearmodulusG23In-planemajorPoissonratioυ21=υ31In-planeminorPoissonratioυ12=υ13Cross-sectionPoissonratioυ23=υ32Value
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    1.46×105Mpa4.23×104Mpa1.68×104Mpa1.59×104Mpa0.2960.08570.327
    3.2MechanicalresponseoffreeendsonbothterminalsflexiblepipeunderinternalpressureThedistributionofdisplacementcomponents,straincomponentsandstresscomponentsoffreeendsonbothterminalstestspecimenunderworkinginternalpressure16Mpaiscalculatedasfollows.(1)Axialdisplacementuz:.(2)Circumferentialdisplacementuθ:.whereradialcoordinaterandaxialcoordinatezadoptinternationalstandardunitm,sameasbelow.Fig.4Theradialdisplacementsofflexiblepipewithfreeendsunderworkinginternalpressure16Mpa(3)Theradialdisplacementsuratdifferentlayersarecontinuousandinthestateofexpansion,anddecreasewiththeincreaseofradius,asshowninFig.4.(4)Axialstrainεz:.(5)Shearstrainγzθ:.Fig.5Thecircumferentialstrainsofflexiblepipewithfreeendsunderworkinginternalpressure16Mpa(6)Thecircumferentialstrainsεθatdifferentlayersarecontinuousastensilestrain,anddecreasewiththeincreaseofradius,asshowninFig.5.Fig.6Theradialstrainsofflexiblepipewithfreeendsunderworkinginternalpressure16Mpa
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    (7)Theradialstrainεrateachsinglelayeriscontinuousascompressivestrain,andisdiscontinuousatinterlayer.Theabsolutevaluesofεratreinforcementlayersandrubberlayersrespectivelydecreasewiththeincreaseofradius,andtheabsolutevaluesofεratrubberlayerisfargreaterthanthatatreinforcementlayer,asshowninFig.6.(8)Theabsolutevaluesofaxialstressesσzatreinforcementlayersandrubberlayersrespectivelydecreasewiththeincreaseofradius.Theaxialstressatrubberlayeriscompressivestress,buttensilestressatreinforcementlayer.Theaxialstresseateachsinglelayeriscontinuous,andisdiscontinuousatinterlayer.Theabsolutevaluesofσzatrubberlayerarefarlessthantheonesatreinforcementlayer,asshowninFig.7.(9)Thedistributionofcircumferentialstressesσθissimilartothecaseofaxialstressesσz,andtheabsolutevaluesofcircumferentialstressesσθareapproximatelytwicetheabsolutevaluesofaxialstressesσzateachsinglelayer,respectively,asshowninFig.8.(10)Theradialstressesσratdifferentlayersarecontinuousascompressivestress,anddecreasewiththeincreaseofradius,asshowninFig.9.Fig.9Theradialstressesofflexiblepipewithfreeendsunderworkinginternalpressure16Mpa
    (11)Theshearstressτzθatrubberlayerofflexiblepipeisnearlyzero,theabsolutevaluesofshearstressesτzθatreinforcementlayerdecreasewiththeincreaseofradius,andisoppositetotheτzθatreinforcementlayerwithwoundangle±φ,asshowninFig.10.Fig.8Thecircumferentialstressesofflexiblepipewithfreeendsunderworkinginternalpressure16MpaFig.10Theshearstressesofflexiblepipewithendsunderworkinginternalpressure16Mpa3.3Mechanicalresponseofflexiblepipewithfixedendonbothterminalsunderinternalpressure(1)Fortheflexiblepipewithfixedendonbothterminals,itcanbeknownfromdisplacementboundaryconditionthat:Fig.7Theaxialstressesofflexiblepipewithendsunderworkinginternalpressure16Mpa(2)Thedistributionofradialdisplacementuratdifferentlayersissimilartothecaseofflexiblepipewithfreeendonbothterminals.Duetotheradialrestrictionoffixedend,theradialdisplacementoftheformerisslightlylessthanthatofthelatter.(3)Theaxialstrainεzandshearstrainγzθatdifferentlayersarezero,thatis:
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    (4)Thedistributionofcircumferentialstrainεθatdifferentlayersissimilartothecaseofflexiblepipewithfreeendonbothterminals.Duetothecircumferentialrestrictionoffixedend,thevalueεθoftheformerisslightlylessthanthatofthelatter.(5)Thedistributionofaxialstressσzissimilartothecaseofflexiblepipewithfreeendonbothterminals.Thefixedendrestrictsthetrendtowardsaxialshortening.Therefore,thevalueσzatreinforcementlayersoftheformerisgreaterthanthatofthelatter.(6)Thedistributionofradialstrainεr,radialstressσr,circumferentialstressσθandshearstressτzθatdifferentlayersofflexiblepipewithfixedendonbothterminalsissimilartothatoftheabovephysicalquantityatdifferentlayersofflexiblepipewithfreeendonbothterminals.Besides,theirvaluesareveryclose,respectively.3.4TestforradialdisplacementofspecimenwithfixedendsunderinternalpressureTestspecimenadopts4submarineoilpipeswiththeinnerdiameterof10inch.RelevantexperimentwasfinishedinstructurelaboratoryofSchoolofCivilandHydraulicEngineeringD.U.T.andinstructurelaboratoryofDepartmentofEngineeringMechanicsD.U.T..Testspecimenwasweldedandsealedwithblindflangeonbothends.Thejointsonbothendsoftestspecimenwereweldedtotheflange,andtheflangewasrespectivelyconnectedtotwofixedsupportswithbolts,asshowninFig.11.Thejointononeendofspecimenwasdrilled,andwasconnectedtopressuregauge,asshowninFig.12.Thejointontheotherendwasdrilled,andconnectedtomanualpressurepump,asshowninFig.13.MeasuringapparatusforradialdeformationoftestspecimenisasshowninFig.14.Fig.11FixingdeviceontheendofflexiblepipeFig.13ManualpressurepumpconnectedwithflexiblepipeFig.12PressuregaugeconnectedwithflexiblepipeFig.14MeasuringapparatusforradialdeformationTestspecimenwasfixedontothesupportsonbothterminalsandwaterwasinjectedintoit,andthen,manualpressurepumpwasconnectedtotestspecimen.Pressurewasputontotheinsideoftestspecimenviamanualpressurepump,whenpressuregaugeindicatedthecurrentinternalpressure.Viaradialdisplacementmeasurementdevice,theouterdiameterincrementoftestspecimenundercurrentinternalpressurewasmeasured.AsshowninFig.4,twicetheradialdisplacementur(r=rout)onoutsidesurfaceofflexiblepipewastheouterdiameterincrementofflexiblepipeundercurrentinternalpressure.TestdataandanalyticsolutionareshowninFig.15.Fig.15Theouterdiameterincrementsof1#~4#testspecimenandanalyticvaluesbypresentmethodItcanbeseenfromFig.15thattheouterdiameterincrementofflexiblepipeunderinternalpressurethatiscalculatedbypresentmethodisconsistentwiththetrendinchangeoftestdata,
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    andtheouterdiameterincrementofflexiblepipeapproximatelyincreaseslinearlywiththeincreaseoftheinternalpressure.Forthereasonswhymeasuredouterdiameterincrementsof1#~4#specimensunderinternalpressurearegreaterthananalyticvalues,ononehand,hyper-elastomerrubberissimplifiedaslinearelastomerintheanalyticcalculation;ontheotherhand,thisisrelatedtothepredictionformulaofengineeringelasticconstantatreinforcementlayerthatisusedforanalyticcalculation.ThispaperadoptsChineseengineeringempiricalformula.4ConclusionThispaperregardsflexiblepipeasalaminatedstructureconsistingofmultipleanisotropicreinforcementlayersandmultipleisotropicrubberlayers.Basedon3Danisotropicelastictheory,thispapertakesintoaccounttheeffectsoftensile-shearcouplingatreinforcementlayerandthecompatibledeformationbetweenreinforcementlayerandrubberlayer,andpresentstheanalyticsolutionofdeformationdisplacementdistribution,straindistributionandstressdistributionofflexiblepipeunderinternalpressure.Presentanalyticmethodisbasedonthepremisethatflexiblepipeisinfinite.Therefore,itisonlyapplicabletotheflexiblepipefarawayfromterminals.Astheadjacentreinforcementlayerswithwoundangle±φhavedifferentradii,sothecircumferentialdisplacementofflexiblepipeunderinternalpressureisnotzero.Thesignofstraincomponentatreinforcementlayeristhesameasthatofstraincomponentatrubberlayer(e.g.positivealikeornegativealike).Theaxialstressandcircumferentialstressatreinforcementlayeraretensilestress,whilethoseatrubberlayerarecompressivestress.Asthereisnofreeboundaryonflexiblepipe,theinterlaminarshearstressiszero,whichisconsistentwiththecalculatedresultτθr=τzr=0bypresentmethod.
    References[1]RosenowMWK.Windangleeffectsinglassfiber-reinforcedpolyesterfilamentwoundpipes[J].Composites,1978,9:17-24.[2]BartonMV.Thecircularcylinderwithabandofuniformpressureonafinitelengthofthesurface[J].JournalofAppliedMechanics,1941,8:A97-104.[3]FuL,WaasAM.Bucklingofpolarandrectilinearlyorthotropicannuliunderuniforminternalorexternalpressureloading[J].CompositeStructure,1992,22:47-57.[4]WildPM,VickersGW.Analysisoffilament-woundcylindricalhellsundercombinedcentrifugalpressureandaxialloading[J].Composites,1997,28:47-55.[5]XiaM,TakayanagiH,KemmochiK.Analysisofmulti-layeredfilament-woundcompositepipesunderinternalpressure[J].CompositeStructure,2001,53:483-491.
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    [6]ChouchaouiCS,OchoaOO.Similitudestudyforalaminatedcylindricaltubeundertensile,torsion,bending,internalandexternalpressure.PartI:governingequations[J].CompositeStructures,1999,44:221-229.[7]ChouchaouiCS,OchoaOO.Similitudestudyforalaminatedcylindricaltubeundertensile,torsion,bending,internalandexternalpressure.PartII:scalemodes[J].CompositeStructures,1999,44:231-236.[8]TarnJQ,WangYM.Laminatedcompositetubesunderextension,torsion,bending,shearingandpressuring:astatespaceapproach[J].InternationalJournalofSolidsandStructures,2001,38:9053-9075.[9]WangYaoxian.CompositesStructureDesign[M],Beijing:ChemicalIndustryPress,2001.
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