极限压力和设计准则的圆柱形压力容器与喷嘴-图文

LimitpressureanddesigncriterionofcylindricalpressurevesselswithnozzlesYou-HongLiua,*,Bing-ShengZhangb,Ming-DeXuec,You-QuanLiuaaSchoolofpropulsion,BeihangUniversity,Beijing100083,ChinabDepartmentofMechanicalEngineering,JiangsuInstituteofIndustry,Changzhou213016,ChinacDepartmentofEngineeringMechanics,TsinghuaUniversity,Beijing100084,ChinaReceived15May2002;revised2April2004;accepted2April2004AbstractLimitpressuresandcorrespondingmaximumlocalmembraneStressConcentrationFactors(SCFareassessedfortwoorthogonallyintersectingthin-walledcylindricalshellssubjectedtointernalpressure.Thelimitpressuresof81modelswithparametersr¼d=D#0:8;D=T$10;d=t$10;l¼d=ffiffiffiffiffiDTp#8andd=D#t=T#2arecalculatedusinginelasticanalysesbythe3Dfiniteelementmethod(3DFEMinwhichthematerialiselastic-perfectlyplastic.Theplasticcollapsepressuresobtainedby3DFEMareingoodagreementwithtestresultspresentedbypreviousauthors.ThelocalmembraneSCFattheintersectionsoftwocylindricalshellssubjectedtothelimitpressureloadiscalculatedbyelasticthinshelltheoreticalsolutionspresentedbyXueandHwang.ThelocalmembraneSCFdecreasessignificantlyast=Tincreases,anddecreaseslittleasd=ffiffiffiffiffiDTpdecreaseswhenD=Tisfixed.ThelocalmembraneSCFincreasessignificantlyasD=Tincreases,andvarieslittleasd=ffiffiffiffiffiDTpincreaseswhent=Tisconstant.Thelocalmembranestresscriterionkm#2:2forreinforcementdesignofopeningsinacylindricalpressurevesselsubjectedtointernalpressurecanbeacceptedgenerallyexceptforafewcasesoflargethicknessratiot=T;andsmallopeningratior:q2004ElsevierLtd.Allrightsreserved.Keywords:Localmembranestresscriteria;Limitpressure;Opening;Cylindricalpressurevessel1.IntroductionAccordingtothegeneraldesigncriteriainPressureVesselCode—DesignbyRule,the1:5Smlimitforelasticlocalmembranestressissettoensureagainstplasticcollapseandthe1:5Smlimitontheelasticnormalmaximumstressintensitycomesfromtheshakedowncriterion.However,asshownbyRoderbaugh[1],foropenings,the1:5Smlimitonlocalmembranestressistoorestrictive.Althoughthelocalmembranestressconcentrationfactorkm¼smmax=s0inthemainthinshellcausedbyaverysmallopeningisupto2.5,theopeningdoesnotdecreasethestrengthofthestructure.Xue,Hwangetal.[2–4]presentananalyticalsolutionoftheintersectionoftwocylindricalshellsbasedonelasticthinshelltheory.ThesolutionsareingoodagreementwiththoseobtainedbyelastictestsandbyFEMford=D#0:8andadoptedbytheChinesePressureVesselDesignCodebyAnalysis[5].Onthebasisofthecalculatedresultsof26plastictestmodels,thecriterion,km#2:2forreinforcementdesignofopeningsincylindricalpressurevesselswasproposedbyXueandHwangetal.[2].However,the26plastictestmodelsdonotcoverallstructuralparameters.Therefore,81models,whichincludethe25plastictestmodelsperformedbyCottamandGill[6],ClareandGill[7],Ellyin[8],Schroeder[9],Lu[10],Rodabaugh[1,11],and56othergeometricalparametermodels,coveringmanyengineeringcasesofcylinderintersections,havebeeninvestigated.Inthispaperthedesigncriterionoflocalelasticmembranestressanditsrestrictionsforpracticalapplicationincylindricalpressurevesselswithnozzlesareinvestigated.Pre-investigationshaveshownthatthelimitpressureatthecylindricalshellintersectioncanbeaccuratelypredictedbyfiniteelementanalysisiftheelementtypeandthemeshofthemodelsareproperlychosen.Therefore,thefiniteelementmethodisemployedtoobtaintheplasticcarrying0308-0161/$-seefrontmatterq2004ElsevierLtd.Allrightsreserved.doi:10.1016/j.ijpvp.2004.04.002InternationalJournalofPressureVesselsandPiping81(2004619–624/locate/ijpvp*Correspondingauthor.Tel.:þ86-10-82338358.E-mailaddresses:liuyouhong@,liuyh@(Y.-H.Liu.capacitiesofthevariousmodelswithdifferentgeometricalparameters.2.FiniteelementmodelingandgeometryLimitloadswerecalculatedbyusingnon-linearfiniteelementanalysisbasedontheassumptionofanelastic-perfectlyplasticmaterialandsmalldeformationtheory.Thelimitpressuresweredeterminedbythe‘twiceelasticslopemethod’,the‘fifteenelasticslopemethod’andthe‘finalloadmethod’,definedinSection3.1below.TherangesofgeometryparametersincludedinthisstudyareshowninTable1.ThemeandiameterofthecylindricalshellisheldconstantatD¼1000mm.Thegeometryparametersmeetthepracticalthin-walledpressurevesseldemandsof:d=D#0:8;r#t=T#2:0;l#8:0andD=T$10:0;d=t$10:0:Three-dimensionalsolidmodelswereusedforallthevesselsconsidered.Symmetryconditionswereinvokedsuchthatonlyaquartermodelofthevesselwasrequiredwithappropriatesymmetryboundaryconditionsapplied.Allmodelsusedtwenty-nodesolidisoparametricelementsSOLID95ofANSYSsoftware.ThevesselwassubjectedtointernalpressureP:ThecylindricalshellwasfreeandsubjectedtoalongitudinalmembranestressequaltoPD2i=ðD2o2D2iÞattheend.Thecylindricalnozzlewasaxiallyfixedattheendremotefromtheintersectionoftheshellandthenozzle.Twoorthreesolidelementswereusedthroughallthevesselthickness.AtypicalfiniteelementmeshisshowninFig.1.ThematerialpropertiesusedintheFEManalyseswere:E¼2:07£105MPa,sY¼225MPa,n¼0:3:3.Resultsanddiscussion3.1.DeterminationoflimitpressureTheloadgivingthefinalconvergentsolutioncouldbeobtainedbytheelastic-plasticFEManddefinedasalimitload.Inaddition,theotherdefinitionsoflimitloadaregivenfromtheload–deformationplotsinpressurevesselcodes.Maximumallowabledisplacementsorgraphicalconstructionsonload–deformationplotssuchasthetwiceorfifteenelasticslopecriterionmaybeusedforthispurpose.Thetwice-elasticslopecriterion(asrecommendedinASMESection8Division2Appendix4-136wasoriginallyusedinplasticanalysis,basedontheactualnon-linearstress-strainrelationshipofthevesselmaterial(andincludingnon-lineargeometryTable1RangeofgeometricalparametersNo.ofmodelst=TD=Tlr200.10–2.0010–6250.316–2.500.100–0.199230.20–2.0010–6250.632–5.000.200–0.29940.30–2.0028–472.19–2.480.300–0.39930.44–2.0028–502.19–3.030.400–0.499140.50–2.0010–2561.58–8.000.500–0.59950.60–2.0028–353.29–3.820.600–0.699120.70–2.0010–1002.53–8.000.700–0.799Y.-H.Liuetal./InternationalJournalofPressureVesselsandPiping81(2004619–624620effectsifdesired,todeterminetheplasticcollapseloadofthevessel.Plasticcollapseloadistosomeextentamisnomer,asarealvesselmaynotphysicallycollapseatthisloadlevel;henceGerdeen[12]referstotheplasticcollapseloadastheplasticload.Later,thefifteenelasticslopemethodappeared[13],inwhichelastic-perfectlyplasticmaterialpropertieswereassumedwithnogeo-metricalnon-linearities.Inordertofindthedifferencesintheresultsobtainedbythetwice,fifteenelasticslopecriteriaandthefinalloadmethod,allthreemethodswereusedandassessed.ThenodaldisplacementcharacteristicsforsomedifferentnodesinthesamepressurevesselareshowninFigs.2and3.Therearevisibledifferencesinlimitpressuresbetweenthetwiceelasticslopemethodandthe15elasticslopemethod.However,thelimitpressuredeterminedbythefinalloadmethodisdefinedasthefinalpressurethatcanbeappliedtothecylindricalshellwithoutcollapse.BecausethematerialoftheFEManalysiswasrepresentedaselastic-perfectlyplasticwithoutanymaterialstrengthening,thefinalloadmethodwaschosenasthemethodofcalculatinglimitpressureforalltheanalysesinordertoavoidlimitpressuredifferencesfromdifferentcharacteristicnodaldisplacementversuspressurecurvefigures.3.2.ComparisonoflimitpressurewithprevioustestsBecauselimitpressuresaredirectlyproportionaltotheyieldstrengthoftheelastic-perfectlyplasticmaterial,dimensionlesslimitpressures,calculatedfortheexper-imentsaregiveninTable2.Table2showsthattheelastic-plasticFEManalysescanpredictwelltheplasticcollapsestatesofthin-walledpressurevessels.FromTable2,itcanbeseenthatinsomemodelsthecalculateddimensionlesslimitpressuresaregreaterthantheexperimentaldimensionlesslimitpressures.Thereasonsarethatintheexperiments,thelimitpressureisthe‘plasticcollapse’pressure,nottherupturepressure,andthematerialyieldstressistheaverageyieldstresswithsomestrainhardening.Forexample,inthemodelsofCottamandGill[6],theexperimentallimitpressurePLisP5;definedinthepaperasthepressure,atwhichtherehasbeenconsiderablecircumferentialyieldofthecylindricalshell.However,thispressureisbeforeanysignificantstrainhardeningofthecylindricalshellandismuchlowerthantherupturepressure.Insomespecialcasesofthin-walledtubesattachedtothick-walledcylindricalvessels,thefailuremodemaynotbeplasticcollapsebutelasticorelastic-plasticbuckling.Inusualengineeringcases,thetubestrengthofreinforcementdesignisgreaterthanorequaltotheshellstrengthsothatbucklingcannothappen.Thereforethisspecialcasesisnotconsideredhere.Table2ComparisonbetweencalculatedresultsandtestresultsNo.ReferenceTestPL=ÀsYTRÁPL=ÀsYTRÁ2tanu15tanuFinalP1-1CottamandGill(19660.9550.7830.9260.946P1-2CottamandGill(19660.9070.8170.9370.949P1-3CottamandGill(19660.8970.9941.0091.013P1-4CottamandGill(19660.9011.0011.0721.074P1-5ClareandGill(19660.9450.7600.8290.844P2-1CottamandGill(19660.9130.6780.8300.842P2-2CottamandGill(19660.8790.8390.9070.913P2-3CottamandGill(19660.9010.9331.0041.006P2-4CottamandGill(19660.8820.7730.8260.832P2-5CottamandGill(19660.8630.9040.9360.938P2-6Lu(19930.6480.5620.7390.751P3-1CottamandGill(19660.8700.6650.7490.755P3-2CottamandGill(19660.9070.8700.8750.876P4-1Lu(19930.4960.4950.5880.594P5-1Rodabaugh(19880.9100.6460.6780.681P5-2Rodabaugh(19880.9710.8690.9780.979P5-3Rodabaugh(19880.9200.7980.8420.843P5-4Maxwell(19770.4440.4300.4320.437P6-1Schroeder(19740.7800.5370.5700.572P6-2Ellyin(19770.6600.5260.5630.565P7-1Lu(19930.5010.5260.5490.551P7-2Lu(19930.5440.5230.5530.555P8-1Lu(19930.5550.5180.5390.543P8-2Lu(19930.5810.5190.5340.545Y.-H.Liuetal./InternationalJournalofPressureVesselsandPiping81(2004619–6246214.CriterionofelasticstressdesignMostpressurevesseldesignisbasedonelasticanalysisandstresscategorisation.Theelasticprimaryplussecond-arymembranestressesforcylindricalvesselswithnozzlessubjectedtointernalpressurecanbecalculatedbyanalyticalsolutions[2]andhavebeengivenintheChinesePressureVesselDesignCodebyAnalysis.AsdiscussedinSection1,themembranestresslimitof1:5Smistoorestrictive.Themainaimofthepresentworkistoassestheelasticmembranestressdesigncriterionforengineeringappli-cation.Usingtheanalyticalmethod,thecalculatedvalueofkm0¼smmax=sYofthemodelsatthelimitpressurePLaregiveninTables3and4,respectively,wheresmmaxisthemaximumelasticnormalmembranestressattheintersectioncalculatedbyelasticthinshelltheorycodedinFORTRAN[3]andsYistheyieldstresswhichrepresentsthecircumferentialmembranestressstateinthevesselwithoutopeningunderthelimitpressure.FromTables3and4,itcanbeseenthatkmdecreasessignificantlyast=Tincreasesforlowervaluesofl;anddecreaseslittleasldecreases,whenD=Tisfixed,asshowninFig.4.Fig.4isplottedfromthedataofTable3forD=T¼47:Theminimumvalueofkmappearsinthevesselwithloweropeningratio,comparablethickwalledcylindricalshellandhighthicknessratioofnozzletoshell.Table3showsthattheSCF$2.20forallthetabulatedcases.Atthesametime,kmincreasessignificantlyasD=Tincreases,andvarieslittleaslincreaseswhent=Tisconstant,asshowninFig.5.Theminimumvalueofkm0alsoappearsinthevesselwithloweropeningratio,Table3km0forexperimentalmodelsNo.rlD=Tt=Tkm0P1-10.1350.924470.332.73P1-20.1601.094470.502.59P1-30.1561.070470.672.47P1-40.1491.021471.002.20P1-50.1961.724830.672.53P2-10.2161.476470.502.63P2-20.2131.459470.672.52P2-30.2061.410471.002.31P2-40.2701.847470.672.57P2-50.2621.799471.002.38P2-60.2681.376280.252.85P3-10.3262.236470.672.58P3-20.3192.188471.002.44P4-10.4662.483280.442.68P5-10.5132.947330.752.60P5-20.5463.137331.842.33P5-30.5283.033331.252.48P5-40.4987.5502300.982.54P6-10.6303.727350.702.60P6-20.6003.286300.602.62P6-30.6503.619310.662.61P7-10.7063.747290.662.60P7-20.7063.730290.662.62P8-10.8264.439300.772.58P8-20.8264.341290.762.58Table4km0forFEAmodelsNo.rlD=Tt=TPL=ÀsYTRÁkm0L1-010.09982.4966250.100.5133.21L1-020.09842.4596251.010.8192.66L1-030.09682.4206252.000.9832.42L1-040.09900.9901000.100.8463.00L1-050.09500.9501000.500.9892.57L1-060.09000.9001001.001.0812.20L1-070.09600.480250.101.0452.86L1-080.9000.450250.251.0852.64L1-090.09000.285100.101.1142.78L1-100.09702.4226242.000.9342.37L1-110.09942.4826240.500.6352.68L1-120.09361.6192992.001.0782.08L1-130.10000.995990.100.9443.35L1-140.15601.07047.0.671.0052.45L1-150.13480.924471.001.0902.16L2-010.19974.9926250.200.2932.84L2-020.19824.9566251.100.5632.56L2-030.19684.9206252.000.7572.65L2-040.19912.9872250.200.4332.83L2-050.19512.9272251.100.7652.47L2-060.19112.8672252.000.7691.84L2-070.19200.960250.200.8762.87L2-080.18600.930250.350.9492.71L2-090.18000.900250.501.0092.53L2-100.18000.569100.201.0312.73L2-110.19503.9004002.000.8432.50L2-120.18001.8001002.001.0902.00L2-130.18601.8601001.400.9872.23L2-140.19201.9201000.800.8542.49L2-150.19801.888912.001.0862.01L2-160.21601.972832.001.0752.03L2-170.23402.052772.001.0762.04L3-010.27002.205672.001.0722.08L3-020.30602.347592.001.0662.11L4-010.36002.546502.001.0472.14L4-020.41402.730432.001.0252.19L5-010.49807.9692560.500.2552.35L5-020.49597.9222561.250.4412.34L5-030.48447.8752562.000.6172.54L5-040.49655.9591440.500.3242.40L5-050.49135.8961441.250.5652.46L5-060.48615.8341442.000.7712.56L5-070.49213.938640.500.4532.54L5-080.48053.844641.250.7492.50L5-090.46883.750642.000.9322.32L5-100.45001.423100.500.8432.64L8-010.79207.9201000.800.3432.29L8-020.78607.8601001.400.5052.45L8-030.78007.8001002.000.7032.75L8-040.78585.893560.800.4362.39L8-050.77515.813561.400.6412.51L8-060.76445.733562.000.8282.56L8-070.76803.840250.800.6112.64L8-080.74403.720251.400.8402.59L8-090.72003.600252.001.0012.39L8-100.72002.277100.800.8012.66Y.-H.Liuetal./InternationalJournalofPressureVesselsandPiping81(2004619–624622comparablethickwalledcylindricalshellwhent=Tisconstant.Fig.5isplottedfromthedataofTable4att=T¼2:00:TheboldlineinFig.5isthecontourlineforSCF¼2:20:FromFigs.4and5,therefore,itcanbeconcludedthatkm0$2:20isvalidformostmodelsofengineeringapplicationsexceptforafewcasesofhighthicknessratio,t=T;andsmallopeningratio,r;ofcylindricalvesselswithnozzles.Theregionsofkm0#2:20maybeestimatedfromFig.5asl#4:0andD=T#45whent=T¼2:0:Itcanbeinferredthattheregionofkm0#2:20when1:0,t=T,2:0;issmallerthanthatwhent=T¼2:0:Theregionforkm0#2:20doesnotexistwhent=T#1:0;asshowninFig.4.5.ConclusionsTheproposedconservativelocalmembranestressdesigncriterionkm#2:20forreinforcementdesignofopen-ingsincylindricalpressurevesselscanbeacceptedgenerallyexceptforhighthicknessratio,t=T.1:0;andsmallopeningratio,l,4:0;ofcylindricalvesselswithnozzlesunderinternalpressure.AcknowledgementsTheauthorswishtoacknowledgethesupportfortheworkfromtheChineseAeronauticsSupportingScience624Y.-H.Liuetal./InternationalJournalofPressureVesselsandPiping81(2004619–624[7]ClareKD,GillSS.Effectofvesseldiameter/thicknessratioonthebehaviourbeyondtheelasticlimitofflushtubesincylindricalpressurevessels:experimentalInvest.JMechEngSci1966;8(4:357–62.[8]EllyinF.Anexperimentalstudyofelastic–plasticresponseofbranchpipeteeconnectionssubjectedtointernalpressure,externalcouplesandcombinedloadings.WRCBull1977;230.[9]SchroederJ,Srinivasaiah