CAESARII管道应力分析培训-课件

CAESARII管道应力分析培训王大辉北京艾思弗软件公司2023/6/4BasicStressTheory&2023/6/4BasicStressTheory&介绍培训的目的在于让您了解和掌握应力分析的基础概念模型和边界条件的建立结果的分析和评判往复压缩机的分析专题日常遇到的问题和解决方法2023/6/4BasicStressTheory&介绍3D梁单元的特征无限细的杆单元全部行为靠端点位移决定弯曲变形是主要的2023/6/4BasicStressTheory&介绍3DBeamElementCharacteristics3D梁单元的特征仅说明整体行为无局部作用（表面没有碰撞）忽略二次影响（小转动）遵循胡克定律2023/6/4BasicStressTheory&StressBasics应力基础 局部坐标系下管道应力分类（引发应力的载荷）轴向应力LongitudinalStress-SL环向应力HoopStress-SH径向应力RadialStress-SR剪切应力ShearStress-2023/6/4BasicStressTheory&轴向应力沿管道轴向Alongaxisofpipe轴向力引起AxialForce轴向力/面积(F/A)内压引起PressurePd/4torP*di/(do2-di2)弯矩引起BendingMomentMc/I最大应力环向的外表面某点处

I/radiusZ(截面模量);useM/Z2023/6/4BasicStressTheory&压力引起的环向应力环向（垂直于半径）

Pd/2t和壁厚紧密相关环向应力十分重要，但规范应力不考虑它。Hoopisveryimportant,itsjustnotpartofthe“codestress”环向应力用来确定壁厚：依据直径、许用应力、腐蚀裕量、加工偏差、压力确定管道壁厚。2023/6/4BasicStressTheory&压力引发的径向应力沿半径方向向内内壁的径向应力大小是：-P外壁的径向应力大小为0最大弯曲应力发生在管道的外表面，故该项忽略2023/6/4BasicStressTheory&剪切应力ShearStresses平面内垂直半径ShearForce剪力在外表面剪力很小，应力计算忽略支架设计有时需要考虑Torque扭矩最大应力在外表面

MT/2Z2023/6/4BasicStressTheory&3-D应力评定Aloaded,3-Dpipecontainsarepresentativeinfinitesimalstresscubeaddgraphic(Fig1-13)Thisstresscubeisinequilibriumandcanberotatedinspaceaddgraphic(rotatedcubewithloads)Thiscubecanberotatedsothatshearstressesarezero.ThisresultsinthePrincipalStresses.2023/6/4BasicStressTheory&Simplifyingtoa2-DStressThisplanecanberotatedtoeithereliminateormaximizeshearstressbyusingMohr’sCircle:Sinceweusetheoutsidesurfacewhereradialstressiszero;let’smovetoaplaneelement:2023/6/4BasicStressTheory&UsingMohr’sCircleCutthesquareattocalculateS1Cutthesquareat+90tocalculateS2Cutthesquareat+45tocalculatemax2023/6/4BasicStressTheory&UsingMohr’sCircleBrittlematerial(failurebyfracture)-maxprincipalstressDuctilematerial(failurebygeneralyielding)-maxprincipalstressisusedtosetwallthicknessMaximumshearstressisagoodpredictionanderrsontheconservativesideseep84&85ofAdv.Mech.OfMat’ls2023/6/4BasicStressTheory&基本应力“CodeStress规范应力”应力评定Evaluatinga3-DStressS=F/A+Pd/4t+M/Z轴向力、轴向压力，轴向弯矩一起的分量加和规范不同，上面的算式也不同那些应力没有包含进来？2023/6/4BasicStressTheory&基本应力“CodeStress规范应力”几个实效理论AFewFailureTheories变形能或八面体剪切应力(根据米赛斯理论和其它的理论）。最大剪应力理论

（Columb理论）

。大多数理论都根据这个理论。由于剪切影响而限制最大主应力(Rankine理论)。CAESARII132列输出应力报告中显示了米赛斯或最大剪应力强度理论。应力报告由configuration设置来决定。2023/6/4BasicStressTheory&基本应力“CodeStress规范应力”基于最大剪应力实效理论，ASME规范委员会颁布了规范应力方程Basedonthemaximumshearfailuretheory,theCodeCommitteedevelopedthe“codeequations”目的在于避免管道系统实效Purposewastoreducesystemfailures这种解决办法很实用，但仍然有问题存在Thisapproachworkedwell,buttherewerestillproblems,evenaslateaspostWorldWarII.研究表明直管道比较符合理论Studiesshowedsystemsofstraightpipematchedtheory研究表明元件失效比理论发生的早Studiesshowedsystemswithfittingsfailedearlierthantheorypredicted.ASME规范委员会委托Markl来研究这个问题CodeCommitteecommissionedMarkltostudythis...2023/6/4BasicStressTheory&基本应力“CodeStress规范应力”Markl’s试验和结果将试验用的管道充满水，按某个方向和位移反复摇晃管道。Testconfigurationsfilledwithwaterandcycledthroughapredetermineddisplacement预测失效循环次数Theoryshouldbeabletopredict“cyclestofailure”发现最先失效的管件及其原因Fittingscausedearlyfailure…because…对管件引入应力集中Stressesconcentrationsareintroducedbyfittings分析试验数据，修正轴向应力弯曲项Testdataanalyzedandamodificationtothebendingtermofthecodestressequationwasintroduced:Sbending=iM/z2023/6/4BasicStressTheory&基本应力“CodeStress规范应力”Markl’s试验和结果应力增强系数i和元件的形式有关对于弯头“i”的计算需要如下:我们需要弯头的几何参数计算弯头柔性“h”计算应力增大系数StressIntensificationFactor“i”,石化规范对平面内、外的SIF取值不同，电力取相同的sif2023/6/4BasicStressTheory&基本应力“CodeStress规范应力”Markl’s试验和结果Aload“intheplane”ofthefittingcauses“in-plane”bending平面内Aload“outoftheplane”ofthefittingcauses“out-of-plane”bending平面外2023/6/4BasicStressTheory&基本应力“CodeStress规范应力”Markl’s试验和结果规范上的附注十分重要PetroChemcodesmodifySIF(andflexibilityfactor)basedonpressurestiffeninginanote石化规范规定压力硬化影响ＳＩＦ和柔性系数应力算式变化如下 S=F/A+Pd/4t+iM/z应力增大系数不能小于１2023/6/4BasicStressTheory&Basisfor“CodeStressEquations”Markl’s试验和结果TheSIFisa“fudge”factor

SIF是个近似的参数TheSIFattemptstoincreasethebendingstresscomputedatthenodepoint,tomatchtheactualhigherstressduetothestressconcentrationcausedbythefitting.引入SIF在于改变特殊管件应力集中，让他们的应力根实际大小更接近。Marklonlytested4x4Stdfittings!!!但Markl仅测试了４ｘ４AdditionalworkisstillbeingdonetodayinthefieldofSIFs.Resultsarepublishedin:PVP,WRC,JournalofPressureVesselTechnology.其余的工作人们仍然在继续进行。2023/6/4BasicStressTheory&规范效验的工况两种失效：Primaryfailure一次失效Secondaryfailure二次失效(AthirdfailuremodeaddressedisOccasional,whichissimilartoPrimary.)2023/6/4BasicStressTheory&规范效验的工况PrimaryFailureCase一次失效力的作用ForceDriven非自限性NotSelf-Limiting重量、压力、集中力Weight,Pressure,

ConcentratedForces2023/6/4BasicStressTheory&规范效验的工况PrimaryFailureCase一次失效力的作用ForceDriven非自限性NotSelf-Limiting重量、压力、集中力,Weight、Pressure,

ConcentratedForces2023/6/4BasicStressTheory&规范效验的工况SecondaryFailureCase二次失效位移作用DisplacementDriven自限性IsSelf-Limiting温度、位移和其他变化载荷引起的Temperature,Displacement,plusothervaryingloads-i.e.weight2023/6/4BasicStressTheory&规范效验的工况

(1)=W+T1+P1(OPE)(2)=W+P1(SUS)(3)=DS1-DS2(EXP)Operatingcase,usedfor:热态restraint&equipmentloads推力和弯矩maximumdisplacements最大位移computationofEXPcase计算二次应力SustainedcaseforPRIMARYloadsandstresscompliance计算一次应力Expansioncasefor“extremedisplacementstressrange”膨胀工况，计算二次应力displacementsforcase3aredisplacementsfromcase1minusdisplacementsfromcase22023/6/4BasicStressTheory&规范效验的工况膨胀工况的解释ExpansionCaseExplainedWhatdoes“DS1-DS2(EXP)”mean?Isaloadcasewith“T1(EXP)thesamething?2023/6/4BasicStressTheory&LoadCasesforCodeCompliance膨胀工况的解释ExpansionCaseExplainedThecodestatesthattheexpansionstressesaretobecomputedfromthe"extremedisplacementstressrange".Theseareallveryimportantwords.Considertheirmeaning…EXTREME极端:Inthissenseitmeansthemost,orthelargest.RANGE范围:Typicallyadifference.Whatdifference?Thedifferencebetweentheextremes.Whatextremes?DISPLACEMENT位移:Thisdefineswhatextremestotakethedifferenceof.STRESS应力:Whatweareeventuallyafter.2023/6/4BasicStressTheory&LoadCasesforCodeCompliance膨胀工况的解释ExpansionCaseExplainedPuttingeverythingbacktogether,wearetoldtocomputestressesfromtheextremedisplacementrange.Howcanwedothis?计算最大位移范围的应力Considertheequationbeingsolved;[K]{x}={f}.Inthisequation,weknow[K]and{f},andwearesolvingfor{x},thedisplacementvector.InCAESARII,whenwesetupanexpansioncase,wedefineitas"DS1-DS2",wherethe"1"and"2"refertothedisplacementvector({x})ofloadcases1and2respectively.2023/6/4BasicStressTheory&LoadCasesforCodeCompliance膨胀工况的解释ExpansionCaseExplained(Obviouslytheloadcasenumbersaresubjecttochangeonajobbyjobbasis.)Whatdoyougetwhenyoutake"DS1-DS2"?Well{x1}-{x2}yields{x'},apseudodisplacementvector.{x'}isnotarealsetofdisplacementsthatyoucangooutandmeasurewitharuler,ratheritisthedifferencebetweentwopositionsofthepipe.Oncewehave{x'},wecanusethesameroutinesusedintheOPEorSUScasestocomputeelementforces,andfinallyelementstresses.2023/6/4BasicStressTheory&LoadCasesforCodeCompliance膨胀工况的解释ExpansionCaseExplainedHowever,theseelementforcesarealsopseudoforces,i.ethedifferenceinforcesbetweentwopositionsofthepipe.力的大小是两个工况力的差值Similarly,thestressescomputedarenotrealstresses,butstressdifferences.应力不是真实应力，是应力的差值Thisisexactlywhatthecodewants,thestressdifference,whichwascomputedfromadisplacementrange.二次应力是位移变化量导致的Astowhetherornotthisstressdifferenceistheextreme,wellthatdependsonthejob.2023/6/4BasicStressTheory&LoadCasesforCodeCompliance膨胀工况的解释ExpansionCaseExplainedDS1-DS2和T1“一样吗？.有可能.如果是线性系统，答案是一样的。如果是非线性系统(如你有+Ys,orgaps,orfriction),答案是不一样的。原因是两个工况应用[K]{x}={f}。Thereasonforthiscanbefoundbyexaminingtheequation[K]{x}={f}forthetwodifferentmethods.2023/6/4BasicStressTheory&LoadCasesforCodeComplianceExpansionCaseExplainedForthisdiscussion,rearrangetheequationto{x}={f}/[K],whereweknowwedon'treallydivideby[K],wemultiplybyitsinverse.OPE:{xope}={fope}/[Kope]={W+T1+P1}/[Kope]SUS:{xsus}={fsus}/[Ksus]={W+P1}/[Ksus]EXP:{xexp}={xope}-{xsus}={W+T1+P1}/[Kope] -{W+P1}/[Ksus]Canwesimplifytheaboveequationasfollows? EXP:{xexp}={W+T1+P1}/[K]-{W+P1}/[K}2023/6/4BasicStressTheory&LoadCasesforCodeCompliance膨胀工况解释ExpansionCaseExplainedCanwesimplifytheaboveequationasfollows? EXP:{xexp}={W+T1+P1}/[K]-{W+P1}/[K]Cancelingliketerms(theonesinred)yields: {xexp}={T1}/[K]问题在于[Kope]和[Ksus]是否相等.线性系统相等.非线性系统不相等2023/6/4BasicStressTheory&LoadCasesforCodeCompliance膨胀工况解释ExpansionCaseExplained如果一个系统有两个操作温度。Anotherproofthatthe"DS1-DS2"methodisthecorrectwaytogoistoconsiderajobwithtwooperatingtemperatures,oneaboveambientandonebelowambient.如T1=+300,andT2=-50.CAESARII软件自动建立如下工况:(1)W+T1+P1(OPE)(2)W+T2+P1(OPE)(3)W+P1(SUS)(4)DS1-DS3(EXP)(5)DS2-DS3(EXP)2023/6/4BasicStressTheory&LoadCasesforCodeCompliance膨胀工况解释ExpansionCaseExplained上述工况正确，但没能说明规范要求的最大应力范围因为CII并不能判断荷载所代表的具体含义为满足规范的要求，用户必须自己定义:(6)DS1-DS2(EXP)这个工况是最大位移膨胀应力，正是规范所要求的。您根本不能考虑使用T1来计算膨胀应力.2023/6/4BasicStressTheory&LoadCasesforCodeComplianceExpansionCaseExplained膨胀工况的解释Tosummarize:概括如下Wetakethedifferencebetweentwoloadcasestodetermineadisplacementrange.两个工况确定位移范围Fromthisrangewecomputeaforcerangeandthenastressrange.由此我们确定力的范围和应力范围Thecoderequirestheextremedisplacementstressrange.规范要求极端的应力范围Theuseronlyhastoworryaboutwhetherornotthe“extreme”casehasbeenaddressed.用户仅考虑最大应力范围即可2023/6/4BasicStressTheory&LinearvsNon-Linear线性和非线性Terminologyappliestoboundaryconditions.边界条件的类型Recalltheequationbeingsolved:[K]{x}={f}Thisistheequationofaspring.Thepipingsystemboundaryconditions(i.e.therestraints)arerepresentedasstiffnesses,orsprings.管道边界条件代表刚度或弹簧Morecomplexboundaryconditionscanbedefined,invalidatingthe“linearspring”assumption.2023/6/4BasicStressTheory&LinearvsNon-Linear线性和非线性线性约束

boundaryconditionisadoubleactingrestraint,suchasa“Y”support.一种是上下约束Anotherexampleofalinearboundaryconditionisaspringhanger.一种是弹簧Theforceversusdisplacementcurvefortheserestraintsisastraightline…力和位移是线性关系Thereforetheserestraintsarelinear.约束是线性的Theslopeofthelineisthestiffness.斜率是刚度2023/6/4BasicStressTheory&LinearvsNon-Linear线性和非线性非线性约束A“+Y”supportisanon-linearsupport.支架Itsforcevsdisplacementcurveisnotastraightline.力和位移不是直线关系Stiffnessonlyexistsfornegativedisplacements.向下的位移是刚度是存在的Forpositivedisplacements,thestiffnessiszero.向上的位移，刚度变为０2023/6/4BasicStressTheory&LinearvsNon-Linear线性和非线性A“gap”isalsoanon-linearsupport.间隙的引进Theforcevsdisplacementcurveisnotastraightline.力和位移不是线性关系Thereisnostiffnessinthegap.间隙部分没有刚度2023/6/4BasicStressTheory&LinearvsNon-Linear线性和非线性Frictionmakesarestraintnon-linear摩擦让约束非线性Largerotationrodsarealsonon-linearrestraints大的转动吊杆让约束非线性Non-linearrestraintsinajobmeanthat[Kope]isnotequalto[Ksus].非线性后，热态管道刚度和冷态刚度不一致(EXP)and(OCC)loadcasesmustbeconstructedusingthedifferencebetweentwootherloadcasestoaccountfornon-linearrestraints.2023/6/4BasicStressTheory&偶然工况的建立Occasionalloadsareconsidered“primary”,sincetheyareforcedriven.偶然荷载是主要载荷，力引起的。Occasionalloadsoccurinfrequently.不经常发生Thecodesemployan“allowableincrease”factorbasedonthefrequencyofoccurrenceinthedeterminationoftheallowable,i.e.k*Sh.基于发生的频率，确定ｋ值的大小Examplesofoccasionalloadsarewindandearthquake.偶然载荷是风载荷和地震载荷2023/6/4BasicStressTheory&偶然工况的建立ThecodeequationfortheOCCasionalloadcaseis:

MA/Z+MB/Z<kShHere,MAisthemomenttermfromtheSUStainedloads,冷态荷载引发力矩andMBisthemomentfromtheOCCasionalloads.偶然荷载引发力矩ThisequationstatesthattheOCCasionalcaseisthesumoftheSUStainedstressesandtheOCCasionalstresses.偶然工况是冷态和偶然的叠加Sowecan’trunaloadcasewithjusta“WIND”loadandsatisfythiscoderequirement.Whatabout“W+P1+WIND”asaloadcase?2023/6/4BasicStressTheory&OccasionalLoadCaseSetupThe“W+P1+WIND”casewillworkfor“linear”systemsonly.For“non-linear”systems,thisisnotsufficient,forthesamereason“T1”isnotsufficientfortheEXPansionloadcase.ThebestwaytosetupOCCasionalloadcasesis:(1)W+P1+T1(OPE)(2)W+P1+T1+WIND(OPE)(3)W+P1(SUS)(4)DS1-DS3(EXP)(5)DS2-DS1(OPE)(6)ST5+ST3(OCC)2023/6/4BasicStressTheory&OccasionalLoadCaseSetup(1)W+P1+T1(OPE)(2)W+P1+T1+WIND(OPE)(3)W+P1(SUS)(4)DS1-DS3(EXP)(5)DS2-DS1(OPE)(6)ST5+ST3(OCC)ThisisthenormalOPEratingcaseThisisacombinedOPEratingcasewhichincludestheOCCloadsThisisthestandardSUStainedcaseThisisthestandardEXPansioncaseThisdifferenceyieldstheeffectsoftheOCCasionalloadonthesystem.Thisisnotacodecase,onlyaconstructioncase,therefore(OPE).Thishandlesnon-linearities.ThisisourOCCasionalcodecompliancecase,stressesfromPrimaryplusOccasionalloads.2023/6/4BasicStressTheory&工况的定义和维护CAESARIIwillrecommendloadcasesfor“new”jobs.By“new”jobs,wemeanjobsthatdonothavea“._J”file.For“old”jobs,havinga“._J”file,CAESARIIreadsinthedefinedloadcasesandpresentsthemtotheuser.Theloadcaseeditingscreenisshownattheright.2023/6/4BasicStressTheory&工况的定义和维护Onthisdialog,availableloadtypesarelistedintheupperleftlistbox.载荷类型Availableloadcasetypesarelistedinthelowerleftlistbox.工况类型Loadcases(recommendedorpreviouslydefined)areshowninthegridattheright.推荐生成的工况Recommendedloadcasescanalwaysbeobtainedbyclickingonthe[Recommend]button.Theanalysiscommencesbyclickingon“therunningman”.2023/6/4BasicStressTheory&LoadCaseGeneration&MaintenanceSayfora“new”job,theloadcasesattherightarerecommended.Sayyouacceptandruntheseloadcases.Uponreviewingtheoutputyoudiscoverthatpre-defineddisplacementsatnode5wereomitted.Youreturntoinput,addthedisplacements,andstarttheStaticAnalysisprocessoragain.2023/6/4BasicStressTheory&LoadCaseGeneration&MaintenanceCAESARIIreadstheseexistingloadcasesandpresentsthem.Whatwillyourresultsbeifyouruntheseloadcases?Exactlythesameasbefore,becausetheseloadcasesdon’tincludethepredefineddisplacements.Youmustmanuallyadd“D1”totheOPEloadcase,oraskCAESARIItore-recommendtheloadcases.2023/6/4BasicStressTheory&LoadCaseGeneration&MaintenanceNoticetheloadtypelistintheupperleftcontains“D1”now.Thecorrectedloadcasesareshownattheright.2023/6/4BasicStressTheory&LoadCaseGeneration&MaintenanceNoticetheloadtypelistintheupperleftcontains“D1”now.Thecorrectedloadcasesareshownattheright.2023/6/4BasicStressTheory&LoadCaseGeneration&MaintenanceNoticetheloadtypelistintheupperleftcontains“D1”now.Thecorrectedloadcasesareshownattheright.Anytimeyouaddorremoveacompleteloadtype,theloadcasesareinsufficient.Ifyouaddeddisplacementstonode110,wouldtheloadcasesbesufficient?2023/6/4BasicStressTheory&确保您分析对象的正确性RememberCAESARIIisafiniteelementprogram.有限元RememberCAESARIIusesa3Dbeamelement.3D梁单元Rememberyoumusthaveequilibrium:保持平衡Resultantloadsshouldequalappliedloads作用力等于反作用力Gravity(weightonly)loadcaseshouldequaltheweightofthesystem重力等于整个系统的总重量OtherbasicchecksVerifynodal3Dcoordinates尺寸输入是否正确Checkforextremedisplacementsand/orloads最大位移和推力(seehandout)2023/6/4BasicStressTheory&ProblemSolving问题的处理Whatdoyoudowhenyoudon’tliketheresults?Recalltheequationbeingsolved:

[K]{x}={f} wherewesolvefor{x},thedisplacementsFromthesedisplacements,wecomputeelementforces&momentsFromtheseforces&moments,theCodeequationsareappliedandwecomputestresses.2023/6/4BasicStressTheory&ProblemSolvingWhatdoyoudowhenyoudon’tliketheresults?Soifyouhaveastressproblem,itcanonlybecausedbytwothings:ACoderelatedissue(SIFs,codeequation,etc.)Extremeforcesand/ormomentsIfyouhaveaforce/momentproblem,theycanbecausedbyonlytwothings:ImproperelementcharacteristicsExtremedisplacements2023/6/4BasicStressTheory&ProblemSolvingWhatdoyoudowhenyoudon’tliketheresults?Ifyouhaveadisplacementproblem,itcanonlybecausedbytwothings:Improperinput(density,elasticmodulus,appliedloads)ImproperboundaryconditionsDon’tforgettocheckandrechecktheinput.Rememberthatin3Dsystems,aloadinonelocationcancausepivotingsomewhereelsedownstream,resultinginexcessiveforcesandmoments.Trytoisolatetheloadcausingthepr