CAESARII管道应力分析理论

CAESARII_管道应力分析_理论2024/3/28CAESARII管道应力分析理论绪论3D梁单元的特征仅说明了总体的行为。没有考虑局部的作用(表面没有碰撞)。忽略了二次影响。(使转角很小)遵循Hook’s定律。CAESARII管道应力分析理论基本应力 使用局部坐标系可以将管系应力(以及产生这些应力的载荷）theloadsthatcausethem)分为下面几种：纵向应力-SL环向应力-SH径向应力-SR剪切应力-

CAESARII管道应力分析理论纵向应力分量沿着管子的轴向。轴向力轴向力除以面积(F/A)压力Pd/4torP*di/(do2-di2)弯曲力矩Mc/I最大应力发生在圆周的最外面。I/半径

Z(抗弯截面系数);使用M/ZCAESARII管道应力分析理论由于压力产生的环向应力垂直于半径(圆周)Pd/2t再一次用薄壁的近似值。环向应力很重要，尽管它不是“综合应力”的一部分。环向应力根据直径、操作温度下的许用应力、腐蚀余量，加工偏差和压力用来定义管子的壁厚。根据Barlow,Boardman,Lamé来计算。CAESARII管道应力分析理论由于压力产生的径向应力垂直于表面。内表面应力为-P。外表面应力通常为0。由于最大的弯曲应力发生在外表面，所以这一项被忽略。CAESARII管道应力分析理论剪切应力平面内垂直于半径。剪切力这个载荷在外表面最小，因此在管系应力计算中省略了这一项。在支撑处要求局部考虑。扭矩最大的应力发生在外表面。MT/2ZCAESARII管道应力分析理论“综合应力”中的基本应力评价3-D应力S=F/A+Pd/4t+M/Z轴向、环向压力和纵向弯曲所产生的应力之和。根据规范和载荷工况的不同上式将发生变化。CAESARII管道应力分析理论Basisfor“CodeStressEquations”失效理论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。CAESARII管道应力分析理论规范要求的载荷工况规范要求使用两个主要失效方式的失效理论。一次失效。二次失效。(第三种失效方式是偶然失效，它与一次失效相似。）CAESARII管道应力分析理论规范要求的载荷工况一次失效情况力所引起。非自限性。重量、压力和集中力所产生。CAESARII管道应力分析理论规范要求的载荷工况二次失效情况位移所引起。自限性。温度、位移和其它变化载荷——例如，重力。CAESARII管道应力分析理论规范要求的载荷工况(1)=W+T1+P1(OPE)(2)=W+P1(SUS)(3)=DS1-DS2(EXP)操作工况,用于:约束&设备载荷最大位移计算EXP工况持续工况，用于一次载荷下规范应力的计算。膨胀工况，用于“extremedisplacementstressrange”工况3的位移是从工况1的位移减去工况2的位移而得到。CAESARII管道应力分析理论规范要求的载荷工况膨胀工况说明Whatdoes“DS1-DS2(EXP)”mean?Isaloadcasewith“T1(EXP)thesamething?CAESARII管道应力分析理论规范要求的载荷工况膨胀工况说明Thecodestatesthattheexpansionstressesaretobecomputedfromthe"extremedisplacementstressrange".Theseareallveryimportantwords.Considertheirmeaning…EXTREME:Inthissenseitmeansthemost,orthelargest.RANGE:Typicallyadifference.Whatdifference?Thedifferencebetweentheextremes.Whatextremes?DISPLACEMENT:Thisdefineswhatextremestotakethedifferenceof.STRESS:Whatweareeventuallyafter.CAESARII管道应力分析理论规范要求的载荷工况膨胀工况说明Puttingeverythingbacktogether,wearetoldtocomputestressesfromtheextremedisplacementrange.Howcanwedothis?Considertheequationbeingsolved;[K]{x}={f}.Inthisequation,weknow[K]and{f},andwearesolvingfor{x},thedisplacementvector.InCAESARII,whenwesetupanexpansioncase,wedefineitas"DS1-DS2",wherethe"1"and"2"refertothedisplacementvector({x})ofloadcases1and2respectively.CAESARII管道应力分析理论规范要求的载荷工况膨胀工况说明(Obviouslytheloadcasenumbersaresubjecttochangeonajobbyjobbasis.)Whatdoyougetwhenyoutake"DS1-DS2"?Well{x1}-{x2}yields{x'},apseudodisplacementvector.{x'}isnotarealsetofdisplacementsthatyoucangooutandmeasurewitharuler,ratheritisthedifferencebetweentwopositionsofthepipe.Oncewehave{x'},wecanusethesameroutinesusedintheOPEorSUScasestocomputeelementforces,andfinallyelementstresses.CAESARII管道应力分析理论规范要求的载荷工况膨胀工况说明However,theseelementforcesarealsopseudoforces,i.ethedifferenceinforcesbetweentwopositionsofthepipe.Similarly,thestressescomputedarenotrealstresses,butstressdifferences.Thisisexactlywhatthecodewants,thestressdifference,whichwascomputedfromadisplacementrange.Astowhetherornotthisstressdifferenceistheextreme,wellthatdependsonthejob.CAESARII管道应力分析理论规范要求的载荷工况膨胀工况说明Considerthequestionagain;"IsDS1-DS2thesameasaloadcasewithjustT1?".Theanswertothisismaybe.Ifyouhavealinearsystem(fromaboundaryconditionpointofview),thentheanswerisyes.Youwillgetexactlythesameresults.However,ifthesystemisnon-linear(i.e.youhave+Ys,orgaps,orfriction),thentheanswerisno.Youwillgetdifferentresults-howdifferentdependsonthejob.Thereasonforthiscanbefoundbyexaminingtheequation[K]{x}={f}forthetwodifferentmethods.CAESARII管道应力分析理论规范要求的载荷工况膨胀工况说明Forthisdiscussion,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}CAESARII管道应力分析理论规范要求的载荷工况膨胀工况说明Canwesimplifytheaboveequationasfollows? EXP:{xexp}={W+T1+P1}/[K]-{W+P1}/[K]Cancelingliketerms(theonesinred)yields: {xexp}={T1}/[K]Theassumptionhereisthat[Kope]isthesameas[Ksus].Thisassumptionisonlytrueforlinearsystems.Fornon-linearsystems,thestiffnessmatrixisuniqueforeachloadcaseandtheabovecancellationofloadingtermsisincorrect.Yougetthewrongstressresultsfortheexpansioncaseifyousetuploadcasesthisway.CAESARII管道应力分析理论规范要求的载荷工况膨胀工况说明Anotherproofthatthe"DS1-DS2"methodisthecorrectwaytogoistoconsiderajobwithtwooperatingtemperatures,oneaboveambientandonebelowambient.SayT1=+300,andT2=-50.CAESARIIwouldsetuploadcasesasfollows:(1)W+T1+P1(OPE)(2)W+T2+P1(OPE)(3)W+P1(SUS)(4)DS1-DS3(EXP)(5)DS2-DS3(EXP)CAESARII管道应力分析理论规范要求的载荷工况膨胀工况说明Thesecases,whilecorrect,don'taddressthe"extreme"termofthecoderequirements.ThisisbecauseCAESARIIisn'tlookingatwhattheloadcomponentsrepresent.Tosatisfytherequirementsofthecode,theusermustdefineanadditionalloadcase:(6)DS1-DS2(EXP)Thisloadcasewillbethe"extreme",thatwilltypicallygoverntheEXPstresscriteria.Youcan'tdothisatallusingthe"T1"onlymethod.CAESARII管道应力分析理论规范要求的载荷工况膨胀工况说明Tosummarize:Wetakethedifferencebetweentwoloadcasestodetermineadisplacementrange.Fromthisrangewecomputeaforcerangeandthenastressrange.Thecoderequirestheextremedisplacementstressrange.Theuseronlyhastoworryaboutwhetherornotthe"extreme"casehasbeenaddressed.CAESARII管道应力分析理论线性vs非线性这个术语指的是边界条件。方程重新被求解:[K]{x}={f}这是弹簧方程。管系边界条件（例如，约束）指的是刚度或弹簧。可以定义更复杂的边界条件，此时“线性弹簧”的假设将不适用。CAESARII管道应力分析理论线性Vs非线性线性边界条件的一个实例是双向约束，例如：“Y”向支撑。线性边界条件的另一个实例是弹簧支吊架。这些约束中力与位移的关系曲线是一条直线。所以这些约束是线性的。直线的斜率为刚度。CAESARII管道应力分析理论线性Vs非线性“+Y”支撑是非线性支撑。力与位移的关系曲线不是一直线。刚度仅存在于负位移方向。对于正位移，刚度是零。CAESARII管道应力分析理论线性Vs非线性“间隙”也是一个非线性支撑。力与位移的关系曲线不是一直线。间隙中没有刚度。CAESARII管道应力分析理论LinearvsNon-Linear摩擦使约束成为非线性。大的旋转杆也是非线性约束。文件中的非线性约束意味着[Kope]不等于[Ksus]。使用两个其它载荷工况之间的差值来建立(EXP)和(OCC)载荷工况来说明非线性约束。CAESARII管道应力分析理论OccasionalLoadCaseSetupOccasionalloadsareconsidered“primary”,sincetheyareforcedriven.Occasionalloadsoccurinfrequently.Thecodesemployan“allowableincrease”factorbasedonthefrequencyofoccurrenceinthedeterminationoftheallowable,i.e.k*Sh.Examplesofoccasionalloadsarewindandearthquake.CAESARII管道应力分析理论OccasionalLoadCaseSetupThecodeequationfortheOCCasionalloadcaseis:

MA/Z+MB/Z<kShHere,MAisthemomenttermfromtheSUStainedloads,andMBisthemomentfromtheOCCasionalloads.ThisequationstatesthattheOCCasionalcaseisthesumoftheSUStainedstressesandtheOCCasionalstresses.Sowecan’trunaloadcasewithjusta“WIND”loadandsatisfythiscoderequirement.Whatabout“W+P1+WIND”asaloadcase?CAESARII管道应力分析理论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)CAESARII管道应力分析理论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.CAESARII管道应力分析理论LoadCaseGeneration&MaintenanceCAESARIIwillrecommendloadcasesfor“new”jobs.By“new”jobs,wemeanjobsthatdonothavea“._J”file.For“old”jobs,havinga“._J”file,CAESARIIreadsinthedefinedloadcasesandpresentsthemtotheuser.Theloadcaseeditingscreenisshownattheright.CAESARII管道应力分析理论LoadCaseGeneration&MaintenanceCAESARIIwillrecommendloadcasesfor“new”jobs.By“new”jobs,wemeanjobsthatdonothavea“._J”file.For“old”jobs,havinga“._J”file,CAESARIIreadsinthedefinedloadcasesandpresentsthemtotheuser.Theloadcaseeditingscreenisshownattheright.CAESARII管道应力分析理论LoadCaseGeneration&MaintenanceOnthisdialog,availableloadtypesarelistedintheupperleftlistbox.Availableloadcasetypesarelistedinthelowerleftlistbox.Loadcases(recommendedorpreviouslydefined)areshowninthegridattheright.Recommendedloadcasescanalwaysbeobtainedbyclickingonthe[Recommend]button.Theanalysiscommencesbyclickingon“therunningman”.CAESARII管道应力分析理论LoadCaseGeneration&MaintenanceSayfora“new”job,theloadcasesattherightarerecommended.Sayyouacceptandruntheseloadcases.Uponreviewingtheoutputyoudiscoverthatpre-defineddisplacementsatnode5wereomitted.Youreturntoinput,addthedisplacements,andstarttheStaticAnalysisprocessoragain.CAESARII管道应力分析理论LoadCaseGeneration&MaintenanceCAESARIIreadstheseexistingloadcasesandpresentsthem.Whatwillyourresultsbeifyouruntheseloadcases?Exactlythesameasbefore,becausetheseloadcasesdon’tincludethepredefineddisplacements.Youmustmanuallyadd“D1”totheOPEloadcase,oraskCAESARIItore-recommendtheloadcases.CAESARII管道应力分析理论LoadCaseGeneration&MaintenanceNoticetheloadtypelistintheupperleftcontains“D1”now.Thecorrectedloadcasesareshownattheright.CAESARII管道应力分析理论LoadCaseGeneration&MaintenanceNoticetheloadtypelistintheupperleftcontains“D1”now.Thecorrectedloadcasesareshownattheright.CAESARII管道应力分析理论LoadCaseGeneration&MaintenanceNoticetheloadtypelistintheupperleftcontains“D1”now.Thecorrectedloadcasesareshownattheright.Anytimeyouaddorremoveacompleteloadtype,theloadcasesareinsufficient.Ifyouaddeddisplacementstonode110,wouldtheloadcasesbesufficient?CAESARII管道应力分析理论InsuringYouAnalyzeWhatYouThinkYou’reAnalyzingRememberCAESARIIisafiniteelementprogram.RememberCAESARIIusesa3Dbeamelement.Rememberyoumusthaveequilibrium:ResultantloadsshouldequalappliedloadsGravity(weightonly)loadcaseshouldequaltheweightofthesystemOtherbasicchecksVerifynodal3DcoordinatesCheckforextremedisplacementsand/orloads(seehandout)CAESARII管道应力分析理论问题解决当不满意结果时，你应做什么？重新求解方程：

[K]{x}={f} 其中我们求解的{x}是位移。由这些位移，我们可以计算单元力&力矩。由这些力&力矩，使用规范方程计算出应力。CAESARII管道应力分析理论问题解决当不满意结果时，你应做什么？如果是应力问题，它可能是由于下面两个问题引起的：与规范有关的问题(SIFs、规范方程等等）极限力和/或力矩如果是力/力矩问题，它可能是由下面两个问题所引起：不正确的单元特性极限位移CAESARII管道应力分析理论ProblemSolvingWhatdoyoudowhenyoudon’tliketheresults?Ifyouhaveadisplacementproblem,itcanonlybec