CAESARII管道應力分析培訓-課件

CAESARII管道應力分析培訓王大輝北京艾思弗軟件公司2023/1/5BasicStressTheory&CAESARII管道應力分析培訓王大輝2022/12/212023/1/5BasicStressTheory&2022/12/26Ba2介紹培訓的目的在于讓您了解和掌握應力分析的基礎概念模型和邊界條件的建立結果的分析和評判往復壓縮機的分析專題日常遇到的問題和解決方法2023/1/5BasicStressTheory&介紹培訓的目的在于讓您了解和掌握2022/12/26Ba3介紹3D梁單元的特征無限細的桿單元全部行為靠端點位移決定彎曲變形是主要的2023/1/5BasicStressTheory&介紹3D梁單元的特征2022/12/26BasicSt4介紹3DBeamElementCharacteristics3D梁單元的特征僅說明整體行為無局部作用（表面沒有碰撞）忽略二次影響（小轉動）遵循胡克定律2023/1/5BasicStressTheory&介紹3DBeamElementCharacteri5StressBasics應力基礎 局部坐標系下管道應力分類（引發(fā)應力的載荷）軸向應力LongitudinalStress-SL環(huán)向應力HoopStress-SH徑向應力RadialStress-SR剪切應力ShearStress-2023/1/5BasicStressTheory&StressBasics應力基礎 局部坐標系下管道應力分類6軸向應力沿管道軸向Alongaxisofpipe軸向力引起AxialForce軸向力/面積(F/A)內壓引起PressurePd/4torP*di/(do2-di2)彎矩引起B(yǎng)endingMomentMc/I最大應力環(huán)向的外表面某點處

I/radiusZ(截面模量);useM/Z2023/1/5BasicStressTheory&軸向應力沿管道軸向Alongaxisofpipe2027壓力引起的環(huán)向應力環(huán)向（垂直于半徑）

Pd/2t和壁厚緊密相關環(huán)向應力十分重要，但規(guī)范應力不考慮它。Hoopisveryimportant,itsjustnotpartofthe“codestress”環(huán)向應力用來確定壁厚：依據直徑、許用應力、腐蝕裕量、加工偏差、壓力確定管道壁厚。2023/1/5BasicStressTheory&壓力引起的環(huán)向應力環(huán)向（垂直于半徑）2022/12/26B8壓力引發(fā)的徑向應力沿半徑方向向內內壁的徑向應力大小是：-P外壁的徑向應力大小為0最大彎曲應力發(fā)生在管道的外表面，故該項忽略2023/1/5BasicStressTheory&壓力引發(fā)的徑向應力沿半徑方向向內2022/12/26Basi9剪切應力ShearStresses平面內垂直半徑ShearForce剪力在外表面剪力很小，應力計算忽略支架設計有時需要考慮Torque扭矩最大應力在外表面

MT/2Z2023/1/5BasicStressTheory&剪切應力ShearStresses平面內垂直半徑2022/103-D應力評定Aloaded,3-Dpipecontainsarepresentativeinfinitesimalstresscubeaddgraphic(Fig1-13)Thisstresscubeisinequilibriumandcanberotatedinspaceaddgraphic(rotatedcubewithloads)Thiscubecanberotatedsothatshearstressesarezero.ThisresultsinthePrincipalStresses.2023/1/5BasicStressTheory&3-D應力評定Aloaded,3-Dpipecon11Simplifyingtoa2-DStressThisplanecanberotatedtoeithereliminateormaximizeshearstressbyusingMohr’sCircle:Sinceweusetheoutsidesurfacewhereradialstressiszero;let’smovetoaplaneelement:2023/1/5BasicStressTheory&Simplifyingtoa2-DStressThi12UsingMohr’sCircleCutthesquareattocalculateS1Cutthesquareat+90tocalculateS2Cutthesquareat+45tocalculatemax2023/1/5BasicStressTheory&UsingMohr’sCircleCutthesqu13UsingMohr’sCircleBrittlematerial(failurebyfracture)-maxprincipalstressDuctilematerial(failurebygeneralyielding)-maxprincipalstressisusedtosetwallthicknessMaximumshearstressisagoodpredictionanderrsontheconservativesideseep84&85ofAdv.Mech.OfMat’ls2023/1/5BasicStressTheory&UsingMohr’sCircleBrittlemat14基本應力“CodeStress規(guī)范應力”應力評定Evaluatinga3-DStressS=F/A+Pd/4t+M/Z軸向力、軸向壓力，軸向彎矩一起的分量加和規(guī)范不同，上面的算式也不同那些應力沒有包含進來？2023/1/5BasicStressTheory&基本應力“CodeStress規(guī)范應力”應力評定Eval15基本應力“CodeStress規(guī)范應力”幾個實效理論AFewFailureTheories變形能或八面體剪切應力(根據米賽斯理論和其它的理論）。最大剪應力理論

（Columb理論）

。大多數理論都根據這個理論。由于剪切影響而限制最大主應力(Rankine理論)。CAESARII132列輸出應力報告中顯示了米賽斯或最大剪應力強度理論。應力報告由configuration設置來決定。2023/1/5BasicStressTheory&基本應力“CodeStress規(guī)范應力”幾個實效理論A16基本應力“CodeStress規(guī)范應力”基于最大剪應力實效理論，ASME規(guī)范委員會頒布了規(guī)范應力方程Basedonthemaximumshearfailuretheory,theCodeCommitteedevelopedthe“codeequations”目的在于避免管道系統實效Purposewastoreducesystemfailures這種解決辦法很實用，但仍然有問題存在Thisapproachworkedwell,buttherewerestillproblems,evenaslateaspostWorldWarII.研究表明直管道比較符合理論Studiesshowedsystemsofstraightpipematchedtheory研究表明元件失效比理論發(fā)生的早Studiesshowedsystemswithfittingsfailedearlierthantheorypredicted.ASME規(guī)范委員會委托Markl來研究這個問題CodeCommitteecommissionedMarkltostudythis...2023/1/5BasicStressTheory&基本應力“CodeStress規(guī)范應力”基于最大剪應力實17基本應力“CodeStress規(guī)范應力”Markl’s試驗和結果將試驗用的管道充滿水，按某個方向和位移反復搖晃管道。Testconfigurationsfilledwithwaterandcycledthroughapredetermineddisplacement預測失效循環(huán)次數Theoryshouldbeabletopredict“cyclestofailure”發(fā)現最先失效的管件及其原因Fittingscausedearlyfailure…because…對管件引入應力集中Stressesconcentrationsareintroducedbyfittings分析試驗數據，修正軸向應力彎曲項Testdataanalyzedandamodificationtothebendingtermofthecodestressequationwasintroduced:Sbending=iM/z2023/1/5BasicStressTheory&基本應力“CodeStress規(guī)范應力”Markl’s18基本應力“CodeStress規(guī)范應力”Markl’s試驗和結果應力增強系數i和元件的形式有關對于彎頭“i”的計算需要如下:我們需要彎頭的幾何參數計算彎頭柔性“h”計算應力增大系數StressIntensificationFactor“i”,石化規(guī)范對平面內、外的SIF取值不同，電力取相同的sif2023/1/5BasicStressTheory&基本應力“CodeStress規(guī)范應力”Markl’s19基本應力“CodeStress規(guī)范應力”Markl’s試驗和結果Aload“intheplane”ofthefittingcauses“in-plane”bending平面內Aload“outoftheplane”ofthefittingcauses“out-of-plane”bending平面外2023/1/5BasicStressTheory&基本應力“CodeStress規(guī)范應力”Markl’s20基本應力“CodeStress規(guī)范應力”Markl’s試驗和結果規(guī)范上的附注十分重要PetroChemcodesmodifySIF(andflexibilityfactor)basedonpressurestiffeninginanote石化規(guī)范規(guī)定壓力硬化影響ＳＩＦ和柔性系數應力算式變化如下 S=F/A+Pd/4t+iM/z應力增大系數不能小于１2023/1/5BasicStressTheory&基本應力“CodeStress規(guī)范應力”Markl’s21Basisfor“CodeStressEquations”Markl’s試驗和結果TheSIFisa“fudge”factor

SIF是個近似的參數TheSIFattemptstoincreasethebendingstresscomputedatthenodepoint,tomatchtheactualhigherstressduetothestressconcentrationcausedbythefitting.引入SIF在于改變特殊管件應力集中，讓他們的應力根實際大小更接近。Marklonlytested4x4Stdfittings!!!但Markl僅測試了４ｘ４AdditionalworkisstillbeingdonetodayinthefieldofSIFs.Resultsarepublishedin:PVP,WRC,JournalofPressureVesselTechnology.其余的工作人們仍然在繼續(xù)進行。2023/1/5BasicStressTheory&Basisfor“CodeStressEquatio22規(guī)范效驗的工況兩種失效：Primaryfailure一次失效Secondaryfailure二次失效(AthirdfailuremodeaddressedisOccasional,whichissimilartoPrimary.)2023/1/5BasicStressTheory&規(guī)范效驗的工況兩種失效：2022/12/26BasicSt23規(guī)范效驗的工況PrimaryFailureCase一次失效力的作用ForceDriven非自限性NotSelf-Limiting重量、壓力、集中力Weight,Pressure,

ConcentratedForces2023/1/5BasicStressTheory&規(guī)范效驗的工況PrimaryFailureCase20224規(guī)范效驗的工況PrimaryFailureCase一次失效力的作用ForceDriven非自限性NotSelf-Limiting重量、壓力、集中力,Weight、Pressure,

ConcentratedForces2023/1/5BasicStressTheory&規(guī)范效驗的工況PrimaryFailureCase20225規(guī)范效驗的工況SecondaryFailureCase二次失效位移作用DisplacementDriven自限性IsSelf-Limiting溫度、位移和其他變化載荷引起的Temperature,Displacement,plusothervaryingloads-i.e.weight2023/1/5BasicStressTheory&規(guī)范效驗的工況SecondaryFailureCase226規(guī)范效驗的工況

(1)=W+T1+P1(OPE)(2)=W+P1(SUS)(3)=DS1-DS2(EXP)Operatingcase,usedfor:熱態(tài)restraint&equipmentloads推力和彎矩maximumdisplacements最大位移computationofEXPcase計算二次應力SustainedcaseforPRIMARYloadsandstresscompliance計算一次應力Expansioncasefor“extremedisplacementstressrange”膨脹工況，計算二次應力displacementsforcase3aredisplacementsfromcase1minusdisplacementsfromcase22023/1/5BasicStressTheory&規(guī)范效驗的工況(1)=W+T1+P1(OPE27規(guī)范效驗的工況膨脹工況的解釋ExpansionCaseExplainedWhatdoes“DS1-DS2(EXP)”mean?Isaloadcasewith“T1(EXP)thesamething?2023/1/5BasicStressTheory&規(guī)范效驗的工況膨脹工況的解釋ExpansionCaseE28LoadCasesforCodeCompliance膨脹工況的解釋ExpansionCaseExplainedThecodestatesthattheexpansionstressesaretobecomputedfromthe"extremedisplacementstressrange".Theseareallveryimportantwords.Considertheirmeaning…EXTREME極端:Inthissenseitmeansthemost,orthelargest.RANGE范圍:Typicallyadifference.Whatdifference?Thedifferencebetweentheextremes.Whatextremes?DISPLACEMENT位移:Thisdefineswhatextremestotakethedifferenceof.STRESS應力:Whatweareeventuallyafter.2023/1/5BasicStressTheory&LoadCasesforCodeCompliance29LoadCasesforCodeCompliance膨脹工況的解釋ExpansionCaseExplainedPuttingeverythingbacktogether,wearetoldtocomputestressesfromtheextremedisplacementrange.Howcanwedothis?計算最大位移范圍的應力Considertheequationbeingsolved;[K]{x}={f}.Inthisequation,weknow[K]and{f},andwearesolvingfor{x},thedisplacementvector.InCAESARII,whenwesetupanexpansioncase,wedefineitas"DS1-DS2",wherethe"1"and"2"refertothedisplacementvector({x})ofloadcases1and2respectively.2023/1/5BasicStressTheory&LoadCasesforCodeCompliance30LoadCasesforCodeCompliance膨脹工況的解釋ExpansionCaseExplained(Obviouslytheloadcasenumbersaresubjecttochangeonajobbyjobbasis.)Whatdoyougetwhenyoutake"DS1-DS2"?Well{x1}-{x2}yields{x'},apseudodisplacementvector.{x'}isnotarealsetofdisplacementsthatyoucangooutandmeasurewitharuler,ratheritisthedifferencebetweentwopositionsofthepipe.Oncewehave{x'},wecanusethesameroutinesusedintheOPEorSUScasestocomputeelementforces,andfinallyelementstresses.2023/1/5BasicStressTheory&LoadCasesforCodeCompliance31LoadCasesforCodeCompliance膨脹工況的解釋ExpansionCaseExplainedHowever,theseelementforcesarealsopseudoforces,i.ethedifferenceinforcesbetweentwopositionsofthepipe.力的大小是兩個工況力的差值Similarly,thestressescomputedarenotrealstresses,butstressdifferences.應力不是真實應力，是應力的差值Thisisexactlywhatthecodewants,thestressdifference,whichwascomputedfromadisplacementrange.二次應力是位移變化量導致的Astowhetherornotthisstressdifferenceistheextreme,wellthatdependsonthejob.2023/1/5BasicStressTheory&LoadCasesforCodeCompliance32LoadCasesforCodeCompliance膨脹工況的解釋ExpansionCaseExplainedDS1-DS2和T1“一樣嗎？.有可能.如果是線性系統，答案是一樣的。如果是非線性系統(如你有+Ys,orgaps,orfriction),答案是不一樣的。原因是兩個工況應用[K]{x}={f}。Thereasonforthiscanbefoundbyexaminingtheequation[K]{x}={f}forthetwodifferentmethods.2023/1/5BasicStressTheory&LoadCasesforCodeCompliance33LoadCasesforCodeComplianceExpansionCaseExplainedForthisdiscussion,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}2023/1/5BasicStressTheory&LoadCasesforCodeCompliance34LoadCasesforCodeCompliance膨脹工況解釋ExpansionCaseExplainedCanwesimplifytheaboveequationasfollows? EXP:{xexp}={W+T1+P1}/[K]-{W+P1}/[K]Cancelingliketerms(theonesinred)yields: {xexp}={T1}/[K]問題在于[Kope]和[Ksus]是否相等.線性系統相等.非線性系統不相等2023/1/5BasicStressTheory&LoadCasesforCodeCompliance35LoadCasesforCodeCompliance膨脹工況解釋ExpansionCaseExplained如果一個系統有兩個操作溫度。Anotherproofthatthe"DS1-DS2"methodisthecorrectwaytogoistoconsiderajobwithtwooperatingtemperatures,oneaboveambientandonebelowambient.如T1=+300,andT2=-50.CAESARII軟件自動建立如下工況:(1)W+T1+P1(OPE)(2)W+T2+P1(OPE)(3)W+P1(SUS)(4)DS1-DS3(EXP)(5)DS2-DS3(EXP)2023/1/5BasicStressTheory&LoadCasesforCodeCompliance36LoadCasesforCodeCompliance膨脹工況解釋ExpansionCaseExplained上述工況正確，但沒能說明規(guī)范要求的最大應力范圍因為CII并不能判斷荷載所代表的具體含義為滿足規(guī)范的要求，用戶必須自己定義:(6)DS1-DS2(EXP)這個工況是最大位移膨脹應力，正是規(guī)范所要求的。您根本不能考慮使用T1來計算膨脹應力.2023/1/5BasicStressTheory&LoadCasesforCodeCompliance37LoadCasesforCodeComplianceExpansionCaseExplained膨脹工況的解釋Tosummarize:概括如下Wetakethedifferencebetweentwoloadcasestodetermineadisplacementrange.兩個工況確定位移范圍Fromthisrangewecomputeaforcerangeandthenastressrange.由此我們確定力的范圍和應力范圍Thecoderequirestheextremedisplacementstressrange.規(guī)范要求極端的應力范圍Theuseronlyhastoworryaboutwhetherornotthe“extreme”casehasbeenaddressed.用戶僅考慮最大應力范圍即可2023/1/5BasicStressTheory&LoadCasesforCodeCompliance38LinearvsNon-Linear線性和非線性Terminologyappliestoboundaryconditions.邊界條件的類型Recalltheequationbeingsolved:[K]{x}={f}Thisistheequationofaspring.Thepipingsystemboundaryconditions(i.e.therestraints)arerepresentedasstiffnesses,orsprings.管道邊界條件代表剛度或彈簧Morecomplexboundaryconditionscanbedefined,invalidatingthe“l(fā)inearspring”assumption.2023/1/5BasicStressTheory&LinearvsNon-Linear線性和非線性Term39LinearvsNon-Linear線性和非線性線性約束

boundaryconditionisadoubleactingrestraint,suchasa“Y”support.一種是上下約束Anotherexampleofalinearboundaryconditionisaspringhanger.一種是彈簧Theforceversusdisplacementcurvefortheserestraintsisastraightline…力和位移是線性關系Thereforetheserestraintsarelinear.約束是線性的Theslopeofthelineisthestiffness.斜率是剛度2023/1/5BasicStressTheory&LinearvsNon-Linear線性和非線性線性約束40LinearvsNon-Linear線性和非線性非線性約束A“+Y”supportisanon-linearsupport.支架Itsforcevsdisplacementcurveisnotastraightline.力和位移不是直線關系Stiffnessonlyexistsfornegativedisplacements.向下的位移是剛度是存在的Forpositivedisplacements,thestiffnessiszero.向上的位移，剛度變?yōu)椋?023/1/5BasicStressTheory&LinearvsNon-Linear線性和非線性非線性約41LinearvsNon-Linear線性和非線性A“gap”isalsoanon-linearsupport.間隙的引進Theforcevsdisplacementcurveisnotastraightline.力和位移不是線性關系Thereisnostiffnessinthegap.間隙部分沒有剛度2023/1/5BasicStressTheory&LinearvsNon-Linear線性和非線性A“g42LinearvsNon-Linear線性和非線性Frictionmakesarestraintnon-linear摩擦讓約束非線性Largerotationrodsarealsonon-linearrestraints大的轉動吊桿讓約束非線性Non-linearrestraintsinajobmeanthat[Kope]isnotequalto[Ksus].非線性后，熱態(tài)管道剛度和冷態(tài)剛度不一致(EXP)and(OCC)loadcasesmustbeconstructedusingthedifferencebetweentwootherloadcasestoaccountfornon-linearrestraints.2023/1/5BasicStressTheory&LinearvsNon-Linear線性和非線性Fric43偶然工況的建立Occasionalloadsareconsidered“primary”,sincetheyareforcedriven.偶然荷載是主要載荷，力引起的。Occasionalloadsoccurinfrequently.不經常發(fā)生Thecodesemployan“allowableincrease”factorbasedonthefrequencyofoccurrenceinthedeterminationoftheallowable,i.e.k*Sh.基于發(fā)生的頻率，確定ｋ值的大小Examplesofoccasionalloadsarewindandearthquake.偶然載荷是風載荷和地震載荷2023/1/5BasicStressTheory&偶然工況的建立Occasionalloadsareco44偶然工況的建立ThecodeequationfortheOCCasionalloadcaseis:

MA/Z+MB/Z<kShHere,MAisthemomenttermfromtheSUStainedloads,冷態(tài)荷載引發(fā)力矩andMBisthemomentfromtheOCCasionalloads.偶然荷載引發(fā)力矩ThisequationstatesthattheOCCasionalcaseisthesumoftheSUStainedstressesandtheOCCasionalstresses.偶然工況是冷態(tài)和偶然的疊加Sowecan’trunaloadcasewithjusta“WIND”loadandsatisfythiscoderequirement.Whatabout“W+P1+WIND”asaloadcase?2023/1/5BasicStressTheory&偶然工況的建立Thecodeequationfort45OccasionalLoadCaseSetupThe“W+P1+WIND”casewillworkfor“l(fā)inear”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)2023/1/5BasicStressTheory&OccasionalLoadCaseSetupThe46OccasionalLoadCaseSetup(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.2023/1/5BasicStressTheory&OccasionalLoadCaseSetup(1)47工況的定義和維護CAESARIIwillrecommendloadcasesfor“new”jobs.By“new”jobs,wemeanjobsthatdonothavea“._J”file.For“old”jobs,havinga“._J”file,CAESARIIreadsinthedefinedloadcasesandpresentsthemtotheuser.Theloadcaseeditingscreenisshownattheright.2023/1/5BasicStressTheory&工況的定義和維護CAESARIIwillrecomme48工況的定義和維護Onthisdialog,availableloadtypesarelistedintheupperleftlistbox.載荷類型Availableloadcasetypesarelistedinthelowerleftlistbox.工況類型Loadcases(recommendedorpreviouslydefined)areshowninthegridattheright.推薦生成的工況Recommendedloadcasescanalwaysbeobtainedbyclickingonthe[Recommend]button.Theanalysiscommencesbyclickingon“therunningman”.2023/1/5BasicStressTheory&工況的定義和維護Onthisdialog,availa49LoadCaseGeneration&MaintenanceSayfora“new”job,theloadcasesattherightarerecommended.Sayyouacceptandruntheseloadcases.Uponreviewingtheoutputyoudiscoverthatpre-defineddisplacementsatnode5wereomitted.Youreturntoinput,addthedisplacements,andstarttheStaticAnalysisprocessoragain.2023/1/5BasicStressTheory&LoadCaseGeneration&Mainten50LoadCaseGeneration&MaintenanceCAESARIIreadstheseexistingloadcasesandpresentsthem.Whatwillyourresultsbeifyouruntheseloadcases?Exactlythesameasbefore,becausetheseloadcasesdon’tincludethepredefineddisplacements.Youmustmanuallyadd“D1”totheOPEloadcase,oraskCAESARIItore-recommendtheloadcases.2023/1/5BasicStressTheory&LoadCaseGeneration&Mainten51LoadCaseGeneration&MaintenanceNoticetheloadtypelistintheupperleftcontains“D1”now.Thecorrectedloadcasesareshownattheright.2023/1/5BasicStressTheory&LoadCaseGeneration&Mainten52LoadCaseGeneration&MaintenanceNoticetheloadtypelistintheupperleftcontains“D1”now.Thecorrectedloadcasesareshownattheright.2023/1/5BasicStressTheory&LoadCaseGeneration&Mainten53LoadCaseGeneration&MaintenanceNoticetheloadtypelistintheupperleftcontains“D1”now.Thecorrectedloadcasesareshownattheright.Anytimeyouaddorremoveacompleteloadtype,theloadcasesareinsufficient.Ifyouaddeddisplacementstonode110,wouldtheloadcasesbesufficient?2023/1/5BasicStressTheory&LoadCaseGeneration&Mainten54確保您分析對象的正確性RememberCAESARIIisafiniteelementprogram.有限元RememberCAESARIIusesa3Dbeamelement.3D梁單元Rememberyoumusthaveequilibrium:保持平衡Resultantloadsshouldequalappliedloads作用力等于反作用力Gravity(weightonly)loadcaseshouldequaltheweightofthesystem重力等于整個系統的總重量OtherbasicchecksVerifynodal3Dcoordinates尺寸輸入是否正確Checkforextremedisplacementsand/orloads最大位移和推力(seehandout)2023/1/5BasicStressTheory&確保您分析對象的正確性RememberCAESARII55ProblemSolving問題的處理Whatdoyoudowhenyoudon’tliketheresults?Recalltheequationbeingsolved:

[K]{x}={f} wherewesolvefor{x},thedisplacementsFromthesedisplacements,wecomputeelementforces&momentsFromtheseforces&moments,theCodeequationsareappliedandwecomputestresses.2023/1/5BasicStressTheory&ProblemSolving問題的處理Whatdoyo56ProblemSolvingWhatdoyoudowhenyoudon’tliketheresults?Soifyouhaveastressproblem,itcanonlybecausedbytwothings:ACoderelatedissue(SIFs,codeequation,etc.)Extremeforcesand/ormomentsIfyouhaveaforce/momentproblem,theycanbecausedbyonlytwothings:ImproperelementcharacteristicsExtremedisplacements2023/1/5BasicStressTheory&ProblemSolvingWhatdoyoudo57ProblemSolvingWhatdoyoudowhenyoudon’tliketheresults?Ifyouhaveadisplacementproblem,itcanonlybecausedbytwothings:Improperinput(density,elasticmodulus,appliedloads)ImproperboundaryconditionsDon’tforgettocheckandrechecktheinput.Rememberthatin3Dsystems,aloadinonelocationcancausepivotingsomewhereelsedownstream,resultinginexcessiveforcesandmoments.Trytoisolatetheloadcausingtheproblem,andtraceitsorigin.2023/1/5BasicStressTheory&ProblemSolvingWhatdoyoudo58ProblemSolving設計和分析過程DesignbyAnalysis-TheDesignCycle收集數據Gatherallthedata,withassumptions建立分析模型和工況Generatethemodelandloadsets分析計算Performtheanalysis檢查結果Checktheresultsandassumptions診斷問題Diagnoseanyproblems調整、改進和精細模型Makecorrectionsandrefinementsasnecessary再分析Re-runthemodifiedmodel/loadsets報告和輸出Documenttheanalysis2023/1/5BasicStressTheory&ProblemSolving設計和分析過程Designb59其他話題OtherImportantTopics關聯節(jié)點ConnectingNodes-CNODEsImportanttopic-CNODEswillbediscussedseveraltimesduringthisseminar.CNODEs十分靈活，是CII的一大特色。使用CNODE的關鍵是切記：自由度關聯

AssociationofDegreesofFreedom可以將CNODE假設為球頭關節(jié)ThinkofaCNODEasa“ball&socketjoint”,有些自由度是關聯的(如移動），而其他不關聯(如轉動).2023/1/5BasicStressTheory&其他話題OtherImportantTopics關聯節(jié)點60其他話題OtherImportantTopicsCNODE應用案例…管道支撐在結構上面Pipeonstructuralsteel設備管口和設備的關系Nozzleonavesselshell2023/1/5BasicStressTheory&其他話題OtherImportantTopicsCNOD61其他話題OtherImportantTopicsCNODE應用案例…膨脹節(jié)拉桿ExpansionJointTie-bar彈簧和吊桿的連接SpringHangerrodconnection2023/1/5BasicStressTheory&其他話題OtherImportantTopicsCNOD62其他話題OtherImportantTopicsCNODE應用案例…管道支撐在結構上面支架為U型螺栓如果我們同時建立結構模型，我們如何分析？首先，我們的判斷那些自由度DOFs是關聯的，而那些是不關聯的。Y&X關聯,Z,RX,RY,andRZ不關聯.2023/1/5BasicStressTheory&其他話題OtherImportantTopicsCNOD63其他話題OtherImportantTopicsCNODE應用案例…CII約束信息的輔助狀態(tài)欄IfwespecifyanodenumberintheCNODEfield,wehavedefinedaCNODEconnection.Herewespecifytworestraints.WiththeCNODEfieldspecified,therestraintisnottoafixedpointinspace,butrathertotheCNODE.2023/1/5BasicStressTheory&其他話題OtherImportantTopicsCNOD64其他話題OtherImportantTopicsConnectingNodes-CNODES膨脹節(jié)TheCAESARIIexpansionjointmodelerautomaticallysetsupCNODEsfortie-bars.柔性管口Thenozzleauxiliaries(WRC-297,API-650,&BS-5500)alsoautomaticallysetupCNODEsforthenozzle/shellconnection.其他ManualdefinitionofCNODEsisthenreducedtospecialconnectiontypes:管道支撐在結構上pipeonsteel彈簧吊桿hangerrods夾套管道jacketedpiping2023/1/5BasicStressTheory&其他話題OtherImportantTopicsConn65CAESARII管道應力分析培訓王大輝北京艾思弗軟件公司2023/1/5BasicStressTheory&CAESARII管道應力分析培訓王大輝2022/12/2662023/1/5BasicStressTheory&2022/12/26Ba67介紹培訓的目的在于讓您了解和掌握應力分析的基礎概念模型和邊界條件的建立結果的分析和評判往復壓縮機的分析專題日常遇到的問題和解決方法2023/1/5BasicStressTheory&介紹培訓的目的在于讓您了解和掌握2022/12/26Ba68介紹3D梁單元的特征無限細的桿單元全部行為靠端點位移決定彎曲變形是主要的2023/1/5BasicStressTheory&介紹3D梁單元的特征2022/12/26BasicSt69介紹3DBeamElementCharacteristics3D梁單元的特征僅說明整體行為無局部作用（表面沒有碰撞）忽略二次影響（小轉動）遵循胡克定律2023/1/5BasicStressTheory&介紹3DBeamElementCharacteri70StressBasics應力基礎 局部坐標系下管道應力分類（引發(fā)應力的載荷）軸向應力LongitudinalStress-SL環(huán)向應力HoopStress-SH徑向應力RadialStress-SR剪切應力ShearStress-2023/1/5BasicStressTheory&StressBasics應力基礎 局部坐標系下管道應力分類71軸向應力沿管道軸向Alongaxisofpipe軸向力引起AxialForce軸向力/面積(F/A)內壓引起PressurePd/4torP*di/(do2-di2)彎矩引起B(yǎng)endingMomentMc/I最大應力環(huán)向的外表面某點處

I/radiusZ(截面模量);useM/Z2023/1/5BasicStressTheory&軸向應力沿管道軸向Alongaxisofpipe20272壓力引起的環(huán)向應力環(huán)向（垂直于半徑）

Pd/2t和壁厚緊密相關環(huán)向應力十分重要，但規(guī)范應力不考慮它。Hoopisveryimportant,itsjustnotpartofthe“codestress”環(huán)向應力用來確定壁厚：依據直徑、許用應力、腐蝕裕量、加工偏差、壓力確定管道壁厚。2023/1/5BasicStressTheory&壓力引起的環(huán)向應力環(huán)向（垂直于半徑）2022/12/26B73壓力引發(fā)的徑向應力沿半徑方向向內內壁的徑向應力大小是：-P外壁的徑向應力大小為0最大彎曲應力發(fā)生在管道的外表面，故該項忽略2023/1/5BasicStressTheory&壓力引發(fā)的徑向應力沿半徑方向向內2022/12/26Basi74剪切應力ShearStresses平面內垂直半徑ShearForce剪力在外表面剪力很小，應力計算忽略支架設計有時需要考慮Torque扭矩最大應力在外表面

MT/2Z2023/1/5BasicStressTheory&剪切應力ShearStresses平面內垂直半徑2022/753-D應力評定Aloaded,3-Dpipecontainsarepresentativeinfinitesimalstresscubeaddgraphic(Fig1-13)Thisstresscubeisinequilibriumandcanberotatedinspaceaddgraphic(rotatedcubewithloads)Thiscubecanberotatedsothatshearstressesarezero.ThisresultsinthePrincipalStresses.2023/1/5BasicStressTheory&3-D應力評定Aloaded,3-Dpipecon76Simplifyingtoa2-DStressThisplanecanberotatedtoeithereliminateormaximizeshearstressbyusingMohr’sCircle:Sinceweusetheoutsidesurfacewhereradialstressiszero;let’smovetoaplaneelement:2023/1/5BasicStressTheory&Simplifyingtoa2-DStressThi77UsingMohr’sCircleCutthesquareattocalculateS1Cutthesquareat+90tocalculateS2Cutthesquareat+45tocalculatemax2023/1/5BasicStressTheory&UsingMohr’sCircleCutthesqu78UsingMohr’sCircleBrittlematerial(failurebyfracture)-maxprincipalstressDuctilematerial(failurebygeneralyielding)-maxprincipalstressisusedtosetwallthicknessMaximumshearstressisagoodpredictionanderrsontheconservativesideseep84&85ofAdv.Mech.OfMat’ls2023/1/5BasicStressTheory&UsingMohr’sCircleBrittlemat79基本應力“CodeStress規(guī)范應力”應力評定Evaluatinga3-DStressS=F/A+Pd/4t+M/Z軸向力、軸向壓力，軸向彎矩一起的分量加和規(guī)范不同，上面的算式也不同那些應力沒有包含進來？2023/1/5BasicStressTheory&基本應力“CodeStress規(guī)范應力”應力評定Eval80基本應力“CodeStress規(guī)范應力”幾個實效理論AFewFailureTheories變形能或八面體剪切應力(根據米賽斯理論和其它的理論）。最大剪應力理論

（Columb理論）

。大多數理論都根據這個理論。由于剪切影響而限制最大主應力(Rankine理論)。CAESARII132列輸出應力報告中顯示了米賽斯或最大剪應力強度理論。應力報告由configuration設置來決定。2023/1/5BasicStressTheory&基本應力“CodeStress規(guī)范應力”幾個實效理論A81基本應力“CodeStress規(guī)范應力”基于最大剪應力實效理論，ASME規(guī)范委員會頒布了規(guī)范應力方程Basedonthemaximumshearfailuretheory,theCodeCommitteedevelopedthe“codeequations”目的在于避免管道系統實效Purposewastoreducesystemfailures這種解決辦法很實用，但仍然有問題存在Thisapproachworkedwell,buttherewerestillproblems,evenaslateaspostWorldWarII.研究表明直管道比較符合理論Studiesshowedsystemsofstraightpipematchedtheory研究表明元件失效比理論發(fā)生的早Studiesshowedsystemswithfittingsfailedearlierthantheorypredicted.ASME規(guī)范委員會委托Markl來研究這個問題CodeCommitteecommissionedMarkltostudythis...2023/1/5BasicStressTheory&基本應力“CodeStress規(guī)范應力”基于最大剪應力實82基本應力“CodeStress規(guī)范應力”Markl’s試驗和結果將試驗用的管道充滿水，按某個方向和位移反復搖晃管道。Testconfigurationsfilledwithwaterandcycledthroughapredetermineddisplacement預測失效循環(huán)次數Theoryshouldbeabletopredict“cyclestofailure”發(fā)現最先失效的管件及其原因Fittingscausedearlyfailure…because…對管件引入應力集中Stressesconcentrationsareintroducedbyfittings分析試驗數據，修正軸向應力彎曲項Testdataanalyzedandamodificationtothebendingtermofthecodestressequationwasintroduced:Sbending=iM/z2023/1/5BasicStressTheory&基本應力“CodeStress規(guī)范應力”Markl’s83基本應力“CodeStress規(guī)范應力”Markl’s試驗和結果應力增強系數i和元件的形式有關對于彎頭“i”的計算需要如下:我們需要彎頭的幾何參