緒論3D梁單元的特征無限薄的桿。描述的所有行為都是根據(jù)端點的位移。彎曲是粱單元的主要行為。*基本應(yīng)力理論&第一頁，共五十三頁。緒論3D梁單元的特征僅說明了總體的行為。沒有考慮局部的作用(表面沒有碰撞)。忽略了二次影響。(使轉(zhuǎn)角很小)遵循Hook’s定律。*基本應(yīng)力理論&第二頁，共五十三頁?；緫?yīng)力 使用局部坐標(biāo)系可以將管系應(yīng)力(以及產(chǎn)生這些應(yīng)力的載荷）theloadsthatcausethem)分為下面幾種：縱向應(yīng)力-SL環(huán)向應(yīng)力-SH徑向應(yīng)力-SR剪切應(yīng)力-*基本應(yīng)力理論&第三頁，共五十三頁?？v向應(yīng)力分量沿著管子的軸向。軸向力軸向力除以面積(F/A)壓力Pd/4torP*di/(do2-di2)彎曲力矩Mc/I最大應(yīng)力發(fā)生在圓周的最外面。I/半徑

Z(抗彎截面系數(shù));使用

M/Z*基本應(yīng)力理論&第四頁，共五十三頁。由于壓力產(chǎn)生的環(huán)向應(yīng)力垂直于半徑(圓周)Pd/2t再一次用薄壁的近似值。環(huán)向應(yīng)力很重要，盡管它不是“綜合應(yīng)力”的一部分。環(huán)向應(yīng)力根據(jù)直徑、操作溫度下的許用應(yīng)力、腐蝕余量，加工偏差和壓力用來定義管子的壁厚。根據(jù)Barlow,Boardman,Lamé來計算。*基本應(yīng)力理論&第五頁，共五十三頁。由于壓力產(chǎn)生的徑向應(yīng)力垂直于表面。內(nèi)表面應(yīng)力為-P。外表面應(yīng)力通常為0。由于最大的彎曲應(yīng)力發(fā)生在外表面，所以這一項被忽略。*基本應(yīng)力理論&第六頁，共五十三頁。剪切應(yīng)力平面內(nèi)垂直于半徑。剪切力這個載荷在外表面最小，因此在管系應(yīng)力計算中省略了這一項。在支撐處要求局部考慮。扭矩最大的應(yīng)力發(fā)生在外表面。MT/2Z*基本應(yīng)力理論&第七頁，共五十三頁?！熬C合應(yīng)力”中的基本應(yīng)力評價3-D應(yīng)力S=F/A+Pd/4t+M/Z軸向、環(huán)向壓力和縱向彎曲所產(chǎn)生的應(yīng)力之和。根據(jù)規(guī)范和載荷工況的不同上式將發(fā)生變化。*基本應(yīng)力理論&第八頁，共五十三頁。Basisfor“CodeStressEquations”失效理論變形能或八面體剪切應(yīng)力(根據(jù)米賽斯理論和其它的理論）。最大剪應(yīng)力理論

（Columb理論）

。大多數(shù)理論都根據(jù)這個理論。由于剪切影響而限制最大主應(yīng)力(Rankine理論)。CAESARII132列輸出應(yīng)力報告中顯示了米賽斯或最大剪應(yīng)力強度理論。應(yīng)力報告由configuration設(shè)置來決定。*基本應(yīng)力理論&第九頁，共五十三頁。規(guī)范要求的載荷工況規(guī)范要求使用兩個主要失效方式的失效理論。一次失效。二次失效。(第三種失效方式是偶然失效，它與一次失效相似。）*基本應(yīng)力理論&第十頁，共五十三頁。規(guī)范要求的載荷工況一次失效情況力所引起。非自限性。重量、壓力和集中力所產(chǎn)生。*基本應(yīng)力理論&第十一頁，共五十三頁。規(guī)范要求的載荷工況二次失效情況位移所引起。自限性。溫度、位移和其它變化載荷——例如，重力。*基本應(yīng)力理論&第十二頁，共五十三頁。規(guī)范要求的載荷工況(1)=W+T1+P1(OPE)(2)=W+P1(SUS)(3)=DS1-DS2(EXP)操作工況,用于:約束&設(shè)備載荷最大位移計算EXP工況持續(xù)工況，用于一次載荷下規(guī)范應(yīng)力的計算。膨脹工況，用于“extremedisplacementstressrange”工況3的位移是從工況1的位移減去工況2的位移而得到。*基本應(yīng)力理論&第十三頁，共五十三頁。規(guī)范要求的載荷工況膨脹工況說明Whatdoes“DS1-DS2(EXP)”mean?Isaloadcasewith“T1(EXP)thesamething?*基本應(yīng)力理論&第十四頁，共五十三頁。規(guī)范要求的載荷工況膨脹工況說明Thecodestatesthattheexpansionstressesaretobecomputedfromthe"extremedisplacementstressrange".Theseareallveryimportantwords.Considertheirmeaning…EXTREME:Inthissenseitmeansthemost,orthelargest.RANGE:Typicallyadifference.Whatdifference?Thedifferencebetweentheextremes.Whatextremes?DISPLACEMENT:Thisdefineswhatextremestotakethedifferenceof.STRESS:Whatweareeventuallyafter.*基本應(yīng)力理論&第十五頁，共五十三頁。規(guī)范要求的載荷工況膨脹工況說明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.*基本應(yīng)力理論&第十六頁，共五十三頁。規(guī)范要求的載荷工況膨脹工況說明(Obviouslytheloadcasenumbersaresubjecttochangeonajobbyjobbasis.)Whatdoyougetwhenyoutake"DS1-DS2"?Well{x1}-{x2}yields{x'},apseudodisplacementvector.{x'}isnotarealsetofdisplacementsthatyoucangooutandmeasurewitharuler,ratheritisthedifferencebetweentwopositionsofthepipe.Oncewehave{x'},wecanusethesameroutinesusedintheOPEorSUScasestocomputeelementforces,andfinallyelementstresses.*基本應(yīng)力理論&第十七頁，共五十三頁。規(guī)范要求的載荷工況膨脹工況說明However,theseelementforcesarealsopseudoforces,i.ethedifferenceinforcesbetweentwopositionsofthepipe.Similarly,thestressescomputedarenotrealstresses,butstressdifferences.Thisisexactlywhatthecodewants,thestressdifference,whichwascomputedfromadisplacementrange.Astowhetherornotthisstressdifferenceistheextreme,wellthatdependsonthejob.*基本應(yīng)力理論&第十八頁，共五十三頁。規(guī)范要求的載荷工況膨脹工況說明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.*基本應(yīng)力理論&第十九頁，共五十三頁。規(guī)范要求的載荷工況膨脹工況說明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}*基本應(yīng)力理論&第二十頁，共五十三頁。規(guī)范要求的載荷工況膨脹工況說明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.*基本應(yīng)力理論&第二十一頁，共五十三頁。規(guī)范要求的載荷工況膨脹工況說明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)*基本應(yīng)力理論&第二十二頁，共五十三頁。規(guī)范要求的載荷工況膨脹工況說明Thesecases,whilecorrect,don'taddressthe"extreme"termofthecoderequirements.ThisisbecauseCAESARIIisn'tlookingatwhattheloadcomponentsrepresent.Tosatisfytherequirementsofthecode,theusermustdefineanadditionalloadcase:(6)DS1-DS2(EXP)Thisloadcasewillbethe"extreme",thatwilltypicallygoverntheEXPstresscriteria.Youcan'tdothisatallusingthe"T1"onlymethod.*基本應(yīng)力理論&第二十三頁，共五十三頁。規(guī)范要求的載荷工況膨脹工況說明Tosummarize:Wetakethedifferencebetweentwoloadcasestodetermineadisplacementrange.Fromthisrangewecomputeaforcerangeandthenastressrange.Thecoderequirestheextremedisplacementstressrange.Theuseronlyhastoworryaboutwhetherornotthe"extreme"casehasbeenaddressed.*基本應(yīng)力理論&第二十四頁，共五十三頁。線性vs非線性這個術(shù)語指的是邊界條件。方程重新被求解:[K]{x}={f}這是彈簧方程。管系邊界條件（例如，約束）指的是剛度或彈簧。可以定義更復(fù)雜的邊界條件，此時“線性彈簧”的假設(shè)將不適用。*基本應(yīng)力理論&第二十五頁，共五十三頁。線性Vs非線性線性邊界條件的一個實例是雙向約束，例如：“Y”向支撐。線性邊界條件的另一個實例是彈簧支吊架。這些約束中力與位移的關(guān)系曲線是一條直線。所以這些約束是線性的。直線的斜率為剛度。*基本應(yīng)力理論&第二十六頁，共五十三頁。線性Vs非線性“+Y”支撐是非線性支撐。力與位移的關(guān)系曲線不是一直線。剛度僅存在于負(fù)位移方向。對于正位移，剛度是零。*基本應(yīng)力理論&第二十七頁，共五十三頁。線性Vs非線性“間隙”也是一個非線性支撐。力與位移的關(guān)系曲線不是一直線。間隙中沒有剛度。*基本應(yīng)力理論&第二十八頁，共五十三頁。LinearvsNon-Linear摩擦使約束成為非線性。大的旋轉(zhuǎn)桿也是非線性約束。文件中的非線性約束意味著[Kope]不等于[Ksus]。使用兩個其它載荷工況之間的差值來建立(EXP)和(OCC)載荷工況來說明非線性約束。*基本應(yīng)力理論&第二十九頁，共五十三頁。OccasionalLoadCaseSetupOccasionalloadsareconsidered“primary”,sincetheyareforcedriven.Occasionalloadsoccurinfrequently.Thecodesemployan“allowableincrease”factorbasedonthefrequencyofoccurrenceinthedeterminationoftheallowable,i.e.k*Sh.Examplesofoccasionalloadsarewindandearthquake.*基本應(yīng)力理論&第三十頁，共五十三頁。OccasionalLoadCaseSetupThecodeequationfortheOCCasionalloadcaseis:

MA/Z+MB/Z<kShHere,MAisthemomenttermfromtheSUStainedloads,andMBisthemomentfromtheOCCasionalloads.ThisequationstatesthattheOCCasionalcaseisthesumoftheSUStainedstressesandtheOCCasionalstresses.Sowecan’trunaloadcasewithjusta“WIND”loadandsatisfythiscoderequirement.Whatabout“W+P1+WIND”asaloadcase?*基本應(yīng)力理論&第三十一頁，共五十三頁。OccasionalLoadCaseSetupThe“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)*基本應(yīng)力理論&第三十二頁，共五十三頁。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.*基本應(yīng)力理論&第三十三頁，共五十三頁。LoadCaseGeneration&MaintenanceCAESARIIwillrecommendloadcasesfor“new”jobs.By“new”jobs,wemeanjobsthatdonothavea“._J”file.For“old”jobs,havinga“._J”file,CAESARIIreadsinthedefinedloadcasesandpresentsthemtotheuser.Theloadcaseeditingscreenisshownattheright.*基本應(yīng)力理論&第三十四頁，共五十三頁。LoadCaseGeneration&MaintenanceCAESARIIwillrecommendloadcasesfor“new”jobs.By“new”jobs,wemeanjobsthatdonothavea“._J”file.For“old”jobs,havinga“._J”file,CAESARIIreadsinthedefinedloadcasesandpresentsthemtotheuser.Theloadcaseeditingscreenisshownattheright.*基本應(yīng)力理論&第三十五頁，共五十三頁。LoadCaseGeneration&MaintenanceOnthisdialog,availableloadtypesarelistedintheupperleftlistbox.Availableloadcasetypesarelistedinthelowerleftlistbox.Loadcases(recommendedorpreviouslydefined)areshowninthegridattheright.Recommendedloadcasescanalwaysbeobtainedbyclickingonthe[Recommend]button.Theanalysiscommencesbyclickingon“therunningman”.*基本應(yīng)力理論&第三十六頁，共五十三頁。LoadCaseGeneration&MaintenanceSayfora“new”job,theloadcasesattherightarerecommended.Sayyouacceptandruntheseloadcases.Uponreviewingtheoutputyoudiscoverthatpre-defineddisplacementsatnode5wereomitted.Youreturntoinput,addthedisplacements,andstarttheStaticAnalysisprocessoragain.*基本應(yīng)力理論&第三十七頁，共五十三頁。LoadCaseGeneration&MaintenanceCAESARIIreadstheseexistingloadcasesandpresentsthem.Whatwillyourresultsbeifyouruntheseloadcases?Exactlythesameasbefore,becausetheseloadcasesdon’tincludethepredefineddisplacements.Youmustmanuallyadd“D1”totheOPEloadcase,oraskCAESARIItore-recommendtheloadcases.*基本應(yīng)力理論&第三十八頁，共五十三頁。LoadCaseGeneration&MaintenanceNoticetheloadtypelistintheupperleftcontains“D1”now.Thecorrectedloadcasesareshownattheright.*基本應(yīng)力理論&第三十九頁，共五十三頁。LoadCaseGeneration&MaintenanceNoticetheloadtypelistintheupperleftcontains“D1”now.Thecorrectedloadcasesareshownattheright.*基本應(yīng)力理論&第四十頁，共五十三頁。LoadCaseGeneration&MaintenanceNoticetheloadtypelistintheupperleftcontains“D1”now.Thecorrectedloadcasesareshownattheright.Anytimeyouaddorremoveacompleteloadtype,theloadcasesareinsufficient.Ifyouaddeddisplacementstonode110,wouldtheloadcasesbesufficient?*基本應(yīng)力理論&第四十一頁，共五十三頁。InsuringYouAnalyzeWhatYouThinkYou’reAnalyzingRememberCAESARIIisafiniteelementprogram.RememberCAESARIIusesa3Dbeamelement.Rememberyoumusthaveequilibrium:ResultantloadsshouldequalappliedloadsGravity(weightonly)loadcaseshouldequaltheweightofthesystemOtherbasicchecksVerifynodal3DcoordinatesCheckforextremedisplacementsand/orloads(seehandout)*基本應(yīng)力理論&第四十二頁，共五十三頁。問題解決當(dāng)不滿意結(jié)果時，你應(yīng)做什么？重新求解方程：

[K]{x}={f} 其中我們求解的{x}是位移。由這些位移，我們可以計算單元力&力矩。由這些力&力矩，使用規(guī)范方程計算出應(yīng)力。*基本應(yīng)力理論&第四十三頁，共五十三頁。問題解決當(dāng)不滿意結(jié)果時，你應(yīng)做什么？如果是應(yīng)力問題，它可能是由于下面兩個問題引起的：與規(guī)范有關(guān)的問題(SIFs、規(guī)范方程等等）極限力和/或力矩如果是力/力矩問題，它可能是由下面兩個問題所引起：不正確的單元特性極限位移*基本應(yīng)力理論&第四十四頁，共五十三頁。ProblemSolvingWhatdoyoudowhenyoudon’tliketheresults?Ifyouhaveadisplacementproblem,itcanonlybecausedbytwothings:Improperinput(density,elasticmodulus,appliedloads)ImproperboundaryconditionsDon’tforgettocheckandrechecktheinput.Rememberthatin3Dsystems,aloadinonelocationcancausepivotingsomewhereelsedownstream,resultinginexcessiveforcesandmoments.Trytoisolatetheload