结构稳定概述

陈伟球交通工程研究所2008年4月13日,结构的稳定性分析概述,Theproofofthepuddinginanytheoryofengineeringscienceliesintheeating,thepracticalapplicationtopertinentproblems,andIbelievethetheoryofbucklingofstructureshaspassedthiscrucialtestwithhonours.W.T.Koiter,1974,KoiterWT.(1976)Currenttrendsinthetheoryofbuckling.In:BucklingofStructures,ITUMASymposium1974,editedbyBudiansky,B.Berlin:Springer.,(1914-1997)1968Timoshenkomedalwinner,DeeBridge,Chester,UK,trussedgirderbridge,failureduetotorsionalinstability,killing5personson25May,1847,InstabilityFailureofBridges,InstabilityFailureofBridges,QuebecBridge,Ste-Foy,Quebec,crossSaintLawrence(mainspan549m),Failuretoupdateconstructionmethodologywithanincreaseinthesizeandthereforeweightofsteelsectionsasdesignprogressedledtoanoverstressingofthecantileverarms.Thebridgecollapsedat5:32pmonAugust29,1907killing75people.,MilfordHavenBridge,Pembrokeshire,Wales,UnitedKingdom,Steelgirderbridge,collapsingduetoplatebucklingduringconstructionkillingfourmenon2June1970.,InstabilityFailureofBridges,WestGateBridge,Melbourne,Victoria,Australia,Steelspancollapsesduringconstructionkilling35.,FailureofBuildingStructuresduetoBuckling,Buckledcolumnanddeformedbeamsina14-storeyofficeblockontheBroadgatedevelopmentinLondonafterafirein1990.,Lateralwebbeambucklingcausedfailureofroofatshoppingcenter,CollapsingofWTC,911,BazantZP,ZhouY.(2002).WhydidtheWorldTradeCentercollapse?Simpleanalysis.ASCEJournalofEngineeringMechanics,128:2.,Oncemorethanhalfofthecolumnsinthecriticalfloor.sufferbuckling(stage3),theweightoftheupperpartofthestructureabovethisfloorcannolongerbesupported,andsotheupperpartstartsfallingdownontothelowerpartbelow,OtherBucklingPhenomena,Abucklingtreefailure.,Bucklingrailduetotemperature,HistoryofTheoryofStability,Tounderstandscienceitisnecessarytoknowitshistory,AugusteComte(1798-1857),HeroofAlexandria(c.100B.C.):Whythestrengthofapieceofwoodreducesasitslengthincreases?LeonardodaVinci(1452-1519)providedtwoempiricalrulesforthestrengthofcolumnsincompression.TheJesuitM.Mersenne(1588-1648)observedthatiron,copperandothermetals,evensinglebodies,whensubjecttoaforceorweight,curveandbendtotheformofanarchbeforebreakingPetrusvanMusschenbroek(16921761)confirmedMersennesconclusionsbyexperiments.JacobBernoulli(16541705)constructedtheequationofaflexiblebardeformedintheplaneconsideringfinitedeflectionandanonlinear(parabolic)dependencebetweencurvatureandbendingmoment.,BeforeEulersWork,Eulersinnovativeworkonstability,Therefore,unlesstheloadPtobebornebegreaterthanCp2/4l2,therewillbeabsolutelynofearofbending;ontheotherhand,iftheweightPbegreater,thecolumnwillbeunabletoresistbending.Nowwhentheelasticityofthecolumnandlikewiseitsthicknessremainthesame,theweightPwhichitcancarrywithoutdangerwillbeinverselyproportionaltothesquareoftheheightofthecolumn;andacolumntwiceashighwillbeabletobearonlyone-fourthoftheload.,EulerL.(1744)Methodusinveniendilineascurvas,AdvancesinStabilityinthe18thand19thcenturies,Lagrange(17361813)providedthelastsignificantcontributiontothetheoryofelasticstabilityinthe18thcentury,responsibleforintroducingthenotionofbifurcationthatconnectslinearizedandfullynonlinearsolutions.ThomasYoung(1773-1829)treatedthelateralbucklingofacolumnwithvariablecross-section.Navier(1785-1836)derivedthecorrectdifferentialequationforathinplatesubjecttouniformcompressiveforces.G.R.Kirchhoff(1824-1887)proposedaneleganttheoryforslenderrodsexperiencinglargedisplacementandsmallstrain.H.Poincar(1854-1912)discoveredageneralmethodfordynamicalsystemsinvolvingseriesprovedconvergentforallvaluesoftime.M.A.Liapunov(1857-1918)proposedacompletelyapriorimethodforassessingstabilitythatdependsuponthetimeevolutionofacertainauxiliaryfunction.A.Fppl(1854-1924)andvonKrmn(1881-1963)derivedasystemoftwoequationsdescribingthelargedeflectionofathinplatewithstressesactinginthemiddleplane.,TragedyofScience,Certainstructuresareabletowithstandloadssignificantlyabovethebucklingload.Experimentallydeterminedbucklingloadsofaxiallycompressedthin-walledcylindersareconsiderablybelowthetheoreticalstabilitylimit.,AbeautifultheorykilledbytheuglyfactsThomasHuxley(1825-1895),Itisnotwhoisright,butwhatisright,thatisofimportance.Itisthecustomaryfateofnewtruths,tobeginasheresies,andtoendassuperstitions.Patienceandtenacityareworthmorethantwicetheirweightofcleverness.,E.Reissner(1913-1996)relaxedsomeofthesimplifyingassumptionsofFppl-vonKrmnstheory.H.L.Cox(1940)performednonlinearanalysisofbucklingproblemsofthinflatplateswhichhavearewardingstablepost-bucklingbehaviorwithasignificantload-carryingcapacity.vonKrmn,L.G.DunnandH.S.Tsien(1940)pioneeredtheinvestigationsofnonlinearimperfection-sensitivecolumnmodels.W.Koiter(1945)finishedhisPh.D.thesis,markinganeweraofbucklingofstructures.J.L.Ericksen(1966)succeededinseparatingthethermaleffectsfromthemechanicalaspectsforestablishingtheenergycriterionofstabilityinitspurelymechanicalform.,Reissner:1973Timoshenkomedal;Ericksen:1979Timoshenkomedal,AdvancesinStabilityinthe20thcentury,SomeWordsaboutKoiter,WhenpressedtostatewhatIregardasthemostremarkablesinglecontributionofanindividualinsolidmechanicsinmylifetime,IaminclinedtosaythatitwasWarnerKoitersPh.D.thesis,“Onthestabilityofelasticequilibrium”,publishedinAmsterdamin1945.Thethesisdevelopedthetheoryofelasticbucklingandpost-bucklingbehavior,theeffectofinitialgeometricimperfectionsonbuckling,andappliedthistheorytocolumns,platesandshells.Butthatwasnotall,mostofKoiterssubsequentseminalcontributionstoshells,bothlinearandnonlinear,hadtheirbeginningsinhisthesis,andmanyaspectswerealreadywelldevelopedthere.J.W.Hutchinson,2002TimoshenkomedalacceptancespeechSamuraiinaworldofPharisees(虚伪世界中的武士)PignataroM.(1998)Obituary:W.Koiter(1914-1997).Meccanica,33:605-606.OneoftheingredientsofthechairKoiteroccupiedwasstiffness.Hevividlyillustratedthisstiffnessofhumanmindattheworldcongress.Buthewasflexibletoo.Inhiswritingshewouldsometimesinsertveryfloweryandelucidatingstatements.Herearetwoexamples:(a)Flexiblebodieslikethinshellsrequireaflexiblemethod.(b)Anytwo-dimensionaltheoryofthinshellsisnecessarilyanapproximatecharacter.Anexacttwo-dimensionaltheoryofshellscannotexist,becausetheactualbodywehavetodealwith,thinasitmaybe,isalwaysthree-dimensional.Wemayperhapsillustratethispointinasomewhatfacetiousway:evenifitappearstobethefashionforladiestobeasthinaspossible,fortunately,inourview,theyremainessentiallythree-dimensional.I.Elishakoff(2000)Meccanica,35:375-380.,Isbucklingalwaysbaneful?,ControlledbucklinginNEMS,SunYG,etal.(2006)Controlledbucklingofsemiconductornanoribbonsforstretchableelectronics.NatureNanotechnology,1:201-207.,Whodoyouthinkyouare!Onecontributeswhatonecan!,TimoshenkosadviceonDenHartog,citedfromthe1991TimoshenkoMedalAcceptanceSpeechbyYuan-ChengFung,Timoshenko:1957Timoshenkomedal;DenHartog:1972;YCFung:1991,(1901-1989),(1878-1972),BasicIdeasandConcepts,Thestateofequilibrium,stable,unstable,Neutral,BasicIdeasandConcepts,Bifurcationpoint,Load-deflectioncurveofacompressedbar,Generalcharacteristicofbifurcationpointinstability,BasicIdeasandConcepts,Limitpoint,f,P,O,Pu,Limitpoint,II:postbucklingequilibriumstate,I:prebucklingequilibriumstate,Generalcharacteristicoflimitpointinstability,Full-scalebridgetest,Classificationofstability,BasicIdeasandConcepts,ElasticstabilityversusplasticstabilityLinearsmalldeformationstabilityversusnonlinearlargedeformationstabilityStaticstabilityversusdynamicstabilityStabilityofperfectstructureversusstabilityofimperfectstructure;Localstabilityversusglobalstability,Criteriaforstability,BasicIdeasandConcepts,Basiccriterion:Supposethatasmalldisturbanceisimposedonasysteminequilibrium.Iftheoriginalstateofequilibriumcanberecoveredaftertheremovalofthedisturbance,wesaythatoriginalstateofequilibriumisstable;if,ontheotherhand,thesystemdeviatesfromtheprimarystateofequilibriumincreasingly,thenitisunstable.,Staticcriterion:Ifasystemisinastateofequilibriumwithinfinitesimallyneighboringpositionsalsoinequilibrium,thenitissaidtobeinastateofneutralequilibrium.Thestaticcriterioniswidelyusedtodeterminethebifurcationcriticalload.Steps:Establishtheequationsofequilibriuminthenewstateofequilibriumundertheactionoftheload(thechangeoftheloadduetothedeformationisomitted);Ifnon-trivialsolutionoftheequationssubjecttohomogeneousboundaryconditions(eigen-problem)exists,thentheoriginalstateofequilibriumisneutral.,BasicIdeasandConcepts,Energycriterion:Foraconservativesystem,ifthetotalpotentialenergyofabasicstateisalwayssmallerthanthatofaneighboring(deviated)state,thenthebasicstateisstable.Stable:Unstable:Neutral:,BasicIdeasandConcepts,Dynamiccriterion:Thesystemisdescribedbyasetofgeneralizedcoordinatesqi(i=1,2,n),withqi=0intheequilibriumstate.Ifthesystemdeviatestheequilibriumstatewithaproperinitialvaluesofandsuchthatandwillnotexceedtheprescribedlimitthatinfinitesimallyapproachestothebasicstateofequilibrium,thenthebasicstateisstable.Steps:SupposethesystemoscillatesaroundtheequilibriumstateduetothesmalldisturbanceEstablishtheequationsofmotionandsolveforthenaturalfrequencyDeterminethecriticalloadaccordingtothevanishingoffrequency,BasicIdeasandConcepts,Pin-endedAxiallyLoadedStrut,A=0w=0:positionofequilibriumwithastraightconfigurationsinmL=0mL=ip(i=1,2,3,):positionofequilibriumwithbuckledconfigurations,Elasticcriticalload:,Loaddisplacementrelationshipsforanaxiallyloadedpin-endedstrut.Comparisonofsmall-displacementanalysis(unbrokenlines)withlarge-displacementanalysis(brokenline),AlongOADthelargeandsmalldisplacementanalysescoincideAlongABthesmalldisplacementanalysissuggeststhatwhenP=PEthestrutisinastateofneutralequilibrium,whichisacloseapproximationtothelarge-displacementcurve.AlongBE,atloadssignificantlygreaterthanPE,thetwopredictionsdifferfromeachotherobviously.,Pin-endedAxiallyLoadedStrut,Pin-endedstrutwithinitialdeformation,EffectofInitialBow,Load-displacementcurvesforstrutwithvariousamountofinitialbow(a1),InelasticBucklingofStrut,Characteristicfeaturesofstress-straindiagramforaninelasticmaterial,Tangentmodulus,Reducedmodulus,F.Engesser(1889)“UeberdieKnickfestigkeit”ZeitschriftfurArchitecturundIngenieurwesen,35:455.,F.Engesser(1895),T.vonKarman(1910),Criticalstress(s)forapin-endedaxiallyloadedstrut,plottedagainsttheslendernessratio(L/r),Ramberg-Osgoodequation:,InelasticBucklingofStrut,Shanleysmodel,Idealizedstrutconsistingoftworigidbarseachoflength(a-h),connectedbytwopin-endedelasticelements(1)and(2).Theloadisappliedeccentrically,Idealizedstress-straincurve,Stressv.totaldisplacementfortheidea