On-the-General-Theory-of-Elastic-Stability--弹性稳定理论

OntheGeneralTheoryofElasticStabilityAuthor(s):R.V.SouthwellSource:PhilosophicalTransactionsoftheRoyalSocietyofLondon.SeriesA,ContainingPapersofaMathematicalorPhysicalCharacter,Vol.213(1914),pp.187-244Publishedby:TheRoyalSocietyStableURL::14/03/201021:51YouruseoftheJSTORarchiveindicatesyouracceptanceofJSTOR'sTermsandConditionsofUse,availableat://=rsl.EachcopyofanypartofaJSTORtransmissionmustcontainthesamecopyrightnoticethatappearsonthescreenorprintedpageofsuchtransmission.JSTORisanot-for-profitservicethathelpsscholars,researchers,andstudentsdiscover,use,andbuilduponawiderangeofcontentinatrusteddigitalarchive.Weuseinformationtechnologyandtoolstoincreaseproductivityandfacilitatenewformsofscholarship.FormoreinformationaboutJSTOR,[e-mail]ratingwithJSTORtodigitize,preserveandextendaccesstoPhilosophicalTransactionsoftheRoyalSocietyofLondon.SeriesA,ContainingPapersofaMathematicalorPhysicalCharacter.[187]V.OntheGeneralTheoryofElasticStability.ByR.V.SOUTHWELL,B.A.,FellowofTrinityCollege,Canbridge.CommunicatedbyProf.A.E.H-.LOVE,F.R.S.ReceivedJanuary4,-ReadJanuary30,1913.CONTENTS.Introductionandsummaryofpaper.................EQUATIONSOFNEUTRALEQUILIBRIUMINRECTANGULARCO-ORDINATES.Methodofderivation.......................Exampleinrectangularco-ordinates.Stabilityofthinplatingunderedgethrust.EQUATIONSOFNEUTRALEQUILIBRIUMINCYLINDRICALCO-ORDINATES.Derivationoftheequations.........Examplesincylindricalco-ordinates.StabilityofboilerfluesandtubularstrutsSolutionforboilerfluewithoutendthrust.ComparisonwithexperimentalresultsValidityofinvestigationbythetheoryofthinshells.Comparisonwithexistingformulae.Thecriticallength.................Solutionfortubularstrut.Specialcase.....ValidityofinvestigationbythetheoryofthinshellsSolutionbythetheoryofthinshells.GeneralcaseComparisonwithexistingformule.......Stabilityoftubesundercombinedendandsurfacepressure.........202........208.....217I......222.....224.....225I.....226227.....230......231.....236......236GENERALTHEORYOFINSTABILITYINMATERIALSOFFINITESTRENGTH.Thepracticalvalueofatheoryofinstability.............Stabilityofshortstruts..........Needforfurtherresearch.Conclusion..................237.242.244IntroductionandSummaryofPaper.PROBLEMSwhichdealwiththestabilityofbodiesinequilibriumunderstressaresodistinctfromtheordinaryapplicationsofthetheoryofelasticitythatitislegitimatetoregardthemasformingaspecialbranchofthesubject.IneveryothercaseweVOL.CCXIII.--A501,2B2Publishedseparately,August6,1913,Page..187..190..198188MR.R.V.SOUTHWELLONTHEGENERALTHEORYOFELASTICSTABILITY.areconcernedwiththeintegrationofcertaindifferentialequations,fundamentallythesameforallproblems,andthesatisfactionofcertainboundaryconditions;andbyatheoremduetoKIRCHHOFF'weareentitledtoassumethatanysolutionwhichwem-aydiscoverisunique.Intheseproblemsweareconfrontedwiththepossibilityoftwoormoreconfigurationsofequilibrium,andwehavetodeterminetheconditionswhichmustbesatisfiedinorderthattheequilibriumofanygivenconfiguratiornmaybestable.Thedevelopmentofbothbrancheshasproceededuponsimilarlines.Thatistosay,theearliestdiscussionswereconcernedwiththesolutionofisolatedexamplesratherthanwiththeformulationofgeneralideas.Inthecaseofelasticstability,acomprehensivetheorywasnotpropoundeduntiltheproblemofthestraightstruthadbeeninvestigatedbyEULE.R,tthatofthecircularringunderradialpressurebyM.LEVYtandG.H.HALPHEN,?andA.G.GREENHILLhaddiscussedthestabilityofastraightrodinequilibriumunderitsownweight,11undertwistingcouples,andwhenrotating.TInapaperwhichhasbecomethefoundationofthetheoryinitsexistingform,-'*G.HI.BEYANhasbroughttheseisolatedproblemsforthefirsttimewithintherangeofasinglegeneralization.ExaminingtheconditionsunderwhichKIRCHHOF'Stheoremofdeterminacymayfail,hewasledtotheconclusionthatinstabilityisonlypossibleinthecaseofsuchbodiesasthinrods,plates,orshells,andintheseonlywrhentypesofdistortioncanoccurwhichdonotinvolveextensionofthecentrallineormiddlesurface,sothatitislegitimatetodiscussanyprobleminelasticstabilitybymethodswhichhavebeendevisedfortheapproximatetreatmentofsuchbodies.Heshowed,moreover,thatthestabilityoftheequilibriumofanygivenconfigurationdependsupontheconditionthatthepotentialenergyshallbeaminimum,inthatconfiguration.AcloserexaminationofBRYAN'Stheorysuggeststhatsomeoftheconclusionswhichhavebeendrawnfromitarescarcelywarranted.Thecontentionthatnoclosedshellcanfailbyinstability,becauseanydistortionwouldinvolveextensionofthemiddlesurface,willbediscussedlater.--t-Forourpresentpurposeitissufficienttor