REG NACA-TN-3781-1957 Handbook of structural stability part I buckling of flat plates.pdf

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1、-e,- :.,.-h “-+-.- *ParaUelogramPlates.m. .- .- =-TriangularPlates - a - -.=APPEWDIXA -APPlzT4TIoNsEtmmN-. - m.-. . . =Intr121- e2arecriticallyexaminedfromthes.dpointoftheirtheoreticaldevelop-mentanQtheagreementof-theorywithtestdaa.Intbesectionentitled“EasicPrinciples”abriefreviewoftheLasicxmthemati

2、calprinciplesinvolvedinsolutionofbucklingproblemlagiven.Theprbaryobjecti-einpresentingthismaterialis toacquahtthereaderwiththeapproximatemethodsusedinordertobeabletaindicatetheaccuracyoftkeresultscfparticularsolutionsdiscussedinsubsequentsections.Tnthesectionentitled%uudaryConditions”theinilu=.ceoft

3、hegeometric.Theeffectofcladdinplasticity-reductionfactorsareperhapsthemastconspicuousem-pleofthis.Thus,therecozzzendationfora particulartheoqyisgen-e- supportedbyexperimentaldata.The=also,shapeparameterforstress-straincurve.normalloadapplieiinplaneofplate,atb,lbnornulpressure,psi4!bi“i;*ed. - . . .

4、- -. . .-J. -,-T-. ., . .!i-,Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-,. . .-;i;.G- veo+) shesrlouding,lb/in.6= E2+ ve(flb/A)2R strezs ratiot thicknessofplate,W.u= ( -ks)/(%+ - + ks%+ -)wwX,y,zy.l+3pfapotentialenergy,in-lbdisplacementnomal top

5、laneofplate,in.coordinatesedgeangle,deg;also,12M/(Pb+ 6M)also,ratioofrotationalrigidityegesti?fenertoro=tionalrigidityofplateplasticity-reductionfactorcladdingreductionfactortotal-reductionfactor,qfibucklehalfwavelength, in.ofplatev inelasticPoissonsl%tiOj V = Vp- p-Je)(%/E) fororthotropicsolids.-.-

6、 . ,- Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-, ,o.7JJo.85T.Subscripts:A,Bavbcc1crePplrBSmX,y+.stressintensity,(x2+stressatsecantmdulus,shearstresspsiangleofdiagonalsupport1/2y2-)axay+3T, ,psio.p.=d 0.85E,taplatewidth,respectively,psiradianso

7、r degvaluesatstationA andstationB;seefig.30averagebendingcompressioncladdingproportionallimitcriticalorbucklingelasticplasticproportionallimitintraverseribofcompressedplateshea”rshearoninfinitelylongplatedirectionsofloadingloadingsproducingtensionloadingsproducingcompression.a71 a15a15Provided by IH

8、SNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-“- u:,.:if:c,:s:c ch!.pdF free.a71a15a15a77a15a13a15a15a15.+-.Ss s iqiy suppurtei(hinged)Insketchesacccnyanyingfigures,supportededgeswithelusticrota-tiofialrestraintareshwnshaded.Unshadedloadededgesaresimplysuported.

9、Unshadedunloadededgesarefree.BASICPRINCIPLESGeneralRenarksThetheoreticalbucklingstressofa flatstructuralelentisthestressatwhichanexchanged stableequilibriumconfigurationsoccurstet-enthestraightand.theslightlybentform.Itmarkstheregioninwhichcontinuedapplicationofloadresultsinacceleratedgrowthofdeflec

10、tionsperpendiculartotheplaneofthe:ate.Itsimportanceliesinthefactthatkucklinginitiatesthephysi-.lprocesseswhichleadtoeventualfailureoftheplate. 74erandlwcrboundsapproachthetme bucklingstrcsc.Thu6,theIagrangianmlti-pliermethodraybeusedtoohtsd.nresultstithir.anydesireddegreeofaccuracy.Inadditiontotheab

11、oveprocedureswhichsrebasedonenergyir.tc-grals,othermethodsof obtainingapproximatesolutionsofbucklingprob-lemshavebeenusewhichinvolvetheequilibriumdifferentialequation.CtiOnSwhichI-, ,. .J.;.!T!,isES.5UT.*2,3.:;,:.TheplateisassumedtobesiMPlysuppmtedalongtheunloadededes” locatedai y =b/2:Incorporation

12、ofbyequation(8)leads(w)yb/2=o()a%+,22* Curlingatthefreeeigesvkrethetressdistributionrermrapgesitselftosatisfythegeometricalbow-simycomiibions.Therestraintofant.i-cksticcurntureres-dtsinm increaseinbendingstiffIMss. Foraverywideeleent,tkek.:. . .-. Provided by IHSNot for ResaleNo reproduction or netw

13、orking permitted without license from IHS-,-,-, . ,7 .,.*- . . . . . . :, -however,thedifferenceswereslight,aswnspointedoutbyStowellandRride,anditcanbeassuredforpracticalpur-posesthattheplasticity-reductionfactorsshownintheappendixaresat-isfactoryforgeneral desiandanalysis.,.a71a15a15a11a14a15claddi

14、nda;:-!Jltlxiyitetl:tareesquiteclosewithtketestdata.Thecladdirgreductioliuckrsmaytlhc:.kc ._usedwiththeexi.stin&inelasti.c-bucKLixcurvesoffiges8,aT.A13.Theformofbucklingeqmtioncomdy useifor detercinint!:c .bucklingstressofabureflatplatewithanytypeofloadingandlmn “-arysuppcrtsisgivenas equation(28).F

15、orclaiplatesthisexprecianisusedtofindcnominalbucklingstress,wlierethethic!v.essistttofthetotl-.lplateandtheraterialpropertiesarethoseofthecore.Theactualbucklingstressofa cladatethenmy befoundbyapplyingasimplentczericalmultiplierfitothisstress.Thisrultlplier,termedthecladdingreductionfactorbecauseitr

16、educestheratioo:thenominalcorestresstothebucklingstressoftkecladplate,isafxnc-tionoftherelativecoreandcladdingstresslevelsandtherespectivemduliofthecoreandcladdingmaterials.Tkeclad-platebucklingstresscanbefoundfrom 1acr = ucr (35)E tinenominalbucklingstressexceedstk.eproportionallimitofthecore =teri

17、al,thenthenominalbucklingstressforthecladplatemy befoundbyusingtheappropriatevalueof q,theplasticity-reductionfactorofthecoremterial.Valuesof q maybeobtainedfromtheclad-platestress-straincurveshowninfigure12,thederi-vationofwhichisdiscussedbelo-w.,Itshouldbenotedthattheplasticity-reductionfactordepe

18、ntiuponthestresslevelandconsequentlyrequiresanestimteofthefinalbucklingstressoftheplatebeforeequation(28)canbeusedtofiffcr.Thecladdingreductionfactorhasbeenfourdtobeofsucha-ture,however,thatlittleerrnrisinmlvedinfirstindingthenominalbuck-lingstressandthenmultiplyingitdirectlybythecladdingreductiaafa

19、ct-ortofindtheactualbucklingstressoftlcecladplate.Theprod-uct qfiis T$whichwasdeterminedbyBuck.ert.Table3containsalistingofthe=riouscladdingreductionfac-torsdeteminedinsubsequentportionsofthissection.Inthetable,allplatesarelor&andsti,plysupported.R.allcasesforwhichtkecladdingproportional-limitstress

20、Ucl exceedsthenoninalbucklingstressUcr thecladdingreductionfactorisequaltounity.Theymn-tity p %sdefinedas P=aclci cr,ad f istheratioofthetotalcladdingthicknesstotheclad-platetotalthi-kness.-.- . -. -.“.-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-