AERSP301PlateTheory：aersp301板理论

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1、AERSP301PlateTheoryJosePalaciosAugust2008TodayPlateTheoryAnalyzingenergymethod(StationaryPrincipleofTotalPotentialEnergy)SimilartoprocessforFEMConsiderplateasawhole(notdiscretized)DisplacementFunctionschangeFinalExam:August142008@10:00RCOEPlateTheoryBeamPlatePlateTheoryPlateTheoryPlateTheor

2、yPlateTheoryNon-zerostrains(invectorform):Thesearethestrains/deformationsthatweareconcernedwithwhenconsideringanalysisofaplatePlateTheoryPlateTheoryStress-StrainRelationsforplates:Butforaplate(2in-planedirections)wemustconsiderPoisson’seffectsPlateTheoryStrainsineachdirectionarefunctionsofs

3、tressinbothdirections:PlateTheoryForanisotropicmaterial,thereareonly2independentconstantsrelatingstresstostrainForisotropicmaterialsweneedtoknowYoung’sModulus,ShearModulus,andpoisson’sratio.Ifweknow2oftheseconstants,wecancalculatethethird.PlateTheoryPutstrain/stressrelationsintomatrixform:P

4、lateTheoryPlateTheoryNowthatwehavestress-strainrelations,weuseEnergymethods(StationaryPrinciple)tofinishtheanalysisStartwithStrainEnergyWeonlyhadtoconsider1axialstressandstrainForplatesweareconcernedwithtwoaxialstressesandstrainsaswellasshearstressandstrainPlateTheoryForplates:PlateTheoryIn

5、tegrateoverthickness,andareaofplatePlateTheory(Exampleofnon-isotropicplate)PlateTheorySimilartoplatesandbarsPlateTheoryAtthispoint,forbarsandbeamswediscretizedthestructureusingthefiniteelementmethodPlateTheoryFortheplate,likethebeamorbar,weneedtoassumeadisplacementfunctionAssumedModesMethod

6、–assumethedisplacementoftheplatecanbewrittenasthesumofanumberofmodeshapes,mn,andcorrespondingcoefficients,Amn.PlateTheoryTheassumeddisplacementsmustmatchthegeometricboundaryconditionsoftheplateandbe2timesdifferentiable.ModeshapesmustmatchBCs2timesdifferentiablesincestrainenergyisafunctiono

7、fcurvaturesSimply-supportedplate(BCs)PlateTheoryClampedplatePlateTheoryOncethedisplacementoftheplateisassumed,thentheTotalstrainenergyoftheplatecanbedetermined.Asbeforetheworkpotentialisafunctionoftheexternalloadingandassumeddisplacement.Wecanthenwriteou