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1、Analyticalsolutionnonrectangularplatewithin-planeVariablestiffnessTian-chongYU,Guo-junNIE,ZhengZHONG,Fu-yunCHU(SchoolofAerospaceEngineeringandAppliedMechanics,TongjiUniversity,Shanghai200092,P.R.China)Abstract:Thebendingproblemofathinrectangularplatewith
2、in-planevariablestiffnessisstudied.Thebasicequationisformulatedforthetwo-opposite-edgesimplysupportedrectangularplateunderthedistributedloads.Theformulationisbasedontheassumptionthattheflexuralrigidityoftheplatevariesintheplanefollowingapowerform,andPois
3、son?sratioisconstant.Afourth-orderpartialdifferentialequationwithvariablecoefficientsisderivedbyassumingaLevy-typeformforthetransversedisplacement.ThegoverningequationcanbetransformedintoaWhittakerequation,andananalyticalsolutionisobtainedforathinrectang
4、ularplatesubjectedtothedistributedloads.Thevalidityofthepresentsolutionisshownbycomparingthepresentresultswiththoseoftheclassicalsolution.Theinfluenceofin-planevariablestiffnessonthedeflectionandbendingmomentisstudiedbynumericalexamples.Theanalyticalsolu
5、tionpresentedhereisusefulinthedesignofrectangularplateswithin-planevariablestiffness.Keywords:in-planevariablestiffness,powerform,Levy-typesolution,rectangularplateChineseLibraryClassification03432010MathematicsSubjectClassification74B051IntroductionThet
6、erirTvariablestiffness"impliesthatthestiffnessparametersvaryspatiallythroughout.Thestructureinhomogeneouscomposites,111?Functionallygradedmaterials(FGMs)areinwhich,themechanicalpropertiesvarysmoothlywiththepositiontomeetthepredeterminedfunctional,perform
7、ance.ThestructurescomposedoftheFGMsareofvariablestiffness.Thereareextensiveliteraturesonthebending,vibration,andfractureoftheFGMstructures12-91.Thedeformationofafunctionallygradedbeamwasstudiedbythedirectapproach1101.Anefficientandsimplyrefinedtheorywasp
8、resentedforthebucklinganalysisoffunctionallygradedplatesbyThaiandChoi[,11.Jodaeietal[,2]dealtwiththethree一dimensionalanalysisoffunctionallygradedannularplatesusingthestate一spacebaseddifferentialquadraturemethod(SSDQM).Wena
