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22-23 September 2011, Baku, Azerbaijan

International Symposiumon Advances in Applied Mechanics and Modern Information Technology(ISAAM&MIT ’ 11). 22-23 September 2011, Baku, Azerbaijan. On The Static Response of Functionally Graded Circular Plate Resting on Linearly Gradient Elastic Foundations Subjected to

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22-23 September 2011, Baku, Azerbaijan

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  1. InternationalSymposiumonAdvancesinAppliedMechanicsandModernInformationTechnology(ISAAM&MIT’11)InternationalSymposiumonAdvancesinAppliedMechanicsandModernInformationTechnology(ISAAM&MIT’11) 22-23September2011,Baku,Azerbaijan OnTheStaticResponseofFunctionallyGradedCircularPlate RestingonLinearlyGradientElasticFoundationsSubjectedto CombinedAxisymmetricTransverseandShearLoads A.BehravanRad DepartmentofmechanicalEngineering,KarajBranch,IslamicAzadUniversity,Karaj,Iran E-mail:behravanrad@gmail.com Abstract Inthispaper,thestaticbehavioroffunctionallygraded(FG)solidcircularplaterestingonlinearlygradient elasticfoundationsundercombinedloadsisinvestigatedbyusingthestatespaceanddifferentialquadrature methods.Thestateequationsarederivedbasedon3Dtheoryofelasticity,andassumingthematerialproperties exceptthePoisson’sratiovariescontinuouslythroughoutthethicknessdirectionintheformofanexponential function.Thestressesanddisplacementsdistributionareobtainedbysolvingthesestateequations. Theeffectsoftheelasticfoundationcoefficients(Winkler–Shearlayer)togetherwithchangingthesurfaces conditionoftheplatesupportedbythefoundation,materialheterogeneityindex,gradientfactorvariationand loadsratioonthedeformationandstressdistributionsoftheFGcircularplateareinvestigated. Themechanicalbehavioroftheplatewiththesofter(metalrich)surfacesupportedbyelasticfoundation differsignificantlyfromthatoftheplatewiththeharder(ceramicrich)surfacesubjectedtothesamefoundation. Theresultsarereportedforthefirsttimeandarediscussedindetail. Keywords:FGCircularPlate,Elasticity,GradientElasticFoundations,State-Space,DQMethod. 1Introduction Functionallygradedmaterials(FGMs)havegainedconsiderableattentioninrecentyears.Themechanical behaviorofFGMscircularplateswith/withoutrestingonelasticfoundation,suchasbendingduetomechanical loads,vibration,stabilityandbuckling,etc.,havealsobeenstudiedbymanyscientists.Forexample,Reddyetal. investigatedaxisymmetricbendingofanFGMcircularplatebasedonthefirst-orderplatetheoryandobtained therelationshipsbetweenthefirst-orderplatetheoryandtheclassicalthinplatetheory.Lietal.presentedthe elasticitysolutionsforatransverselyisotropicFGMcircularplatesubjecttoanaxisymmetrictransverseloadin termsofthepolynomialsofevenorder.Huang,ZY.,etal.presentedanexactsolutionforFGMsrectangular thickplatesrestingonelasticfoundationbasedonthethree-dimensionaltheoryofelasticityusinginfinitedual seriesoftrigonometricfunctionscombinedwiththestate-spacemethod.Wang,Y.etalapplieddirect displacementmethodtoinvestigatethefreeaxisymmetricvibrationoftransverselyisotropicCircularplate. AlibeiglooA.discussedbendingbehaviorofFGMrectangularplatewithintegratedsurfacepiezoelectriclayers restingonelasticfoundation.BehravanRadA.etalstudiedthestaticbehaviorofFGMannularplaterestingon uniformelasticfoundationsunderaxisymmetrictransverseloadbasedonthe3Dtheoryofelasticityandusing semi-analyticalmethod.SburlatiR.etalobtainedelasticsolutionsforFGthickcircularplatesubjectto axisymmetricconditions.GolmakaniM.E.etalanalyzedtheaxisymmetricnonlinearbendingofanannular 351

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