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1、西安建筑科技大学硕士学位论文BendingofPlateRestingonNon-uniformElasticFoundationSpecialty：EngineeringMechanicsPostgraduate：ChenHaoInstructor：Prof.HeFangsheABSTRACTThebendingofplaterestingonnon-uniformelasticfoundationisasupplementfortheresearchfieldofinteractionbetweengro
2、undandfoundation,beingaveryimportantscientificresearchvalueandapplicationvalue.Inthepresentstudy,thebendingofplatewithfourfreeedgesrestingonnon-uniformWinklerfoundationisdiscussed.Theraftfoundationismodeledasaelasticthinplaterestingonnon-uniformWinklerfound
3、ation,themechanicsequationsforbendingofarectangularplateareestablished,thedisplacementfunctionformeetingtheboundaryconditionsisselected,RitzMethod,ModifiedRitzMethodandGalerkinMethodareusedtoanalyzethebendingofplaterestingonnon-uniformWinklerfoundation,givi
4、ngthedeflectionandbendingmomentforthebendingofrectangularplatewithfourfreeedgesunderlateralloads.Combinedwiththespecificformofalgebraicequations,usingmathematicalsoftwareMatlabprogrammingnumericalanalysis.Firstly,discussingtheconvergencewiththebendingproble
5、mofrectangularplate;secondly,analysisthedifferencesofrectangularplatedeflectionandbendingmomentwhichonuniformfoundationandonnon-uniformfoundation;finally,analysistheinfluenceofthenon-uniformfoundationarea,thefonudationcoefficient,theplateside-to-thicknessra
6、tioandtheareaofloadstobendingofrectangularplate.TheresultsshowthattheconvergenceandtheprecisionofGalerkinMethodisthebest,ModifiedRitzMethodisthesecond,RitzMethodistheslowest;andwhenthefonudationcoefficientk1andk2havegreatdifferences,thebendingofplateonunifo
7、rmfoundationandthebendingofplateonnon-uniformfoundationhaveobviousdifferences,thosedifferencesshouldbepaidattentioninthedesignsofplate;withthecenterarea,theareaofloadsincrease,thedeflectionandbendingmomentoftherectangularplateareincreasingconstantly;inthece
8、nterareaofthesamepremise,along西安建筑科技大学硕士学位论文withthecentralregionfonudationcoefficientconstantlydecreases,thedeflectionandbendingmomentoftherectangularplateareincreasingconstantly;withtheplateside-to-th
