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1、MODIFIEDVLASOVMODELFORBEAMSONELASTICFOUNDATIONSByC.V.GirtjaVallabhan,1Fellow,ASCE,andY.C.Das,2Member,ASCEABSTRACT:RealizingtheinadequacyoftheclassicalWinklermodeltorepresentanelasticcontinuum,VlasovandLeont'evdevelopedatwo-parametermodelforabeamonanelasticfoundation.TheVlasovmodelrequiredanestim
2、ationofaparameter,7,thatcontrolsthedecayofstressesinthecontinuum.VallabhanandDasdevelopedauniqueiterativetechniquetodetermineaconsistentvalueoftheyparameter.Theirmodeliscalleda"modified"or"refinedVlasov"model.Here,thefinitedifferenttechniqueisemployedtosolvethefourth-orderdifferentialequations.T
3、heresultsofsampleproblemsobtainedbyusingthemodifiedVlasovmodelarecomparedwithmoresophisticatedfiniteelementsolutions.INTRODUCTIONTheconceptofabeamorslabonanelasticfoundationhasbeenamajortoolforanalysisofgeotechnical,highway,andrailroadengineeringprob•lems.Whilematerialpropertiesofthebeamorslabca
4、nbeestablishedfairlyaccurately,thecharacteristicsorparametersthatrepresentthebehaviorofthesubsoilortheelasticfoundationaredifficulttomodel,eveniflinear,homogeneous,isotropicbehaviorforthesoilisassumed.Winkler(1867)representedtheverticaldeformationcharacteristicsoftheelasticfoundationbymeansofcon
5、tinuouslinearsprings;theconstantofproportionalityofthesespringsisknownasthe"modulusofsubgradereaction,"usuallyrep•resentedbyk.TheWinklermodel,oftenreferredtoasa"one-parametermodel,"hasbeenshowntobeinconsistenttorepresentacontinuousme•dium.ResearcherslikePasternak(1954),VlasovandLeont'ev(1966),an
6、dNogamiandLam(1987)developedtwo-parametermodelsthatareslightlydifferentfromeachother.Vlasov,inhismodel,introducedanarbitrarypa•rameter,7,tocharacterizethedistributionoftheverticaldisplacementinanelasticfoundation.JonesandXenophontos(1977),usingvariationalprin•ciples,strengthenedtheVlasovmodelbye
7、stablishingarelationshipbetweenthe7parameterandthedisplacementofthebeamorslabonthetop.Val•labhanandDas(1988)developedasimpleiterativeproceduretodeterminethe7parameter;thisprocedureisreferredtohereinasa"modified"or"re•finedVl
