Application Of A Rigorous Subgrade Model In The Analysis Of Rectangular Plates On An Elastic Foundation Using Finite Difference Method

Plate on elastic foundation establishes an adequate idealization in the analysis of shallowrnfoundations, which includes isolated footings, combined footings, mat foundations, and flexiblernpavement.rnThernimportantrnissuerninrnthernanalysisrnisrnmodelingrntherncontactrnbetweenrnthernplaternrnandrnthernsoilrnmediumrnthatrnisrnarnsoil-structurerninteractionrn(SSI)rnproblem.rnThernprimaryrndifficultyrnrninrnthernanalysisrnofrnthernsoil–structurerninteractionrnliesrninrntherndeterminationrnofrntherncontactrnpressure.rnThernsimplestrnsubgradernmodelrnisrnthernsinglernparameterrnWinklerrnmechanicalrnmodel,rnwhichrnrnrepresentsrnthernfoundationrnsoilrnbyrnarnseriesrnofrnindependentrnsprings.rnWinklerrnmodelrnisrnwidelyrnrnusedrnandrnpracticedrninrnspiternofrnitsrndeficiencyrninrnrepresentingrntherncontinuousrnbehaviorrnofrnrealrnrnsoils.rnrnLater, many advanced mechanical subgrade models have been proposed in order tornimprove on the inherent lack of shear interaction among the individual springs. However,rnthese models still have their drawbacks in that they do not represent the subgrade shearrninteraction adequately. With the objective to improve on such drawbacks, a generalized continuum-basedrnmodelrnhasrnbeenrnrecentlyrnproposedrnbyrnWorku.rnThisrngeneralizedrnsubgradernmodelrnrnsatisfiesrnthernfundamentalrnelasticrnlawsrnandrnallrnthernboundaryrnconditionsrnsincernitrnisrnderivedrnbyrnrnconsideringrnallrnstress,rnstrainrnandrndisplacementrncomponents.rnrnThe main objective of this work is to implement and calibrate the generalized continuumrnbased subgrade model for the analysis of rectangular plates on an elastic foundation. Therngoverning differential equation of a rectangular plate that incorporates Pasternak type subgradernmodelrnisrnformulated.rnThus,rnanrnordinaryrnfiniterndifferencernmethodrnisrndevelopedrntornsolvernrnthernpartialrndifferentialrnequations.rnCodernbasedrnonrnMATLABrn® rnprogramming language is writ-rnten for determining deflections and internal actions of the plate. Finite Element based softwarernisrnusedrnasrnarntoolrntorndeterminernanrnadjustmentrnfactorrnforrntherngeneralizedrnmodel.rnFinally,rnrnthernproposedrnmethodrnhasrnbeenrnvalidatedrnbyrncomparingrnthernresultsrnwithrnotherrnnumericalrnmodelsrnforrnselectedrnloadingrnconditions.rnThernresultsrnofrntherncomparisonrnshowrnthatrntherngeneralizedrnrnmodelrnshowsrnanrnexcellentrnagreementrnwithrnthernFErnoutputsrnandrncapablernofrnpredictingrnthernbehaviorrnofrnthernrectangularrnplatesrnonrnelasticrnfoundations.

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