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1、7.INTRODUCTIONTOTHEFINITEELEMENTMETHODEngineersuseawiderangeoftoolsandtechniquestoensurethatthedesignstheycreatearesafe.However,accidentssometimeshappenandwhentheydo,companiesneedtoknowifaproductfailedbecausethedesignwasinadequateorifthereisanothercause,suchas
2、anusererror.Buttheyhavetoensurethattheproductworkswellunderawiderangeofconditions,andtrytoavoidtothemaximumafailureproducedbyanycause.Oneimportanttooltoachievethisisthefiniteelementmethod.“Thefiniteelementmethodisoneofthemostpowerfulnumericaltechniqueseverdevi
3、sedforsolvingdifferential(andintegral)equationsofinitialandboundary-valueproblemsingeometricallycomplicatedregions.”(Reddy,1988).Thereissomedatathatcannotbeignoredwhenanalyzinganelementbythefiniteelementmethod.Thisinputdataistodefinethedomain,theboundaryandini
4、tialconditionsandalsothephysicalproperties.Afterknowingthisdata,iftheanalysisisdonecarefully,itwillgivesatisfactoryresults.Itcanbesaidthattheprocesstodothisanalysisisverymethodical,andthatitiswhyitissopopular,becausethatmakesiteasiertoapply.“Thefiniteelementan
5、alysisofaproblemissosystematicthatitcanbedividedintoasetoflogicalstepsthatcanbeimplementedonadigitalcomputerandcanbeutilizedtosolveawiderangeofproblemsbymerelychangingthedatainputtothecomputerprogram.”(Reddy,1988).Thefiniteelementanalysiscanbedoneforone,twoand
6、three-dimensionalproblems.Butgenerally,theeasierproblemsarethoseincludingoneandtwodimensions,andthosecanbesolvedwithouttheaidofacomputer,becauseeveniftheygivealotofequations,iftheyarehandledwithcare,anexactresultcanbeachieved.Butiftheanalysisrequiresthree-dime
7、nsionaltools,thenitwouldbealotmorecomplicated,becauseitwillinvolvealotofequationsthatareverydifficulttosolvewithouthavinganerror.Thatiswhyengineershavedevelopedsoftwaresthatcanperformtheseanalysesbycomputer,makingeverythingeasier.Thesesoftwarescanmakeanalysiso
8、fone,twoandthreedimensionalproblemswithaverygoodaccuracy.Abasicthingtounderstandhowfiniteelementworksistoknowthatitdividesthewholeelementintoafinitenumberofsmallelements.“Thedomain