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1、有限元分析离散方法（Discretemethodoffiniteelementanalysis）Discretizationmethod:finitedifferencemethod,finiteelementmethod,finitevolumemethodRegionaldiscretization,Inessence,afinitesetofdiscretepointsisusedtoreplacetheoriginalcontinuousspace.Theimplementationprocessistodivide
2、thecalculatedregionintomanyoverlappingsubregions,determinethelocationofeachsubregionandthecontrolvolumerepresentedbythenode.Node:thegeometricpositionofunknownphysicalquantitiestobesolved;controlvolume:thesmallestgeometricunitofappliedcontrolequationsorconservationl
3、aws.Nodesaregenerallyregardedasrepresentativesofcontrolvolume.Thecontrolvolumeandthesubregionarenotalwayscoincident.Atthebeginningoftheregiondiscretizationprocess,asmallareadividedbyaseriesoflinearorcurveclusterscorrespondingtothecoordinateaxisiscalledasubregion.Gr
4、idisthebasisofdiscretization,andgridnodeisthestoragelocationofdiscretephysicalquantities.Asweallknow,thecommonlyuseddiscretizationmethodsare:finitedifferencemethod,finiteelementmethod,finitevolumemethod.The1.finitedifferencemethodisthemostclassicalmethodinnumerical
5、solution.Itisthedomainisdividedintodifferencegrid,solvingthecontinuousdomainwithafinitenumberofgridnodesinstead,thenthepartialdifferentialequation(equations)ofthederivativewithdifferencequotientinstead,derivedwithdiscretepointfinitedifferenceequations.Thismethodisd
6、evelopedearlierandmoremature,andisusedtosolvehyperbolicandparabolicproblems.Itisnotconvenienttousefiniteelementmethodorfinitevolumemethodtosolvecomplexboundaryconditions,especiallyellipticproblems.2.thefiniteelementmethodisasmallelementofmanycontinuoussolutiondomai
7、nisarbitrarilydividedintopropershape,andthepiecewiseinterpolationfunctionineachunit,andthenaccordingtotheextremumprinciple(variationalorweightedresidualmethod),thecontrolequationistransformedintofiniteelementequationsofallunits,theoverallextremevalueastheunitandthe
8、unitaboutlocalextremum,totalsynthesis,algebraicequationsformembeddedinthespecifiedboundarycondition,solvingtheequationshavefunctiononeachnodetofi
