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2.Numericalproblemanalysis
whichisequivalenttowriting
(2.15)
Asaresult,asystemofnequationsisgeneratedwhitchcontainsnnodalvalues.In
thematrixrecord,thesystemofequationswithintroducedboundaryconditionshas
theform:
(2.16)
TheYmatrixisasymmetricmatrix(inmostcases),bandedandsparse.Itresultsfrom
thefactthatonlytheelementsincontactinthei-nodewillhavetheirshareintheex-
pression
.Ifthei-thnodeisnotpartofthee-thelement,thenthecontributionofthis
elementintheexpression
isequaltozero.Accordingtotheaboveassumptions,
thefunctiondefinedforanyelementhastheform
(2.17)
AfterdifferentiatingthefunctionI(e)inrelationtothefunctionvalueuintheelement
nodes,thefollowingexpressionisobtained:
Havingdependence
and
(2.18)
(2.19)
(2.20)
(2.21)
andsubstituting(2.18)and(2.21)intoequation(2.19),thefollowingformulais
obtained:
21
(2.22)
