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1、Comput.MethodsAppl.Mech.Engrg.200(2011)665–674ContentslistsavailableatScienceDirectComput.MethodsAppl.Mech.Engrg.journalhomepage:www.elsevier.com/locate/cmaPredictionofrankdeficiencyinpartitionofunity-basedmethodswithplanetriangularorquadrilateralmeshesaba,c,⇑dX.M.An,L.X.Li,G.W
2、.Ma,H.H.ZhangaSchoolofCivilandEnvironmentalEngineering,NanyangTechnologicalUniversity,Singapore639798,SingaporebMOEKeyLaboratoryforStrengthandVibration,SchoolofAerospace,Xi’anJiaotongUniversity,Xi’an,Shaanxi710049,PRChinacSchoolofCivilandResourceEngineering,UniversityofWestern
3、Australia,35StirlingHighway,CrawleyWA6009,AustraliadSchoolofCivilEngineeringandArchitecture,NanchangHangkongUniversity,Nanchang,Jiangxi330063,PRChinaarticleinfoabstractArticlehistory:Inthepartitionofunity(PU)-basedmethods,theglobalapproximationisbuiltbymultiplyingapartitionRec
4、eived25May2010ofunitybylocalapproximations.Withinthisframework,high-orderapproximationsareachievedbyReceivedinrevisedform25August2010directlyadoptinghigh-orderpolynomialsaslocalapproximations,andthereforenodesalongsidesorAccepted21September2010insideelements,whichareusuallyado
5、ptedintheconventionalfiniteelementmethods,arenomoreAvailableonline25September2010required.However,thePU-basedapproximationconstructedinthiswaymaysufferfromrankdeficiencyduetothelineardependenceoftheglobaldegreesoffreedom.Inthispaper,theoriginoftherankdefi-Keywords:ciencyinthePU-b
6、asedapproximationspaceisfirstdissectedatanelementlevel,andthenanapproachtoPartitionofunity-basedmethodspredicttherankdeficiencyforameshisproposedtogetherwiththeprincipleoftheincreaseofrankdefi-LineardependenceRankdeficiencyciency.Finally,examplesareinvestigatedtovalidatethepresent
7、approach.Thecurrentworkindicatessuchafactthattherankdeficiencyisanunrelatedissuetothenullityoftheglobalmatrix.Itcanberesolvedinitsownmanner.Ó2010ElsevierB.V.Allrightsreserved.1.Introductionapproximation.TheyfoundthateventhoughtheDirichletbound-aryconditionsarepreciselyprescribe
8、d,thenumberofshapefunc-Duetotheinefficiencyoftheconventionalfin
