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1、Version2.01-October17,2005Scienti?cProgrammingII”IntroductiontoC++andMFC”O(jiān)lafKolditzCenterforAppliedGeosciencesUniversityofT¨ubingenWS2005/2006°cZAGPublisher2005Chapter1Object-oriented?niteelementanalysisDesign,implementationandapplicationofaconceptforobject-orie
2、ntationin?niteelementanalysisofmulti-?eldproblemsispresentedinthispaper.Thebasicideaofthisconceptisthattheunderlyinggoverningequationsofporousmediamechanicscanbeclassi?edintodi?erenttypesofpartialdi?erentialequations(PDEs).Inprinciple,equaltypesofPDEsfordiverseph
3、ysicalproblemsdi?eronlyinmaterialcoe?cients.Localelementmatricesandvectorsarisingfromthe?niteelementdiscretizationofthePDEsarecategorizedintoseveraltypes,regardlessofwhichphysicalproblem(i.e.?uid?ow,massandheattransportordeformationprocesses)theybelongto.Element(
4、ELE)objectsareintroducedtocarryoutthelocalassem-blyofthealgebraicequations.Theobject-orientationincludesastrictencapsulationofgeometrical(GEO),topological(MSH),process-related(FEM)dataandmethodsofelementobjects.Geometricentitiesofanelementsuchasnodes,edges,faces,
5、neighborsareabstractedintocorrespondinggeometricelementobjects(ELE-GEO).Therelationshipsamongofthesegeometricentitiesformthetopologyofelementmeshes(ELE-MSH).Finiteelementobjects(ELE-FEM)arepresentedforthelocalelementcalculations,inwhicheachclassi?cationtypeofmatr
6、icesandvectorsiscomputedbyauniquefunction.Theseelementfunctionsareabletodealwithdi?erentgeometrictypes(lines,triangles,quads,tetrahedra,prisms,hexhedra)au-tomaticallyapplyingtherelatedelementinterpolationfunctions.Foreachprocessofamulti-?eldproblem,onlyasingleins
7、tanceofthe?niteelementobjectisre-quired.Theelementobjectsprovidea?exiblycodingenvironmentformulti-?eldproblemswithdi?erentelementtypes.TheC++implementationsoftheobjectsaregivenanddescribedindetail.Thee?ciencyofthenewelementobjectsisdemonstratedbyseveraltestcasesd
8、ealingwiththermo-hydro-mechanical(THM)coupledproblemsforgeotechnicalapplications.21.1INTRODUCTION31.1IntroductionThenumericalanalysisofcomplexmulti-?eldproblem