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1、CoupledSystemsMechanics,Vol.1,No.1(2012)19-3719FEM-BEMiterativecouplingprocedurestoanalyzeinteractingwavepropagationmodels:fluid-fluid,solid-solidandfluid-solidanalysesDelfimSoaresJr.*StructuralEngineeringDepartment,FederalUniversityofJuizdeFora,CEP36036-330JuizdeFora,M
2、G,Brazil(ReceivedDecember20,2011,RevisedFebruary10,2012,AcceptedFebruary13,2012)Abstract.Inthiswork,theiterativecouplingoffiniteelementandboundaryelementmethodsfortheinvestigationofcoupledfluid-fluid,solid-solidandfluid-solidwavepropagationmodelsisreviewed.Inordertoperf
3、ormthecouplingofthetwonumericalmethods,asuccessiverenewalofthevariablesonthecommoninterfacebetweenthetwosub-domainsisperformedthroughaniterativeprocedureuntilconvergenceisachieved.Inthecaseoflocalnonlinearitieswithinthefiniteelementsub-domain,itisstraightforwardtoperfor
4、mtheiterativecouplingtogetherwiththeiterationsneededtosolvethenonlinearsystem.Inparticular,amoreefficientandstableperformanceofthecouplingprocedureisachievedbyaspecialformulationthatallowstousedifferenttimestepsineachsub-domain.Optimizedrelaxationparametersarealsoconsid
5、eredintheanalyses,inordertospeedupand/ortoensuretheconvergenceoftheiterativeprocess.Keywords:wavepropagation;iterativecoupling;finiteelementmethod;boundaryelementmethod;multi-domaindecomposition;differenttime-steps;nonlinearcalculations1.IntroductionThenumericalsimulati
6、onofarbitrarilyshapedcontinuousbodies-solidsand/orfluids-subjectedtoharmonicortransientloadsremains,despitemucheffortandprogressoverthelastdecades,achallengingareaofresearch.Inmostcases,discretetechniques,suchastheFiniteElementMethod(FEM)andtheBoundaryElementMethod(BEM)
7、havebeenemployedandcontinuouslyfurtherdevelopedwithrespecttoaccuracyandefficiency.Bothmethodologiescanbeformulatedinthetimedomainorinthefrequencydomain,andeachapproachhasrelativebenefitsandlimitations.TheFiniteElementMethod,forinstance,iswellsuitedforinhomogeneousandani
8、sotropicmaterialsaswellasfordealingwiththenonlinearbehaviorofabody.Forsystemswithinfiniteextensionandregionsof
