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1、Comput.MethodsAppl.Mech.Engrg.195(2006)5257–5296www.elsevier.com/locate/cmaIsogeometricanalysisofstructuralvibrationsJ.A.Cottrell,A.Reali,Y.Bazilevs,T.J.R.Hughes*InstituteforComputationalEngineeringandSciences,ComputationalandAppliedMathematicsChairIII,TheUniversityofTexasatAustin,201East24thStr
2、eet,ACES5.430A,1UniversityStationC0200,Austin,TX78712,USAReceived29August2005;receivedinrevisedform29September2005;accepted29September2005‘‘Letnomanignorantofgeometryenter,’’–inscriptionabovetheentrytoPlato’sAcademy,circa360BCAbstractThispaperbeginswithpersonalrecollectionsofJohnH.Argyris.Thegeo
3、metricalspiritembodiedinArgyris’sworkisrevivedinthesequelinapplyingthenewlydevelopedconceptofisogeometricanalysistostructuralvibrationproblems.Afterreviewingsomefunda-mentalsofisogeometricanalysis,applicationismadetoseveralstructuralmodels,includingrods,thinbeams,membranes,andthinplates.Rotation
4、lessbeamandplatemodelsareutilizedaswellasthree-dimensionalsolidmodels.Theconceptofk-refinementisexploredandshowntoproducemoreaccurateandrobustresultsthancorrespondingfiniteelements.Throughtheuseofnonlinearparameteri-zation,‘‘optical’’branchesoffrequencyspectraareeliminatedfork-refinedmeshes.Optical
5、brancheshavebeenidentifiedascontributorstoGibbsphenomenainwavepropagationproblemsandthecauseofrapiddegradationofhighermodesinp-methodfiniteelements.AgeometricallyexactmodeloftheNASAAluminumTestbedCylinderisconstructedandfrequenciesandmodeshapesarecomputedandshowntocomparefavorablywithexperimentalr
6、esults.Ó2006ElsevierB.V.Allrightsreserved.Keywords:Isogeometricanalysis;Structuralvibrations;Invariantfrequencyspectra;Nonlinearparameterization;Finiteelements;Rotationlessbendingelements;Massmatrices1.ThomasJ.R.Hughes’spersonalrecollectionsofJohnH.ArgyrisJohnArgyriswasmyinitialinspirationinscie
7、nce.Ifirstheardofthefiniteelementmethodin1967whileIwasworkingatGeneralDynamics,ElectricBoatDivisioninGroton,Connecticut.Scientificjournalsweremadeavailabletostaffandone,inparticular,caughtmyattention,theAeronauticalJournaloftheR
