* GraduateStudent.Presently,AssistantProfessor,InstituteofPaperScience&Technology,Atlanta,GA30318,U.S.A.  ProfessorofMechanicalEngineering CCC 0029— 5981/97/112001— 17$17.50 Received 7 December 1995  1997byJohnWiley&Sons,Ltd. Revised 8 July 1996 INTERNATIONALJOURNALFORNUMERICALMETHODSINENGINEERING, VOL.40,2001 — 2017(1997) DISPLACEMENT/PRESSUREBASEDMIXEDFINITE ELEMENTFORMULATIONSFORACOUSTIC FLUID— STRUCTUREINTERACTIONPROBLEMS XIAODONGWANG* ANDKLAUS-JU RGENBATHE Massachusetts Institute of ¹echnology, Cambridge, MA 02139, º.S .A. SUMMARY We present reliable finite element discretizations based on displacement/pressure interpolations for the analysisofacousticfluid—structureinteractionproblems.Thefiniteelementinterpolationsareselectedusing theinf-supcondition,andemphasisisgiventothefactthattheboundaryconditionsmustsatisfythemass andmomentumconservation.Weshowthatwithouranalysisprocedurenospuriousnon-zerofrequencies areencountered,asheretoforecalculatedwithotherdisplacement-baseddiscretizations.  1997byJohn Wiley&Sons,Ltd. KEYWORDS: acoustics;fluid—structureinteractions;mixedformulations 1. INTRODUCTION Manyinteractionproblemsinvolvingdifferentcontinuousmediaexistinpracticalengineering fields. One of them is the so-called fluid—structure interaction problem where the interaction betweenthefluidandastructurecansignificantlyaffecttheresponseofthestructureandneedsto be taken into account properly. Fluid—structure interaction problems are encountered in the analysisofoffshorestructures,acousticalmedia,liquidorgasstoragetanks,pipelinesystems, nuclearreactorsandbiomechanicalsystems. Anumberoffiniteelementformulationshavebeenproposedtomodelanacousticfluidforthe analysisoffluid— structureinteractionproblems,namely,thedisplacementformulation, the displacementpotentialandpressureformulation,andthevelocitypotentialformulation. Primitive variable formulations have received considerable attention because they do not require any special interface conditions or new solution strategies (for example, in frequency calculationsandresponsespectrumanalysis).Withtheever-increasingavailabilityofhigh-speed andlarge-capacitycomputers,thisapproachshowsgreatpromiseingeneralapplicationstothe solutionofabroadrangeofproblems(specificallynon-linearproblems).Unfortunately,some difficultieshaveremainedunsolvedtouseprimitivevariablefiniteelementformulationsinthe analysisoffluidflowsandfluid—structureinteractions. In linear analyses, it has been widely reported that the displacement-based fluid elements employed in frequency or dynamic analyses exhibit spurious non-zero frequency circulation modes. Variousapproacheshavebeenintroducedtoobtainimprovedformulations.The