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2002ABAQUSUsers’Conference1ModelingSubmergedStructuresLoadedbyUnderwaterExplosionswithABAQUS/ExplicitDavidB.WoyakABAQUSSolutionsNortheast,LLCAbstract:FiniteelementanalysiscanbeusedtopredictthetransientresponseofsubmergedstructuresthatareexternallyloadedbyanacousticpressureshockwaveresultingfromanUnderwaterExplosion(UNDEX).Thisclassofproblemischaracterizedbyastrongcouplingbetweenthestructuralmotionsandacousticpressuresatthefluid-structurewettedinterface.Thestructuralbehaviorisacombinationoflongtime(lowfrequency)responsedominatedbyanaddedmasseffect,shorttime(highfrequency)responsedominatedbyradiationdamping,andintermediatetime-frequencyresponsewherebothaddedmassandradiationdampingbehaviorarepresent.Forthefiniteelementmethodtobeuseful,theanalystmustdevelopmodelingtechniquesandproceduresthatyieldaccurateandcomputationallytractablesolutions.Modelingproceduresandguidelinesweredevelopedforusewithanexplicitdynamicscodethatoffersadvancedfeaturessuchas:pressureformulatedacousticelements,surfacebasedfluid-structurecoupling,surfacebasedabsorbing(radiation)boundaries,andautomatedincidentwaveloadingforthefluid-structurewettedinterface.Themodelingguidelinesaddressissuessuchas:locationofthefluidacousticdomainouterboundary,meshingoftheacousticdomain,representationoftheshockwave,andsolutionefficiency.ThesemodelingproceduresandguidelinesaredemonstratedwithanABAQUS/ExplicitanalysisofanUNDEXexperimentinwhichasubmergedtestcylinderwasexposedtoa60-poundHBX-1explosivecharge(Kwon&Fox,1993).GeneralBackgroundABAQUS/Explicitisanefficienttoolforsimulatingthetransientresponseofstructural-acousticsystems,ofwhichtheresponseofsubmergedstructuresloadedbyacousticshockwavesresultingfromanUnderwaterExplosion(UNDEX)isanimportantproblemclass.Thispaperprovidesabriefdiscussiononthegeneralnatureofthestructural-acousticinteractionanddescribesmodelingstudiesthataddressgeneralFiniteElementAnalysis(FEA)requirementsfortheaccuratesimulationofUNDEXproblems.Thestudiesdescribedinthisreporthavegeneralapplicationtoawiderangeofstructural-acousticproblems,notjusttheanalysisofsubmergedstructures.AnexampleanalysisofasubmergedcylinderisusedtoillustrateanUNDEXproblem.UNDEXanalysescanbegenerallycharacterizedastransientsimulationsofacousticscatteringbehavior.However,theobjectiveofanUNDEXanalysisistoevaluatetheresponseofthesubmergedstructureandnotnecessarilytheacousticresponse.Thefiniteelementmodelfortheexternalacousticdomainmustbeadequatetorepresenttheinfluenceofthewateronthestructuralresponse.Thediscussionhereinwillberestrictedtothosecaseswheretheexternalfluidbehavesasalinearacousticfluidwithnocavitation.Therefore,themodeloftheexternalacousticdomainneedonlybetailoredtoprovideanaccurateloadingonthestructureanddoesnotneedtoaccuratelyrepresenttheacousticwavesthatwilltravelawayfromthestructure.Itshouldbenoted22002ABAQUSUsers’ConferencethatproceduresforUNDEXanalyseswhichincludefluidcavitationwillbeavailableinABAQUS/ExplicitwiththereleaseofVersion6.3(Prasad&Cipolla,2001).Thetotalacousticpressureintheexternalfluidthatresultsfromanunderwaterexplosionconsistsoftheknownincidentshockwave(incoming)pressureandtheunknownscatteredwave(outgoing)pressure.Thescatteredwavepressureconsistsoftwoparts,areflectedpartthatisassociatedwiththeshockwaveinteractingwithanidealrigid,immovablestructureandavibratorypartthatresultsfromthemotionsofthestructureattheinterfacewiththefluid.Whencavitationisnotpresent,itisdesirabletolettheexternalacousticdomainrepresentonlythescatteredportionofthetotalacousticpressure.Theshockwaveincidentpressureloadisapplieddirectlytothestructuralmeshatthefluid-structurewettedinterface.Acousticloadsassociatedwiththereflectedpartofthescatteredpressureareappliedtothefluidmeshatthewettedinterface.Thefullscatteredpressure(reflectedandvibratory)isobtainedasthesolutionfortheacousticelementpressuredegreesoffreedom,andthecompletescatteredpressureloadingonthestructureisgeneratedthroughthefluid-structurecouplingequations.Theacousticloadsareacharacteristicoftheincidentshockwave,andareobtainedfromthefluidparticleaccelerationsinadirectionnormaltothesurfacethatdefinesthefluid-structurewettedinterface.InthediscussionthatfollowsthecapabilityofABAQUS/ExplicittoefficientlyperformUNDEXanalysesisdemonstrated.TheABAQUSfeaturesutilizedinsolvingthisclassofproblemare:1.Computationallyefficientpressurebasedacousticelements.2.Surfacebasedautomatedacoustic-structurecoupling.3.Acoustic-structurecouplingformis-matchedmeshes.4.Surfacebasedimpedancemodelsforrepresentingnon-reflectingfluidboundaries.5.Automatedshockwaveloadingatthefluid-structureinterface.AcousticDomainOuterBoundaryUNDEXproblemsarecharacterizedbyastrongcouplingbetweenthestructuralmotionsandacousticpressuresatthewettedinterface.Thesystemresponseinastronglycoupledstructural-acousticsystemcanbedescribedasbeingacombinationofthefollowingtypesofresponse:1.LateTime-LowFrequency:Characterizedbystructuralwavelengthsthataresignificantlyshorterthantheassociatedacousticwavelengths.Theeffectoftheexternalfluidonthestructureisthatofaddinganeffectivemas