NA&MELecture2AnalysisofImpact&Newton’sLawsClassObjectiveApplyNewton’sFirst,Second,andThirdLawsUnidirectionalAnalyzeImpactandEnergyAbsorptionFluid-Structure-Interaction(anIntroduction)SomeDefinitions(1D)Position-locationonastraightline-3-2-101234Displacement-changeinlocationonastraightline-3-2-101234xxDx=x2-x1=4-(-2)=6VelocityAverageVelocity-rateofpositionchangewithtime

InstantaneousVelocityAverageandInstantaneousVelocityPositionTimet1

t2x1x2Slope==AverageVelocityx2-x1t2-t1AccelerationAverageAcceleration-rateofvelocitychangewithtimeInstantaneousAccelerationAverageandInstantaneousAccelerationVelocityTimet1

t2v1v2Slope==AverageAccelerationv2-v1t2-t1Forconstantacceleration...

ifaccelerationisconstantintegratingbothsidesv0istheoriginalvalueatthebeginningofthetimeinterval(Definition)ConstantAccelerationsubstitutingthevelocityequationfromthepreviousslideintegratingbothsidesyields(Definition)EquationsofMotion

(ConstantAcceleration)

VelocityPosition(intermsofx)Newton’s1stLaw“Everybodypersistsinitsstateofrestorofuniformmotioninastraightlineunlessitiscompelledtochangethatstatebyforcesimpresseduponit.”NewtonNewton’sSecondLawThetime-rate-of-changeofmomentumisproportionaltothenetforceontheobject.

Ifmassisconstant...Newton’sThirdLaw“Toeveryactionthereisalwaysopposedanequalreaction:or,themutualactionsoftwobodiesuponeachotherarealwaysequalanddirectedincontraryparts.”

NewtonNewton’sThirdLawOtherstatementsForcesalwaysexistbytheinteractionoftwo(ormore)bodiesTheforceononebodyisequalandoppositetotheforceonanotherbodyThedesignationofan“actionforce”anda“reactionforce”isarbitrarybecausethereismutualinteractionbetweenthebodiesUniversalGravitationTheattractionforcebetweentwomassesis:Where:Gisaconstant,miarethemassesofthetwobodiesRisthedistancebetweenthetwocentersofmassEarth’sGravityFieldTheattractionforcebetweenearthandanobjectneartheearth’ssurfaceis(it’sweight):Where:gisaconstant,theaccelerationofgravitymisthemassofthebodyattheearth’ssurface

WhyUseNewton’sLaws?Engineersusemodelstopredictthingssuchasmotion,fluidflow,liftonanairplanewing,movementofneutronsinanuclearreactor,deflectionofbeamsorcolumns,etc.Newton’slawsarewidelyusedandagoodfirstexampleofengineeringmodels.ImpactAnalysisImpactAnalysisUnderstandEnergyConceptsWorkEnergyStrainEnergyImpact(lowvelocity)TheStressStrainCurveStressStrainelasticplasticyieldElastic,Perfectly-PlasticMaterialPermanentsetStressStrainCurve,SteelStress,ksiStrainelasticplasticyieldstrain.002MildSteel0.61000.20.4TheStressStrainCurveStressStrainElasticBrittle/DuctileMaterialBrittleFractureDuctileYieldtensioncompressionBasicConceptsI EnergyIIWorkIII EnergyExchangeIVStrainEnergyApplicationsV AxialStressesVI ImpactTestsStressandForcePressure-forceperunitareaFAImpactWeightMaterialPropertiesDensity-massperunitvolumeHighdensityLowdensityEnergyEnergyisthecapacitytodowork,butworkisaformofenergy...Itiseasiertothinkofenergyasascientificandengineering“unitofexchange”,muchlikemoneyisaunitofexchange.PotentialEnergyEnergymaybeintheformofpotentialenergy.Examplesincludethepotentialenergyofamassinagravitationalfield.Thisenergyisnotabsolutebutmeasuredrelativetoanarbitrarydatum.Oftengivensimplyas“weighttimesheight”orEP=WhKineticEnergyEnergymaybeintheformofkineticenergy.Examplesincludetheenergyofamassmovingatagivenvelocity.Kineticenergyofamass,m,movingwithvelocityvis EK=?mv2TypesofWorkWorkDrivingForceMechanicalForce(Physical)ShaftworkTorqueHydraulicPressureElectricVoltageChemicalConcentrationMechanicalWorkFFDxMechanicalWork(assumeFisnotafunctionofx)i.e.,workistheareaundertheFvs.xcurveWork(Hydraulic)DxPPFADVP=constFStrainEnergyTheinternalenergyassociatedwithelasticdeformationiscalledstrainenergy,denotedU.Notethatelasticdeformationsarereversibleprocesses.StrainEnergy,UniaxialStress

Stress-forceperunitareaStrain-changeinlengthperunitoriginallengthFADLElasticStrainEnergyStrain,e=DL/LStress,s=F/AHooke’sLaws=EeWork=?FDLWork=?[sAeL]=UU=?Ee2VPlasticStrainEnergyStrain,e=DL/LStress,s=F/As=s

yieldWork=FDLWork=[sADL]RecapofProcessesTheinternalenergyassociatedwithelasticdeformationiscalledstrainenergy.Elasticdeformationsarereversible.Plasticdeformationsareirreversible.Energylossesoccurintheformofheat.RecapofProcessesForstructuresundergoinglargeplasticdeformations,elasticdeformationsmaybenegligible.Plasticdeformationsmaybedominant.Fractureisalsoanirreversibleprocess.”Surfaceenergy”islost.StressStrainCurve,SteelStress,ksiStrainelasticplasticyieldstrain.002MildSteel0.61000.20.4BucklingBucklingstresss=0.6Et/RwheretisthecylinderthicknessandRistheradiusProgressivePlasticCollapseProgressivePlasticCollapseProgressivePlasticCollapseProgressivePlasticCollapseFluidStructureInteractionAddfluidtoalternatechambers:FluidStructureInteractionAddfluidtoalternatechambers:FluidStructureInteractionFluidStructureInteractionFluidStructureInteractionFluidStructureInteractionFluidStructureInteractionFluidStructureInteractionAanalyticalmodelofthecollapseprocessforaweightimpactingthesepanelswithfluidencasementisgivenby:FluidStructureInteractionMisthemassoftheimpactingobjectCisadampingconstantassociatedwithfluidlossesandmotionFistheplasticcollapseforceofthepanelFluidStructureInteractionIntroducea=C/MIntroduceb=F/MIntroduceA=v0Wheretheinitialcontactvelocityisv0IntroduceEquationofmotionisthen:FluidStructureInteractionThevelocitysolutiontotheequationofmotionforaninitialcontactvelocityofv0is:FluidStructureInteractionThedisplacementsolutiontotheequationofmotionforaninitialcontactvelocityofv0is:(measuringdisplacementxfromt