講義教程案例expl

Lessoncontent:IntroductionElementTypesOverviewHourglassingandLockingSecond-orderAccuracyLesson2:Elements1hourIntroduction(1/7)ThislectureprovidesageneralintroductiontotheelementsavailableinAbaqus/Explicit.ThefocuswillbeonissuesthatareparticularlyimportantforAbaqus/Explicit.AmorecompletediscussionofAbaquselementscanbefoundintheElementSelectioninAbaquslecturenotes.Introduction(2/7)ThewiderangeofelementsintheAbaqus/Explicitelementlibraryprovidesflexibilityinmodelingdifferentgeometriesandstructures.Eachelementcanbecharacterizedbyconsideringthefollowing:FamilyContinuum,shell,membrane,rigid,beam,trusselements,etc.NumberofnodesElementshapeGeometricorderLinearorquadraticinterpolationDegreesoffreedomDisplacements,rotations,temperatureFormulationSmall-andfinite-strainshells,etc.IntegrationReducedandfullintegrationIntroduction(3/7)EachelementinAbaqushasauniquename,suchasS4R,B31,M3D4R,C3D8RandC3D4.Theelementnameidentifiesprimaryelementcharacteristics.B31:Beam,3-D,

1st-orderinterpolationM3D4R:Membrane,3-D,4-node,Reducedintegration

C3D4:Continuum,3-D,4-nodeC3D8R:Continuum,3-D,8-node,ReducedintegrationS4R:Shell,4-node,ReducedintegrationIntroduction(4/7)GeneralcharacteristicsoftheAbaqus/ExplicitelementlibraryAbaqus/Explicit(likeotherexplicitcodes)usesthelumpedmassformulationforallelements.Abaqus/Explicit(likeotherexplicitcodes)usesprimarilyreduced-integrationelements.Reduced-integrationelementsarecomputationallyinexpensive.Withexplicitmethods,theperformancebottlenecktendstobetheelementcomputations.However,Abaqus/Explicitdoesofferseveralfullyintegratedelements:Three-dimensionalhexahedralelements(C3D8,C3D8I)Quadrilateralshell(S4)andmembrane(M3D4)elementsTriangularandtetrahedralelementsAbaqus/Explicitincludesmostlyfirst-orderinterpolationelements.Exceptions:second-ordertriangularandtetrahedralelements,second-orderbeamelements.Introduction(5/7)Allelementsincludeavarietyofelement-basedloads,forexample:Bodyloads(e.g.,gravity)SurfacepressureloadsonsolidandshellelementsForceperunitlengthloadsonbeamelementsandshellelementedgesAllelementsaresuitableforgeometricallynonlinearanalysis.Largedisplacementsandrotations.Largestrain,exceptforthesmall-strainshellelements.Therearenogeneralrestrictionsontheuseofparticularmaterialbehaviorswithaparticularelementtype.Anycombinationthatmakessenseisacceptable.Introduction(6/7)MostAbaqus/ExplicitelementtypesarealsoavailableinAbaqus/Standard.Exception:small-strainshellelementsareuniquetoAbaqus/ExplicitThereareseveralspecializedelementtypesavailableinAbaqus/StandardwhicharenotavailableinAbaqus/Explicit,including:HybridelementsGeneralizedplanestrainelementsCylindricalelementsElementtypesforanalysistypesthatareonlyavailableforAbaqus/Standard,suchasdiffusive(heattransferormass)elements,coupledthermal-electricalelements,porepressureelements,andpiezoelectricelements.Introduction(7/7)Abaqus/StandardAbaqus/ExplicitFirstorderSecondorderOnlymodifiedtrianglesandtetrahedralsFullintegrationOnlythefollowing:Three-dimensionalhexahedralelements(C3D8,C3D8I)TriangularandtetrahedralelementsReducedintegrationElementTypesOverview(1/6)Solid(continuum)elements:Quadrilateralandhexahedralelementsarethemendedsolidelements.Modifiedtriangular/tetrahedralelementsshouldbeusedwhenquadrilateral/hexahedralmeshgenerationisnotpossibleorpractical.C3D10MC3D8RUndeformedgasketCompressedgasketGasketmodeledwithplanestrainelements(CPE4R)TetrahedralmeshofabracketElementTypesOverview(2/6)Shellelements:Shelltheoryapproximatesathree-dimensionalcontinuumwitha

two-dimensionaltheory.Abaqus/Explicitoffersconventionalshellelementsandcontinuumshellelements.

Membraneelements:Membraneelements(M3D4R,M3D4,M3D3)areused

tomodelthinsurfacesthatofferstrengthin

theplaneoftheelementbuthave

nobendingstiffness.Sidecurtainairbag(M3D3)Conventionalshellfiniteelementmesh(e.g.,S4R)Continuumshellfiniteelementmesh(SC8R)structuralbodybeingmodeledElementTypesOverview(3/6)Beamelements:Beamtheoryapproximatesathree-dimensionalcontinuumwithaone-dimensionaltheory.Trusselements:Trusselementsarerodsthatcancarryonlytensileorcompressiveloads.Usetomodelwires,rope,etc.linemodel3-DcontinuumGholami,T.,J.Lescheticky,andR.Pa?mann(BMWGroup),“CrashworthinessSimulationofAutomobileswithABAQUS/Explicit,”ABAQUSUsers'Conference,Munich,2003.BeamelementstomodelseatreinforcementElementTypesOverview(4/6)Abaqus/Explicithasanumberofspecial-purposeelements,including:MassandrotaryinertiaelementsUsedtospecifyinertialpropertiesatdiscretepoints.NonstructuralmassUsedtomodelfeaturesthatcontributetothemodelmassbuthavenegligiblestructuralstiffness.SurfaceelementsVersatileelementsthatmodelsurfacesinspace.ConnectorelementsandcohesiveelementsUsedtomodelconnectionsbetweenregionsofamodel.TheseelementsarediscussedinLecture6,ConstraintsandConnections.User-definedelementsCreateelementswiththeVUELusersubroutine.ElementTypesOverview(5/6)Rigidbodies:Arigidbodyisacollectionofnodesandelementswhosemotionisgovernedbythemotionofasinglereferencenode.Arigidbodydefinitionmaycontain:Anelementsetwhichmaycontaindeformableand/orrigid(R3D4)elementsNodessets(pinnedortied)AnanalyticalrigidsurfaceAthree-dimensionalsurfaceobtainedbyrevolvingorextrudingatwo-dimensionalgeometricprofileanalyticalrigidanvildiscreterigidpunchWirecrimpingexampleElementTypesOverview(6/6)Eulerianelements:Eulerianelementsstayfixedwhilematerialflowsthroughthemesh.Theseelementsallowforeffectivemodelingofextremedeformation,includingfluidflow.MaterialsintheEulerianmeshcaninteractwithtraditionalLagrangianelementsviageneralcontactYoucanmodelinteractionsbetweenhighlydeformablematerialsandrelativelystiffbodies,suchasinfluid-structureinteractions.Particleelements:SmoothedParticleHydrodynamics(SPH)isameshlessLagrangianmethodformodelingextremedeformation,includingfluidflowSPHallowsforefficientsimulationofhigh-velocityimpacts,extremelyviolentfluidflows,andmaterialphasechanges.TheEulerianandSPHmodelingtechniquesarediscussedindetailintheModelingExtremeDeformationandFluidFlowwithAbaquslecturenotes.TirehydroplaninganalysisWatermovesthroughEulerianelementsTiremodeledwithLagrangianelementsProjectileimpactingsolidplatecontinuumsolidprojectileSPHpatchHourglassingandLocking(1/17)Inmostgeneralproblemsthestiffnessandmassofanelementmustbecalculatednumerically.Thenumericalalgorithmusedtointegratethesevariablesinfluenceshowanelementbehaves.Abaqus/Explicitprimarilyusesreducedintegrationforfirst-orderelements;thatis,onlyoneintegrationpointperelement.Theseelementsarecheapandeffective.Theyminimizethecomputationalexpenseofelementcalculations.HourglassingandLocking(2/17)Theuseofthereduced-integrationschemehasadrawback:itcanresultinmeshinstability,commonlyreferredtoas“hourglassing.”Thehourglassmodedoesnotcauseanystrainand,hence,doesnotcontributetotheenergyintegral.Itbehavesinamannerthatissimilartothatofarigidbodymode.Example:Rubberblockcompresseddiagonallybyarigidsurface.RubberblockmodelFinaldeformedshapeHourglassingandLocking(3/17)FourcommoncausesofexcessivehourglassingandtheirremediesConcentratedforceatasinglenodeRemedy:distributetheforceamongseveralnodesorapplyadistributedload.BoundaryconditionatasinglenodeRemedy:distributetheboundaryconstraintamongseveralnodes.ContactatasinglenodeRemedy:distributethecontactconstraintamongseveralnodes.BendingwithtoofewelementsRemedy:useatleast4elementsthroughthesectionofbendingregions.Roundedcornerpreventshourglassingofrubberblock.undeformeddeformedHourglassingandLocking(4/17)Abaqus/Explicitdoesincludesomefullyintegratedfirst-orderelements.Advantages:Theydonotsufferfromhourglassing.Theycancapturestressgradientswithfewerelements.Disadvantages:Theyarecomputationallyexpensive.Theycansufferfromshearandvolumetriclocking.Mostofthefully-integratedelementsinAbaqusareformulatedtoavoidlocking.Forexample,S4istreatedwithanassumed-strainformulationthatavoidsparasiticlocking.Thefully-integratedsolidelement(C3D8),however,issusceptibletolocking.HourglassingandLocking(5/17)Shearlockingcausestheelementtobehavetoostifflyinbending.Thiswillbediscussednext.Volumetriclockingoccurswhenthematerialbehaviorisnearlypressible.Inthiscase,eachintegrationpoint’svolumemustremainalmostconstant,overconstrainingthekinematicallyadmissibledisplacementfield.Theresultisthattheelementbehavestoostifflyfordeformationsthatshouldcausenovolumechange.Exampleoftheeffectofvolumetriclockingofametalwithlargeplasticstrainsoverlystiffbehaviorofanelastic-plasticmaterialwithvolumetriclockingcorrectbehaviorofanelastic-plasticmaterialHourglassingandLocking(6/17)Considerthephysicalcharacteristicsofpurebending.Theassumedbehaviorofthematerialthatfiniteelementsattempttomodelis:Planecross-sectionsremainplanethroughoutthedeformation.Theaxialstrainxx

varieslinearlythroughthethickness.Thestraininthethicknessdirectionyy

iszeroif

=0.Nomembraneshearstrain.Impliesthatlinesparalleltothebeamaxislieonacirculararc.xxHourglassingandLocking(7/17)Modelingbendingusingfirst-orderfully-integratedsolidelements(CPS4,CPE4,C3D8)Theseelementsdetectshearstrainsattheintegrationpoints.Nonphysical;presentsolelybecauseoftheelementformulationused.Overlystiffbehaviorresultsfromenergygoingintoshearingtheelementratherthanbendingit

(called“shearlocking”).Becausetheelementedgesmustremainstraight,theanglebetweenthedeformedisoparametriclinesisnotequalto90o

(implies).integrationpointDonotusetheseelementsinregionsdominatedbybending!HourglassingandLocking(8/17)Modelingbendingusingfirst-orderreduced-integrationelements(CPE4R,…)Theseelementseliminateshearlocking.However,hourglassingisaconcernwhenusingtheseelements.Onlyoneintegrationpointatthecentroid.Asingleelementthroughthethicknessdoesnotdetectstraininbending.Deformationisazero-energymode(deformationbutnostrain;called“hourglassing”).Changeinlengthiszero(impliesnostrainisdetectedattheintegrationpoint).Bendingbehaviorforasinglefirst-orderreduced-integrationelementHourglassingandLocking(9/17)Hourglassingcanpropagateeasilythroughameshoffirst-orderreduced-integrationelements,causingunreliableresults.Hourglassingisnotaproblemifyouusemultipleelements—atleastfourthroughthethickness.Eachelementcaptureseithercompressiveortensileaxialstrainsbutnotboth.Theaxialstrainsaremeasuredcorrectly.Thethicknessandshearstrainsarezero.Cheapandeffectiveelements.HourglassingandLocking(10/17)Whenishourglassingaproblem?HourglassingisalmostneveraproblemwiththeenhancedhourglasscontrolavailableinAbaqus.MorerobustthanotherschemesNouser-setparametersBasedonenhancedstrainmethodsRubberdiskrollingagainstrigiddrumCombinedhourglasscontrolschemeEnhancedhourglasscontrolschemeloaddiskrolldrumloaddiskrolldrumComparisonofenergyhistoriesALLIEALLIEALLAEALLAEHourglassingandLocking(11/17)Toactivateenhancedhourglasscontrol,usetheoption

*SOLIDSECTION,CONTROLS=name,ELSET=elset *SECTIONCONTROLS,NAME=name,HOURGLASS=ENHANCED

NouserparametersAbaqus/CAEusage:

Meshmodule:Mesh>ElementTypeHourglassingandLocking(12/17)Currently,enhancedhourglasscontrolisnotthedefaultschemeformostelements.

Enhancedhourglasscontrolisthedefaultfor:AllmodifiedtriangleandtetrahedralelementsAllelementsmodeledwithfinite-strainelasticmaterials(hyperelasticandhyperfoam)Abaqus/ExplicithourglasscontrolmethodsRelaxstiffness(defaultformostelements)EnhancedstrainStiffnessViscousCombined(stiffness+viscous)HourglassingandLocking(13/17)Excessiveuseofhourglasscontrolenergycanbeidentifiedbylookingattheenergyhistories.Verifythattheartificialenergyusedtocontrolhourglassingissmall(<1%)relativetotheinternalenergy.UsetheenergyoutputquantitiesALLAEandALLIEtoverifythis.Theexceptiontothisruleisthecaseofelasticbendingwithacoarsemeshwhenenhancedhourglasscontrolisused.Thisisdiscussednext.RubberdiskrollingagainstrigiddrumCombinedhourglasscontrolComparisonofenergyhistoriesloaddiskrolldrumALLIEALLAEloaddiskrolldrumALLIEALLAEEnhancedhourglasscontrolHourglassingandLocking(14/17)ElasticbendingproblemsandcoarsemeshaccuracyForelasticbendingproblems,improvedcoarsemeshaccuracymaybeobtainedusingtheenhancedhourglasscontrolmethod.Theenhancedhourglasscontrolformulationistunedtogiveaccurateresultsforregularlyshapedelementsundergoingelasticbending.Wheretheseconditionsapply,acoarsemeshmaygiveacceptableresultsdespitetheartificialenergybeinggreaterthanafewpercentoftheinternalenergy.Anindependentcheckoftheresultsshouldbemadetodetermineiftheyareacceptable.PlasticbendingproblemsWhenplasticityispresent,thestiffness-basedhourglasscontrolcauseselementstobelessstiffthanintheenhancedcontrolcase.Thismaygivebetterresultswithplasticbending;enhancedhourglasscontrolmaycausedelayedyieldingorexcessivespringback.Inusingenhancedhourglasscontrolinthiscase,theusualrule-of-thumbregardingtheacceptablelevelofartificialenergyshouldbefollowed.RecallthatC3D10Melementsuseenhancedhourglasscontrolbydefault.Usealternativehourglasscontrolforproblemsinvolvingyielding.HourglassingandLocking(15/17)Thefirst-order,patiblemodeelement(C3D8I)modelsbendingeffect