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Making Efficient Connections With RBE2 RBE3 Constraint Equations and CBUSH Elements

Oct 12, 2015

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Vignesh Waran

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  • Page1 of24

    Technical Seminar:TechnicalSeminar:ConnectionElements TheBoringStuff

    Topics: BuildingExpertClassFEModels The Basics: RBE Elements (MPC Elements) TheBasics:RBEElements(MPCElements) ThestandardinSpringElements:CBUSH FemapTipsandTricksoftheMoment:Resolution,TurningoffReferences,SettingViewDisplayOptions

    ABriefQ&APeriod

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  • Page2 of24

    TechnicalSeminar:EfficientConnections

    Building an expertclass FE model is often all about creating efficientBuildinganexpert classFEmodelisoftenallaboutcreatingefficientconnections.

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    TechnicalSeminar:EfficientConnections

    TheBasics:RTypeElements{RigidBody(RBE2)andNot RigidBody(RBE3)}A very useful resource: NX Nastran Element Library ReferenceAveryusefulresource:NXNastranElementLibraryReference

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    TechnicalSeminar:EfficientConnections

    TheBasics:SPCandMPCConstraints(WhatisunderthehoodofRBEs)NX Nastran User Guide: Chapter 9 ConstraintsNXNastranUserGuide:Chapter9Constraints

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  • Page5 of24

    TechnicalSeminar:EfficientConnections

    TheBasics:RTypeElements{RBE2&RBE3}TheRBE2elementdoesntcausenumericaldifficultiesbecauseitdoesntaddtermstothestiffnessmatrix.TheRBE2elementisactuallyaconstraintelementthatprescribesthedisplacementrelationshipbetweentwoormoregridpoints.ThisisthesameconceptusedbytheRBE3.ThecentralthemeisDependentversusIndependentnodes.

    (M t )

    (Master)

    (Master)

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    Note:Note:Usingrigidelementswillcauseincorrectresultsinbucklinganddifferentialstiffnessanalysesbecausethelargedisplacementeffectsarenotcalculated.Exceptions arezerolengthelements(e.g.,tosimulateahinge)andrigidelementsconstrainedsothattheydontrotate.

  • Page6 of24

    TechnicalSeminar:EfficientConnections

    TheBasics:RTypeElements{RBE2}HereisastartingpointtounderstandtheRBE2.Averysimplebeammodelwitha100g p y plbfloadatthecenterofthebeam.ThebeamisheldtogetherwithaRBE2.

    Moment&ForceCalc.M=2.5*50F=100/2

    SimpleBeamwithfixedends TurnOnEquationForce FreeBodyDiagram

    ( )

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    InspectF06(MPCForce)

    ModelFile:FirstRBE2Model.modfem

  • Page7 of24

    TechnicalSeminar:EfficientConnections

    TheBasics:RTypeElements{RBE2}andMPCs{ConstraintEquations}TheunderlyingnumericstoRBEsistheconstraintequation.Onecanbethankfulthatwedonthavetoenterthembyformulabutitisgoodtoseehowtheywork.

    AllRBEsarejustMPCs Th fi t t i th Thefirsttermisthedependentnode(aD)anddependsuponthemovementoftheotherindependent(master)nodes. SettingupMPCsrequiresonetounderstandthebasicequation of mechanics

    NoSpatialRelationship

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    equationofmechanics.

    aDX = a1X1 + a2X2 + a3X3 + + a XaDX a1X1 + a2X2 + a3X3 ++ anXn

    ModelFile:ConstraintEquations.modfem

  • Page8 of24

    TechnicalSeminar:EfficientConnections/NumericalFoundation

    TheBasics:MPCs(i.e.,RBEs)arebasedonconstraintequations.

    Thedependentnodesareremovedfromthedisplacementformulationmatrixsincetheirbehaviorisdescribedbytheindependentnodes.Whydowecare?(i)Onecantapplydisplacementsy pp y ptodependentnodessincetheynolongerexistwithintheucolumn;(ii)However,Forces/Momentscanstillbeappliedtodependentsandindependents;(iii)matrixformulationsareusedandinverted.HenceyourRBEmustnot haveamechanism.RBE2shave6DOFfortheindependentnodewhileRBE3saredefinedbytheuser(hencemechanismscanoccur!). ByusingMPCs,NXNastran createsnumerically

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    perfectRigids /Interpolation/Etc.

  • Page9 of24

    TechnicalSeminar:EfficientConnections/NumericalFoundation

    TheBasics:MPCs(i.e.,RBEs)arebasedonconstraintequations.

    WhathappenswhenyouconstrainadependentDOFofaRBE2orRBE3?Fromthemechanicsweknowthatthesolverhastobeunhappy This is how it tells us:unhappy.Thisishowittellsus:

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  • Page10 of24

    TechnicalSeminar:EfficientConnections/NumericalFoundation

    TheBasics:MPCs(i.e.,RBEs)arebasedonconstraintequations.

    WhathappenswhenyourRBE3hasamechanism?HereweremovethestabilityDOF(RX)fromourRBE3inthepriormodel. Please be careful and dont over constrain Pleasebecarefulanddon toverconstrainsincetherearenowarningmessages.

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    Note thattheerrormessagecallsoutElement11.NXNastran triestohelpfixtheproblemasmuchasitcan.

  • Page11 of24

    TechnicalSeminar:EfficientConnections

    TheBasics:RTypeElements{RBE2&RBE3}AcomparisonispresentedbetweenRBE2andRBE3formulations.MostpeoplecanfigureouttheloaddistributionfortheRBE2elementbutthatfortheRBE3defiessimplelogicifyoudontknowthemathematicalformulation.

    MomentLoad ForceLoad

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    N t F th RBE3 l t t i l d th TX TZ

    ModelFile:StartRBE3withMomentandForceLoads.modfem

    RBE2MomentCalculationM=2*270.88+2*2.5*91.647M 541 76 458 24 1 000 Note:FortheRBE3elementwemustincludetheTX,TZ,

    &RXDOFontheIndependent sidetopreventrigidbodyrotationoftheRBE3element.ThisistrickyseepriorslideonNumericalFoundation.

    M=541.76+458.24=1,000Butwhythedifferentnumbers?Seenextslide.

  • Page12 of24

    TechnicalSeminar:EfficientConnections

    TheBasics:RTypeElements{RBE2andSuperStiff}UnderstandinghowtheRBE2workscanbeillustratedbycomparingitagainstasuperstiffbeam.

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    RBE2MomentCalculationYoureallycantdowithsimpleForceandMomentSummations.Th RBE2 d f t j b f f i th t i id t i t

    ModelFile:RBE2andSuperStiffBeamwithMomentandForceLoads.modfem

    TheRBE2doesaperfectjobofenforcingtheexactrigidconstraint.

  • Page13 of24

    TechnicalSeminar:EfficientConnections

    TheBasics:RTypeElements{RBE3} MechanicsTheRBE3elementdoesnotcreatestiffnessinthestructure.Thetrickisunderstandinghowtheappliedforceandmomentisdistributedoverthemaster(independent)nodes.

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  • Page14 of24

    TechnicalSeminar:EfficientConnections

    TheBasics:RTypeElements{RBE3}HereisthebackgroundmechanicsontheRBE3element.Youtaketheforce/momentandapplyitatthecentroidoftheindependent(master)nodesandthensplititupequally.

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    100 lbf

    150 lbf*in1,000 lbf*in

    M = 2*250 + 2*100*2 5 = 1 000 lbf*in

    M = 2*37.5 + 15*2.5 + 15*2.5 = 150 lbf*inF = (50 15) + (50 + 15) = 100 lbf

    M = 2 250 + 2 100 2.5 = 1,000 lbf in

  • Page15 of24

    TechnicalSeminar:EfficientConnections

    TheBasics:RTypeElements{RBE3}IfwereducetheDependentDOFoftoTY(1DOF),thentheRBE2andRBE3calculatethefollowing:

    MomentLoad ForceLoad

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    WhentheRBE3hasnoRZ youhavenoRZ

    FinalExample:FinalExampleRBE3withMomentandForceLoads.modfem

  • Page16 of24

    TechnicalSeminar:EfficientConnections

    AnExample:RTypeElements{RBE3}Apipestructureismodeledusingplateelements.Itispartofalargerstructurethatisthenconnectedtoabeamelement.ByusingaRBE3elementwecanmakeagracefultransitionbeforethebeamandplateelements.Itsoundssimplebutitcanalsobetrickytoimplement.

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    Thepipeexpandsandcontractsduetopoisonseffect.

    ModelFile:RBE3PlateandTubeModel.modfem

  • Page17 of24

    TechnicalSeminar:EfficientConnections

    RBE3UsageGuidelines:DonotspecifyrotationalDOFforIndependentNodesexcept whennecessaryto p y p p yavoidsingularitycausedbyalinearsetofmastergrids(RememberPriorBeamModel)

    UsingrotationalDOFonIndependentgridscanresultinimplausibleresults

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    ModelFile:RBE3PlateandTubeModelGuidelines.modfem

  • Page18 of24

    TechnicalSeminar:EfficientConnections

    CBUSHElements:PerfectSpringConnectionSettinguptheElementPropertyfortheCBUSHrequiresspecialcaresinceitisnotthedefaultformulationwithintheFemapmenustructure.

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  • Page19 of24

    TechnicalSeminar:EfficientConnections

    CBUSHElements:NXNastranElementLibrary Chapter6

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    TechnicalSeminar:EfficientConnections

    CBUSHElements:Isa6DOFcustomizablepseudobeamelement.Ithasallthe advantages of a beam element with the ability to dial in spring values.theadvantagesofabeamelementwiththeabilitytodialinspringvalues.

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    Note:IftheCBUSHelementisnotproperlyconstrained,itwillcreatemechanismsmuchlikeanyotherelement.ThisexampleworkswellsincethebeamelementthattheCBUSHisattachedtohas6DOFandisfullyconstrained.

  • Page21 of24

    TechnicalSeminar:EfficientConnections

    CBUSHElements:Isa6DOFcustomizablepseudobeamelement.Ithasallthe advantages of a beam element with the ability to dial in spring values.theadvantagesofabeamelementwiththeabilitytodialinspringvalues.

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    TechnicalSeminar:EfficientConnections

    CBUSHElements:ConnectingCBUSHelements(andlikewisebeamelements)to 3DOF solid elements can be problematic due to rigid body motionsto3DOFsolidelementscanbeproblematicduetorigidbodymotions(mechanisms).

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  • Page23 of24

    TechnicalSeminar:EfficientConnections

    MyStandardFemapSettings:HighResolution Graphics and HousekeepingHigh ResolutionGraphicsandHousekeeping

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    TechnicalSeminar:EfficientConnections

    MyStandardFemapSettings:ViewSettings

    ViewSettingsCanBeSaved Think databaseThinkdatabase Thinkdoonce

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    OpenModelFile:PredictiveEngineeringRecommendedViewSettings.modfem