Making Efficient Connections With RBE2 RBE3 Constraint Equations and CBUSH Elements

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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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Q

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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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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.

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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

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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

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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.

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TechnicalSeminar:EfficientConnections/NumericalFoundation

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

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

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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.

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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.

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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.

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TechnicalSeminar:EfficientConnections

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

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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

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TechnicalSeminar:EfficientConnections

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

MomentLoad ForceLoad

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WhentheRBE3hasnoRZ youhavenoRZ

FinalExample:FinalExampleRBE3withMomentandForceLoads.modfem

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TechnicalSeminar:EfficientConnections

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

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Thepipeexpandsandcontractsduetopoisonseffect.

ModelFile:RBE3PlateandTubeModel.modfem

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TechnicalSeminar:EfficientConnections

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

UsingrotationalDOFonIndependentgridscanresultinimplausibleresults

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ModelFile:RBE3PlateandTubeModelGuidelines.modfem

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TechnicalSeminar:EfficientConnections

CBUSHElements:PerfectSpringConnectionSettinguptheElementPropertyfortheCBUSHrequiresspecialcaresinceitisnotthedefaultformulationwithintheFemapmenustructure.

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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.

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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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TechnicalSeminar:EfficientConnections

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

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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