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RBEs and MPCs in MSC.NastranRBEs and MPCs in MSC.Nastran
A Rip-Roarin Review of
Rigid Elements
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Slide 2
RBEs and MPCsRBEs and MPCs
Not necessarily rigid elementsWorking Definition:
The motion of a DOF is dependent on
the motion of at least one other DOF
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Slide 3
Motion at one GRID drives anotherMotion at one GRID drives another
Simple Translation
X motion of Green Grid drives X motion
of Red Grid
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Slide 4
Motion at one GRID drives anotherMotion at one GRID drives another
Simple Rotation
Rotation of Green Grid drives X translation
and Z rotation of Red Grid
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Slide 5
RBEs and MPCsRBEs and MPCs
The motion of a DOF is dependent onthe motion of at least one other DOF
Displacement, not elastic relationship
Not dictated by stiffness, mass, or force
Linear relationship
Small displacement theory
Dependent v. Independent DOFs
Stiffness/mass/loads at dependent DOFtransferred to independent DOF(s)
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Slide 6
Small Displacement Theory & RotationsSmall Displacement Theory & Rotations
Small displacement theory:sin() = tan() =
cos() = 1
For Rz @ A
RzB = RzA=
TxB = (-
)*LABTyB = 0
X
Y
A
B
-
TxB
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Geometry-basedRBAR
RBE2
Geometry- & User-input basedRBE3
User-input based
MPC
Typical Rigid Elements in MSC.NastranTypical Rigid Elements in MSC.Nastran
}Really-rigid rigid elements
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Common Geometry-Based Rigid ElementsCommon Geometry-Based Rigid Elements
RBARRigid Bar with six DOF at
each end
RBE2
Rigid body with
independent DOF at oneGRID, and dependent DOFat an arbitrary number ofGRIDs.
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The RBARThe RBAR
The RBAR is a rigid link between twoGRID points
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The RBARThe RBAR
Can mix/match dependent DOF between theGRIDs, but this is rare
The independent DOFs must be capable ofdescribing the rigid body motion of the element
1234561234561 2RBAR 535
CMA CMBCNA CNBGA GBRBAR EID
Most common to have all thedependent DOFs at one GRID,and all the independent DOFs atthe other
B
A
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RBAR Example: FastenerRBAR Example: Fastener
Use of RBAR to weld two parts of amodel together:
1234561234561 2RBAR 535
CMA CMBCNA CNBGA GBRBAR EID
B
A
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RBAR Example: Pin-JointRBAR Example: Pin-Joint
Use of RBAR to form pin-jointedattachment
1231234561 2RBAR 535
CMA CMBCNA CNBGA GBRBAR EID
B
A
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The RBE2The RBE2
One independent GRID (all 6 DOF)
Multiple dependent GRID/DOFs
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RBE2 ExampleRBE2 Example
Rigidly weld multiple GRIDs to oneother GRID:
32RBE2 4110199 123456
GM5GM3GM2RBE2 GM4GM1GNEID CM
13
2
101
4
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Slide 15
RBE2 ExampleRBE2 Example
Note: No relative motion between
GRIDs 1-4 !No deformation of element(s)
between these GRIDs
32RBE2 4110199 123456
GM5GM3GM2RBE2 GM4GM1GNEID CM
13
2
101
4
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Slide 16
Common RBE2/RBAR UsesCommon RBE2/RBAR Uses
RBE2 or RBAR between 2 GRIDsWeld 2 different parts together
6DOF connection
Bolt 2 different parts together 3DOF connection
RBE2
Spider or wagon wheel connectionsLarge mass/base-drive connection
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Slide 17
RBE3 ElementsRBE3 Elements
NOT a rigid element
IS an interpolation elementDoes not add stiffness to the structure
(if used correctly)
Motion at a dependent GRIDis the weighted average ofthe motion(s) at a set of
master (independent) GRIDs
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Slide 18
RBE3 DescriptionRBE3 Description
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Slide 19
RBE3 DescriptionRBE3 Description
By default, the reference grid DOF willbe the dependent DOF
Number of dependent DOF is equal to
the number of DOF on the REFC field Dependent DOF cannot be SPCd,
OMITted, SUPORTed or be dependent
on other RBE/MPC elements
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Slide 20
U99 = (U1 + U2 + U3) / 3
3 * U99
= U1
+ U2
+ U3
-U1 = + U2 + U3 - 3 * U99
RBE3 DescriptionRBE3 Description
UM fields can be used to move thedependent DOF away from thereference grid
For Example (in 1-D):
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Slide 21
RBE3 Is Not Rigid!RBE3 Is Not Rigid!
RBE3 vs. RBE2 RBE3 allows warping
and 3D effects
In this example, RBE2 enforces beam
theory (plane sections remain planar)RBE3 RBE2
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Slide 22
RBE3: How it Works?RBE3: How it Works?
Forces/moments applied at referencegrid are distributed to the master gridsin same manner as classical bolt patternanalysis
Step 1: Applied loads are transferred to theCG of the weighted grid group using anequivalent Force/Moment
Step 2: Applied loads at CG transferred tomaster grids according to each gridsweighting factor
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Slide 23
RBE3: How it Works?RBE3: How it Works?
Step 1: Transform force/moment atreference grid to equivalent force/moment
at weighted CG of master grids.
MCG
=MA+F
A*e
FCG
=FA
CG
FCG
MCG
FA
MA
Reference Grid
e
CG
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Slide 24
RBE3: How it Works?RBE3: How it Works?
Step 2: Move loads at CG to mastergrids according to their weightingvalues.
Force at CG divided amongst master gridsaccording to weighting factors Wi
Moment at CG mapped as equivalent forcecouples on master grids according toweighting factors Wi
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Slide 25
RBE3: How it Works?RBE3: How it Works?
Step 2: Continued
CG
FCG
MCG
Total force at each master node is sum of...
Forces derived from force at CG: Fif = FCG{Wi/Wi}
F1m
F3mF2m
Plus Forces derived from moment at CG:
Fim = {McgWiri/(W1r12+W2r2
2+W3r32)}
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Slide 26
RBE3: How it Works?RBE3: How it Works?
Masses on reference grid are smearedto the master grids similar to how forcesare distributed
Mass is distributed to the master grids accordingto their weighting factors
Motion of reference mass results in inertial forcethat gets transferred to master grids
Reference node inertial force is distributed insame manner as when static force is applied to
the reference grid.
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Slide 27
Example 1Example 1
RBE3 distribution of loads when force atreference grid at CG passes throughCG of master grids
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Slide 28
Example 1: Force Through CGExample 1: Force Through CG
Simply supported beam10 elements, 11 nodes numbered 1
through 11
100 LB. Force in negative Y onreference grid 99
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Slide 29
Example 1: Force Through CGExample 1: Force Through CG
Load through CG with uniform weightingfactors results in uniform load distribution
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Slide 30
Example 1: Force Through CGExample 1: Force Through CG
CommentsSince master grids are co-linear, the x
rotation DOF is added so that master grids
can determine all 6 rigid body motions,otherwise RBE3 would be singular
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Slide 31
Example 2Example 2
How does the RBE3 distribute loadswhen force on reference grid does notpass through CG of master grids?
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Slide 32
Example 2: Load not through CGExample 2: Load not through CG
The resulting force distribution is not intuitivelyobvious
Note forces in the opposite direction on the left sideof the beam.
Upward loads on left
side of beam result
from moment caused
by movement ofapplied load to the CG
of master grids.
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Slide 33
Example 3Example 3
Use of weighting factors to generaterealistic load distribution: 100 LB.transverse load on 3D beam.
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Slide 34
Example 3: Transverse Load on BeamExample 3: Transverse Load on Beam
If uniformweightingfactors are
used, the loadis equallydistributed to allgrids.
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Slide 35
Example 3: Transverse Load on BeamExample 3: Transverse Load on Beam
Displacement Contour
The uniform load distribution results intoo much transverse load in flangescausing them to droop.
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Slide 36
Example 3: Transverse Load on BeamExample 3: Transverse Load on Beam
Assume quadraticdistribution of load in web
Assume thin flanges carry
zero transverse load Master DOF 1235. DOF 5
added to make RY rigid
body motion determinate
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Slide 37
Displacements with quadratic weightingfactors virtually equivalent to those fromRBE2 (Beam Theory), but do not
impose plane sections remain planaras does RBE2.
Example 3: Transverse Load on BeamExample 3: Transverse Load on Beam
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Slide 38
Example 3: Transverse Load on BeamExample 3: Transverse Load on Beam
RBE3 Displacement Contour
Max Y disp=.00685
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Slide 39
Example 3: Transverse Load on BeamExample 3: Transverse Load on Beam
RBE2 Displacement contour
Max Y disp=.00685
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Slide 40
Example 4Example 4
Use RBE3 to getunconstrainedmotion
Cylinder underpressure
Which Grid(s) do youpick to constrain out
Rigid body motion, butstill allow for freeexpansion due topressure?
Example 4: Use RBE3 forExample 4: Use RBE3 for
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Slide 41
Example 4: Use RBE3 forExample 4: Use RBE3 for
Unconstrained MotionUnconstrained Motion
Solution: Use RBE3
Move dependent DOF from reference grid to selected mastergrids with UM option on RBE3 (otherwise, reference gridcannot be SPCd)
Apply SPC to reference grid
Example 4: Use RBE3 forExample 4: Use RBE3 for
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Slide 42
Example 4: Use RBE3 forExample 4: Use RBE3 for
Unconstrained MotionUnconstrained Motion
Since reference grid has 6 DOF, wemust assign 6 UM DOF to a set ofmaster grids
Pick 3 points, forming a nice triangle forbest numerical conditioning
Select a total of 6 DOF over the three UMgrids to determine the 6 rigid body motionsof the RBE3
Note: M is the NASTRAN DOF set namefor dependent DOF
Example 4: Use RBE3 forExample 4: Use RBE3 for
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Slide 43
Example 4: Use RBE3 forExample 4: Use RBE3 for
Unconstrained MotionUnconstrained Motion
UM Grids
Example 4: Use RBE3 forExample 4: Use RBE3 for
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Slide 44
Example 4: Use RBE3 forExample 4: Use RBE3 for
Unconstrained MotionUnconstrained Motion
For circular geometry, its convenient touse a cylindrical coordinate system forthe master grids.
Put THETA and Z DOF in UM set for each of thethree UM grids to determine RBE3 rigid bodymotion
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Example 4: Use RBE3 forExample 4: Use RBE3 for
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Slide 46
Example 4: Use RBE3 forExample 4: Use RBE3 for
Unconstrained MotionUnconstrained Motion
ResultingMPC Forcesare numeric
zeroesverifying thatno stiffnesshas beenadded.
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Slide 47
Example 5Example 5
Connect 3D model to stick model 3D model with 7 psi internal pressure
Use RBE3 instead of RBE2 so that 3D
model can expand naturally at interface.RBE3 will also allow warping and other 3D
effects at the interface.
Example 5: 3D to Stick ModelExample 5: 3D to Stick Model
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Slide 48
Example 5: 3D to Stick ModelExample 5: 3D to Stick Model
ConnectionConnection
120 diameter
cylinder 7 psi internal
pressure
10000 Lb.transverse load on
stick model
RBE3: Referencegrid at center with6 DOF, MasterGrids with 3
translations
Example 5: 3D to Stick ModelExample 5: 3D to Stick Model
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Slide 49
Example 5: 3D to Stick ModelExample 5: 3D to Stick Model
ConnectionConnection
Example 5: 3D to Stick ModelExample 5: 3D to Stick Model
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Slide 50
Example 5: 3D to Stick ModelExample 5: 3D to Stick Model
ConnectionConnection
Undeformed/Deformed plot showscontinuity in motion of 3D and Beammodel
Example 5: 3D to Stick ModelExample 5: 3D to Stick Model
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Slide 51
Example 5: 3D to Stick ModelExample 5: 3D to Stick Model
ConnectionConnection
MPC forces atinterface showeffect of both thetip shear and
interfacemoment.
Example 5: 3D to Stick ModelExample 5: 3D to Stick Model
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Slide 52
Example 5: 3D to Stick ModelExample 5: 3D to Stick Model
ConnectionConnection
Shell outer fiberstresses at interfaceslightly higher thanbeam bending
stresses
3D effects
Shell model underinternal pressure andnot bound by beamtheory assumptions
E l 6E l 6
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Slide 53
Example 6Example 6
Use RBE3 to see beam type modesfrom a complex model
Sometimes its difficult to identify and
describe modes of complex structures Solution:
Connect complex structure down to
centerline grids with RBE3.Connect centerline grids with PLOTELs
Example 6: Using RBE3 to VisualizeExample 6: Using RBE3 to Visualize
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Slide 54
Example 6: Using RBE3 to VisualizeExample 6: Using RBE3 to Visualize
Beam ModesBeam Modes
Generic engine courtesy of Pratt &Whitney
Example 6: Using RBE3 to VisualizeExample 6: Using RBE3 to Visualize
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Slide 55
Example 6: Using RBE3 to VisualizeExample 6: Using R E3 to Visualize
Beam ModesBeam Modes
RBE3s used toconnect variouscomponents tocenterline.
Each componentscenterline gridsconnected by its
own set of PLOTELs
Example 6: Using RBE3 to VisualizeExample 6: Using RBE3 to Visualize
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Slide 56
Example 6: Using RBE3 to Visualizep g
Beam ModesBeam Modes
ComplexModeAnimation
Example 6: Using RBE3 to VisualizeExample 6: Using RBE3 to Visualize
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Slide 57
Example 6: Using RBE3 to Visualizep g
Beam ModesBeam Modes
Animation of thePLOTELsegmentsshows that this
is a whirl mode Relative motion
of variouscomponents
more clearlyseen
E l 7E l 7
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Slide 58
Example 7Example 7
Use RBE3 to connect incompatibleelements
Beam to plate
Beam to solidPlate to solid
Alternative to RSSCON
Example 7: RBE3 Connection ofExample 7: RBE3 Connection of
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Slide 59
pp
Incompatible ElementsIncompatible Elements
Example 7: RBE3 Connection ofExample 7: RBE3 Connection of
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Slide 60
pp
Incompatible ElementsIncompatible Elements
Use RBE3 to connect beams to platesat two corners
Use RBE3 to connect beams to solids
at two corners Use RBE3 to connect plates to solid
Plate thickness is same as solid thickness
in this example
Example 7: RBE3 Connection ofExample 7: RBE3 Connection of
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Slide 61
pp
Incompatible ElementsIncompatible Elements
RBE3 connection of beams to platesMap 6 DOF of beam into plate translation DOF
For best results, beam footprint should be similar toRBE3 footprint, otherwise joint will be too stiff
Example 7: RBE3 Connection ofExample 7: RBE3 Connection of
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Slide 62
pp
Incompatible ElementsIncompatible Elements
RBE3 connection ofbeams to solids
Map 6 DOF of beam intosolid translation DOF
For best results, beamfootprint should besimilar to RBE3 footprint,otherwise joint will be too
stiff
Example 7: RBE3 Connection ofExample 7: RBE3 Connection of
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Slide 63
pp
Incompatible ElementsIncompatible Elements
RBE3 connectionof plates to solids Coupling of plate
drilling rotation to solidnot recommended
Plate and solid gridscan be equivalent,coincident, or disjoint(as shown)
Example 7: RBE3 Connection ofExample 7: RBE3 Connection of
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Slide 64
pp
Incompatible ElementsIncompatible Elements
Deformation contours show continuity atRBE3 interfaces
Example 7: RBE3 Connection ofExample 7: RBE3 Connection of
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Slide 65
p
Incompatible ElementsIncompatible Elements
Bending stress contours consistentacross RBE3 interface
RBE3 Usage GuidelinesRBE3 Usage Guidelines
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Slide 66
RBE3 Usage GuidelinesRBE3 Usage Guidelines
Do not specify rotational DOF formaster grids except when necessary toavoid singularity caused by a linear set
of master grids Using rotational DOF on master grids
can result in implausible results (seenext two slides)
RBE3 Usage GuidelinesRBE3 Usage Guidelines
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Slide 67
RBE3 Usage GuidelinesRBE3 Usage Guidelines
Example: What can happen if masterrotations included?
Modified RBE3 from Example 5
Displacements clearly incorrect when all 6DOF listed for master grids (next page)
RBE3 Usage GuidelinesRBE3 Usage Guidelines
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Slide 68
RBE3 Usage GuidelinesRBE3 Usage Guidelines
Deformation withall 6 DOFspecified formaster grids at
interface Deformation with
3 translation DOFspecified formaster grids(same loads/BCs)
RBE3 Usage GuidelinesRBE3 Usage Guidelines
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Slide 69
RBE3 Usage GuidelinesRBE3 Usage Guidelines
Make check run with PARAM,CHECKOUT,YES Section 9.4.1 of MSC.Nastran Reference Manual (V68)
EMH printout should be numeric zeroes (no grounding)
No MAXRATIO error messages from decomposition of Rgmm
and Rm
mm matrices (numerically stable)
Perform grounding check of at least KGG
and KNN matrix
V2001: Case control command GROUNDCHECK (SET=(G,N))=YES
V70.7 and earlier:
Use CHECKA alters from SSSALTER library
RBE3: Additional ReadingRBE3: Additional Reading
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Slide 70
RBE3: Additional ReadingRBE3: Additional Reading
Much RBE3 information has been posted onMSCs Knowledge Base http://www.mechsolutions.com/support/knowbase/index.html
RBE3: Additional ReadingRBE3: Additional Reading
http://www.mechsolutions.com/support/knowbase/index.htmlhttp://www.mechsolutions.com/support/knowbase/index.htmlhttp://www.mechsolutions.com/support/knowbase/index.htmlhttp://www.mechsolutions.com/support/knowbase/index.html8/2/2019 RBEs and MPCs in MSC.nastran2[1]
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Slide 71
RBE3: Additional ReadingRBE3: Additional Reading
Recommended TANs TAN#: 2402 RBE3 - The Interpolation Element.
TAN#: 3280 RBE3 ELEMENT CHANGES IN VERSION
70.5, improved diagnostics
TAN#: 4155 RBE3 ELEMENT CHANGES IN VERSION70.7
TAN#: 4494 Mathematical Specification of the Modern
RBE3 Element
TAN#: 4497 AN ECONOMICAL METHOD TO EVALUATERBE3 ELEMENTS IN LARGE-SIZE MODELS
User-Input based Rigid ElementsUser-Input based Rigid Elements
http://www.mechsolutions.com/support/knowbase/index.htmlhttp://www.mechsolutions.com/support/knowbase/index.htmlhttp://www.mechsolutions.com/support/knowbase/index.htmlhttp://www.mechsolutions.com/support/knowbase/index.htmlhttp://www.mechsolutions.com/support/knowbase/index.htmlhttp://www.mechsolutions.com/support/knowbase/index.htmlhttp://www.mechsolutions.com/support/knowbase/NASTRAN/tan/tan2402.htmlhttp://www.mechsolutions.com/support/knowbase/NASTRAN/tan/tan3280.htmlhttp://www.mechsolutions.com/support/knowbase/NASTRAN/tan/tan4155.htmlhttp://www.mechsolutions.com/support/knowbase/NASTRAN/tan/tan4155.htmlhttp://www.mechsolutions.com/support/knowbase/NASTRAN/tan/tan4494.htmlhttp://www.mechsolutions.com/support/knowbase/NASTRAN/tan/tan4497.htmlhttp://www.mechsolutions.com/support/knowbase/NASTRAN/tan/tan4497.htmlhttp://www.mechsolutions.com/support/knowbase/NASTRAN/tan/tan4494.htmlhttp://www.mechsolutions.com/support/knowbase/NASTRAN/tan/tan4155.htmlhttp://www.mechsolutions.com/support/knowbase/NASTRAN/tan/tan3280.htmlhttp://www.mechsolutions.com/support/knowbase/NASTRAN/tan/tan2402.html8/2/2019 RBEs and MPCs in MSC.nastran2[1]
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Slide 72
User-Input based Rigid ElementsUser-Input based Rigid Elements
MPCsMost general-purpose way to define
motion-based relationships
Couldbe used in place of ALL other RBEi Lack of geometry makes this impractical
Can be changed between SUBCASEs
MPC DefinitionMPC Definition
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Slide 73
MPC DefinitionMPC Definition
Rigid elementsDefinition: The motion of a DOF dependent
on the motion of (at least one) other DOF
Linear Relationship
One (1) dependent DOF
n independent DOF (n >= 1)
ajXi = a1X1 + a2X2 +a3X3++ anXn
General Approach For Use of MPCsGeneral Approach For Use of MPCs
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Slide 74
General Approach For Use of MPCsGeneral Approach For Use of MPCs
Write out desired displacement equalityrelationship on a per DOF level
Dependent motion = (your equation goes here)
0 = - Ux2 + Ux1
Re-arrange so left-hand side is zero
List dependent term first
Ux2 = Ux12
1
MPC FormatMPC Format
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Slide 75
MPC FormatMPC Format
For example:Set X motion of GRID 2
= X motion of GRID 1
UX2 = UX1 0 = - UX2 + UX1
= (-1.)UX2 + (+1.)UX1
1 +1.0-1.0 12 1MPC 535C2 A2A1 G2G1 C1MPC SID
2
1
General Approach to MPCsGeneral Approach to MPCs
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General Approach to MPCsGeneral Approach to MPCs
Write down relationship you want toimpose on a per DOF level:
ajXi = a1X1 + a2X2 ++ anXn
0 = -aiXi + a1X1 + a2X2++ anXn
Move dependent term to 1st term onright hand side:
Why would I want to use an MPC?Why would I want to use an MPC?
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Slide 77
Why would I want to use an MPC?Why would I want to use an MPC?
Tie GRIDs together (RBEi) Determine relative motion between
GRIDs
Maintain separation between GRIDs Determine average motion between
GRIDs
Model bell-crank or control system
Units conversion
Use of MPC to tie GRIDs togetherUse of MPC to tie GRIDs together
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Slide 78
Use of MPC to tie GRIDs togetherUse of MPC to tie GRIDs together
Write down relationship you want toimpose on a per DOF level:
UX2 = UX1
UY2 = UY2
UZ3 = UZ3
X2 =
X1
Y2 = Y1
Z2 = Z1
1
2
Use of MPC to tie GRIDs togetherUse of MPC to tie GRIDs together
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Slide 79
MPC, 535, 2, 1, -1.0, 1, 1, +1.0
MPC, 535, 2, 2, -1.0, 1, 2, +1.0MPC, 535, 2, 3, -1.0, 1, 3, +1.0
MPC, 535, 2, 4, -1.0, 1, 4, +1.0
MPC, 535, 2, 5, -1.0, 1, 5, +1.0
MPC, 535, 2, 6, -1.0, 1, 6, +1.0
Use of MPC to tie GRIDs togetherUse of MPC to tie GRIDs together
Move dependent term to 1st
term onright hand side:
0 = -UX2 + UX1
0 = -UY2 + UY2
0 = -UZ3 + UZ3
0 = -X2 + X1
0 = -Y2 + Y1
0 = -Z2 + Z1
Use of MPC to tie GRIDs togetherUse of MPC to tie GRIDs together
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Slide 80
Use of MPC to tie GRIDs togetherUse of MPC to tie GRIDs together
Use CAUTION when tying non-coincidentGRIDs together!
Watch for how thoserotations andtranslations couple!2
1 UX2 = UX1
Z2 = Z1
MPCs forMPCs for RelativeRelative MotionMotion
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Slide 81
MPCs forMPCs forRelativeRelative MotionMotion
Whats the relative motion betweenGRIDs 1 and 2?
1 2?
MPCs forMPCs for RelativeRelative MotionMotion
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Slide 82
MPCs forMPCs forRelativeRelative MotionMotion
Introduce placeholder variableGood use for SPOINTs
1 2?
Move dependent term to RHS0 = - U1000 + UX2 UX1
Write out desired
relationship as beforeU1000 = UX2 UX1
MPCs forMPCs for RelativeRelative MotionMotion
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Slide 83
MPCs forMPCs forRelativeRelative MotionMotion
Write out MPCs1 2?
0 = -U1000 + UX2 UX1
SPOINT 1000
MPC 535 1000 1 -1.0 2 1 +1.0+ 1 1 -1.0
MPCs for RelativeMPCs for Relative GAPGAP
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Slide 84
Initial
gap
MPCs for Relative GAP
What is the gap between GRIDs 1 and 2?
1 2
MPCs for RelativeMPCs for Relative GAPGAP
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Slide 85
MPCs for Relative GAP
1 2
UGAP= UINIT + UX2 UX1
0 = -UGAP+ UINIT + UX2 UX1
Write equation:Introduce new placeholder
variable for initial gap
MPCs for RelativeMPCs for Relative GAPGAP
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Slide 86
Set initial gap value via SPC! 1 2
SPOINT, 1000 $ Gap value
SPOINT, 1001 $ Initial Gap
MPC, 535, 1000, 1, -1., 1001, 1, +1.
+, , 2, 1, +1., 1, 1, -1.
SPC, 2002, 1001,1,0.5 $ Set initial gap
0 = -U1000+ U1001 + UX2 UX1
MPC used to Maintain SeparationMPC used to Maintain Separation
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Slide 87
pp
Enforce a separation between GRIDsSimilar to using a gap
Changes which DOF aredependent/independent
Example:
Initially 1 apart
Keep separation = 0.25
1
2
0.25
MPC used to Maintain SeparationMPC used to Maintain Separation
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Slide 88
pp
1
2
0.25
U1= U
2+ (desired initial)
0 = -U1+ U2 + U1000SPOINT,1000
MPC, 535, 1, 2, -1.0, 2, 2, +1.0+, , 1000, 1, +1.0
SPC, 2002, 1000, 1, -.75
1.00
Use of MPCs for AVERAGE MotionUse of MPCs for AVERAGE Motion
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Slide 89
Determine average motion of DOFs
U1000 = (U1+ U2 + U3 + U4 +U5 +U6)/6
0 = -6*U1000 +U1+ U2 + U3 + U4 +U5+U6Z
4
5
2
3
6
1
MPCs as Bell-crank or Control SystemMPCs as Bell-crank or Control System
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Slide 90
yy
Output of 1 DOF scales another
U2 = U1/1.65
0 = -1.65*U2 +U12
1
1 +1.0-1.65 12 1MPC 535
C2 A2A1 G2G1 C1MPC SID
1.
65
1.00
Units ConversionUnits Conversion
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Slide 91
Somewhat frivolous application, but whynot?
Convert radians
to degrees 2 = 1* 57.29578
Convert inchesto meters
39.37 * X2 = X1
Rigid Element OutputRigid Element Output
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Slide 92
g pg p
Since Rigid elements are a specializedinput of MPC equations, the output isrequested by MPCFORCE case controlcommand.
COMMON ERROR
The MPCFORCEs are associated with GRIDIDs, not Element IDs. So when selecting a
SET for output, be sure the set is for GRID IDs,not Element IDs.
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MPCs and RBEsMPCs and RBEs
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Off the shelfRBAR
RBE2
CustomizableRBE3
Handmade
MPC
Add them toyour
modelingarsenal
today!
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