rbes and mpcs in msc.nastran a rip-roarin’ review of rigid elements
TRANSCRIPT
Slide 2
RBEs and MPCsRBEs and MPCs
• Not necessarily “rigid” elements– Working Definition:
The motion of a DOF is dependent on
the motion of at least one other DOF
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
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
Slide 5
RBEs and MPCsRBEs and MPCs
The motion of a DOF is dependent on
the 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 DOF
transferred to independent DOF(s)
Slide 6
Small Displacement Theory & RotationsSmall Displacement Theory & Rotations
• Small displacement theory:sin() = tan() = cos() = 1
• For Rz @ ARzB = RzA=
TxB = (-)*LAB
TyB = 0 X
Y
A
B
-
TxB
Slide 7
• Geometry-based– RBAR– RBE2
• Geometry- & User-input based– RBE3
• User-input based– MPC
Typical “Rigid” Elements in MSC.NastranTypical “Rigid” Elements in MSC.Nastran
} Really-rigid “rigid” elements
Slide 8
Common Geometry-Based Rigid ElementsCommon Geometry-Based Rigid Elements
• RBAR– Rigid Bar with six DOF at
each end
• RBE2– Rigid body with
independent DOF at one GRID, and dependent DOF at an arbitrary number of GRIDs.
Slide 10
The RBARThe RBAR
– Can mix/match dependent DOF between the GRIDs, but this is rare
– The independent DOFs must be capable of describing the rigid body motion of the element
1234561234561 2RBAR 535
CMA CMBCNA CNBGA GBRBAR EID
– Most common to have all the dependent DOFs at one GRID, and all the independent DOFs at the other
B
A
Slide 11
RBAR Example: FastenerRBAR Example: Fastener
• Use of RBAR to “weld” two parts of a model together:
1234561234561 2RBAR 535
CMA CMBCNA CNBGA GBRBAR EID
B
A
Slide 12
RBAR Example: Pin-JointRBAR Example: Pin-Joint
• Use of RBAR to form pin-jointed attachment
1231234561 2RBAR 535
CMA CMBCNA CNBGA GBRBAR EID
B
A
Slide 14
RBE2 ExampleRBE2 Example
• Rigidly “weld” multiple GRIDs to one other GRID:
32RBE2 4110199 123456
GM5GM3GM2RBE2 GM4GM1GNEID CM
13
2
101
4
Slide 15
RBE2 ExampleRBE2 Example
• Note: No relative motion between GRIDs 1-4 !– No deformation of element(s)
between these GRIDs
32RBE2 4110199 123456GM5GM3GM2RBE2 GM4GM1GNEID CM
13
2
101
4
Slide 16
Common RBE2/RBAR UsesCommon RBE2/RBAR Uses
• RBE2 or RBAR between 2 GRIDs– “Weld” 2 different parts together
• 6DOF connection
– “Bolt” 2 different parts together• 3DOF connection
• RBE2– “Spider” or “wagon wheel” connections– Large mass/base-drive connection
Slide 17
RBE3 ElementsRBE3 Elements
– NOT a “rigid” element– IS an interpolation element– Does not add stiffness to the structure
(if used correctly)
• Motion at a dependent GRID is the weighted average of the motion(s) at a set of master (independent) GRIDs
Slide 19
RBE3 DescriptionRBE3 Description
• By default, the reference grid DOF will be the dependent DOF
• Number of dependent DOF is equal to the number of DOF on the REFC field
• Dependent DOF cannot be SPC’d, OMITted, SUPORTed or be dependent on other RBE/MPC elements
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 the dependent DOF away from the reference grid
– For Example (in 1-D):
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
Slide 22
RBE3: How it Works?RBE3: How it Works?
• Forces/moments applied at reference grid are distributed to the master grids in same manner as classical bolt pattern analysis– Step 1: Applied loads are transferred to the
CG of the weighted grid group using an equivalent Force/Moment
– Step 2: Applied loads at CG transferred to master grids according to each grid’s weighting factor
Slide 23
RBE3: How it Works?RBE3: How it Works?
• Step 1: Transform force/moment at reference grid to equivalent force/moment at weighted CG of master grids.
MCG=MA+FA*e
FCG=FA
CG
FCG
MCG
FA
MA
Reference Grid
e
CG
Slide 24
RBE3: How it Works?RBE3: How it Works?
• Step 2: Move loads at CG to master grids according to their weighting values.– Force at CG divided amongst master grids
according to weighting factors Wi
– Moment at CG mapped as equivalent force couples on master grids according to weighting factors Wi
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/(W1r1
2+W2r22+W3r3
2)}
Slide 26
RBE3: How it Works?RBE3: How it Works?
• Masses on reference grid are smeared to the master grids similar to how forces are distributed– Mass is distributed to the master grids according
to their weighting factors– Motion of reference mass results in inertial force
that gets transferred to master grids
– Reference node inertial force is distributed in same manner as when static force is applied to the reference grid.
Slide 27
Example 1Example 1
• RBE3 distribution of loads when force at reference grid at CG passes through CG of master grids
Slide 28
Example 1: Force Through CGExample 1: Force Through CG
• Simply supported beam– 10 elements, 11 nodes numbered 1
through 11
• 100 LB. Force in negative Y on reference grid 99
Slide 29
Example 1: Force Through CGExample 1: Force Through CG
• Load through CG with uniform weighting factors results in uniform load distribution
Slide 30
Example 1: Force Through CG Example 1: Force Through CG
• Comments…– Since 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
Slide 31
Example 2Example 2
• How does the RBE3 distribute loads when force on reference grid does not pass through CG of master grids?
Slide 32
Example 2: Load not through CGExample 2: Load not through CG
• The resulting force distribution is not intuitively obvious – Note forces in the opposite direction on the left side
of the beam.
Upward loads on left side of beam result from moment caused by movement of applied load to the CG of master grids.
Slide 33
Example 3Example 3
• Use of weighting factors to generate realistic load distribution: 100 LB. transverse load on 3D beam.
Slide 34
Example 3: Transverse Load on BeamExample 3: Transverse Load on Beam
• If uniform weighting factors are used, the load is equally distributed to all grids.
Slide 35
Example 3: Transverse Load on BeamExample 3: Transverse Load on Beam
Displacement Contour
• The uniform load distribution results in too much transverse load in flanges causing them to droop.
Slide 36
Example 3: Transverse Load on BeamExample 3: Transverse Load on Beam
• Assume quadratic distribution of load in web
• Assume thin flanges carry zero transverse load
• Master DOF 1235. DOF 5 added to make RY rigid body motion determinate
Slide 37
• Displacements with quadratic weighting factors virtually equivalent to those from RBE2 (Beam Theory), but do not impose “plane sections remain planar” as does RBE2.
Example 3: Transverse Load on BeamExample 3: Transverse Load on Beam
Slide 38
Example 3: Transverse Load on BeamExample 3: Transverse Load on Beam
• RBE3 Displacement Contour– Max Y disp=.00685
Slide 39
Example 3: Transverse Load on BeamExample 3: Transverse Load on Beam
• RBE2 Displacement contour– Max Y disp=.00685
Slide 40
Example 4Example 4
• Use RBE3 to get “unconstrained” motion
• Cylinder under pressure
• Which Grid(s) do you pick to constrain out Rigid body motion, but still allow for free expansion due to pressure?
Slide 41
Example 4: Use RBE3 for Example 4: Use RBE3 for Unconstrained MotionUnconstrained Motion
• Solution:– Use RBE3
– Move dependent DOF from reference grid to selected master grids with UM option on RBE3 (otherwise, reference grid cannot be SPC’d)
– Apply SPC to reference grid
Slide 42
Example 4: Use RBE3 for Example 4: Use RBE3 for Unconstrained MotionUnconstrained Motion
• Since reference grid has 6 DOF, we must assign 6 “UM” DOF to a set of master grids– Pick 3 points, forming a nice triangle for
best numerical conditioning– Select a total of 6 DOF over the three UM
grids to determine the 6 rigid body motions of the RBE3
– Note: “M” is the NASTRAN DOF set name for dependent DOF
Slide 43
Example 4: Use RBE3 for Example 4: Use RBE3 for Unconstrained MotionUnconstrained Motion
“UM” Grids
Slide 44
Example 4: Use RBE3 for Example 4: Use RBE3 for Unconstrained MotionUnconstrained Motion
• For circular geometry, it’s convenient to use a cylindrical coordinate system for the master grids.– Put THETA and Z DOF in UM set for each of the
three UM grids to determine RBE3 rigid body motion
Slide 45
Example 4: Use RBE3 for Example 4: Use RBE3 for Unconstrained MotionUnconstrained Motion
• Result is free expansion due to internal pressure. (note: poisson effect causes shortening)
Slide 46
Example 4: Use RBE3 for Example 4: Use RBE3 for Unconstrained MotionUnconstrained Motion
• Resulting MPC Forces are numeric zeroes verifying that no stiffness has been added.
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.
Slide 48
Example 5: 3D to Stick Model Example 5: 3D to Stick Model ConnectionConnection
• 120” diameter cylinder
• 7 psi internal pressure
• 10000 Lb. transverse load on stick model
• RBE3: Reference grid at center with 6 DOF, Master Grids with 3 translations
Slide 50
Example 5: 3D to Stick Model Example 5: 3D to Stick Model ConnectionConnection
• Undeformed/Deformed plot shows continuity in motion of 3D and Beam model
Slide 51
Example 5: 3D to Stick Model Example 5: 3D to Stick Model ConnectionConnection
• MPC forces at interface show effect of both the tip shear and interface moment.
Slide 52
Example 5: 3D to Stick Model Example 5: 3D to Stick Model ConnectionConnection
• Shell outer fiber stresses at interface slightly higher than beam bending stresses– 3D effects – Shell model under
internal pressure and not bound by beam theory assumptions
Slide 53
Example 6Example 6
• Use RBE3 to see “beam” type modes from a complex model
• Sometimes it’s difficult to identify and describe modes of complex structures
• Solution: – Connect complex structure down to
centerline grids with RBE3. – Connect centerline grids with PLOTELs
Slide 54
Example 6: Using RBE3 to Visualize Example 6: Using RBE3 to Visualize “Beam” Modes“Beam” Modes
• Generic engine courtesy of Pratt & Whitney
Slide 55
Example 6: Using RBE3 to Visualize Example 6: Using RBE3 to Visualize “Beam” Modes“Beam” Modes
• RBE3’s used to connect various components to centerline.
• Each component’s centerline grids connected by it’s own set of PLOTELs
Slide 56
Example 6: Using RBE3 to Visualize Example 6: Using RBE3 to Visualize “Beam” Modes“Beam” Modes
• Complex Mode Animation
Slide 57
Example 6: Using RBE3 to Visualize Example 6: Using RBE3 to Visualize “Beam” Modes“Beam” Modes
• Animation of the PLOTEL segments shows that this is a whirl mode
• Relative motion of various components more clearly seen
Slide 58
Example 7Example 7
• Use RBE3 to connect incompatible elements– Beam to plate– Beam to solid– Plate to solid
• Alternative to RSSCON
Slide 59
Example 7: RBE3 Connection of Example 7: RBE3 Connection of Incompatible Elements Incompatible Elements
Slide 60
Example 7: RBE3 Connection of Example 7: RBE3 Connection of Incompatible ElementsIncompatible Elements
• Use RBE3 to connect beams to plates at 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
Slide 61
Example 7: RBE3 Connection of Example 7: RBE3 Connection of Incompatible ElementsIncompatible Elements
• RBE3 connection of beams to plates– Map 6 DOF of beam into plate translation DOF– For best results, beam “footprint” should be similar to
RBE3 “footprint”, otherwise joint will be too stiff
Slide 62
Example 7: RBE3 Connection of Example 7: RBE3 Connection of Incompatible ElementsIncompatible Elements
• RBE3 connection of beams to solids– Map 6 DOF of beam into
solid translation DOF– For best results, beam
“footprint” should be similar to RBE3 “footprint”, otherwise joint will be too stiff
Slide 63
Example 7: RBE3 Connection of Example 7: RBE3 Connection of Incompatible ElementsIncompatible Elements
• RBE3 connection of plates to solids– Coupling of plate
drilling rotation to solid not recommended
– Plate and solid grids can be equivalent, coincident, or disjoint (as shown)
Slide 64
Example 7: RBE3 Connection of Example 7: RBE3 Connection of Incompatible ElementsIncompatible Elements
• Deformation contours show continuity at RBE3 interfaces
Slide 65
Example 7: RBE3 Connection of Example 7: RBE3 Connection of Incompatible ElementsIncompatible Elements
• Bending stress contours consistent across RBE3 interface
Slide 66
RBE3 Usage GuidelinesRBE3 Usage Guidelines
• Do not specify rotational DOF for master grids except when necessary to avoid singularity caused by a linear set of master grids
• Using rotational DOF on master grids can result in implausible results (see next two slides)
Slide 67
RBE3 Usage GuidelinesRBE3 Usage Guidelines
• Example: What can happen if master rotations included?– Modified RBE3 from Example 5– Displacements clearly incorrect when all 6
DOF listed for master grids (next page)
Slide 68
RBE3 Usage GuidelinesRBE3 Usage Guidelines
• Deformation with all 6 DOF specified for master grids at interface
• Deformation with 3 translation DOF specified for master grids (same loads/BC’s)
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 Rmmm 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
Slide 70
RBE3: Additional ReadingRBE3: Additional Reading
• Much RBE3 information has been posted on MSC’s Knowledge Base– http://www.mechsolutions.com/support/knowbase/index.html
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 VERSION
70.7 – TAN#: 4494 Mathematical Specification of the Modern
RBE3 Element
– TAN#: 4497 AN ECONOMICAL METHOD TO EVALUATE
RBE3 ELEMENTS IN LARGE-SIZE MODELS
Slide 72
User-Input based “Rigid” ElementsUser-Input based “Rigid” Elements
• MPCs– Most general-purpose way to define
motion-based relationships– Could be used in place of ALL other RBEi
• Lack of geometry makes this impractical
– Can be changed between SUBCASEs
Slide 73
MPC DefinitionMPC Definition
• “Rigid” elements– Definition: 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
Slide 74
General Approach For Use of MPCsGeneral Approach For Use of MPCs
• Write out desired displacement equality relationship 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 = Ux1
2
1
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 535
C2 A2A1 G2G1 C1MPC SID
2
1
Slide 76
General Approach to MPCsGeneral Approach to MPCs
• Write down relationship you want to impose on a per DOF level:
ajXi = a1X1 + a2X2 +…+ anXn
0 = -aiXi + a1X1 + a2X2+…+ anXn
• Move dependent term to 1st term on right hand side:
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
Slide 78
Use of MPC to tie GRIDs togetherUse of MPC to tie GRIDs together
• Write down relationship you want to impose on a per DOF level:
UX2 = UX1
UY2 = UY2
UZ3 = UZ3
X2 = X1
Y2 = Y1
Z2 = Z1
12
Slide 79
MPC, 535, 2, 1, -1.0, 1, 1, +1.0
MPC, 535, 2, 2, -1.0, 1, 2, +1.0
MPC, 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 on right hand side:
0 = -UX2 + UX1
0 = -UY2 + UY2
0 = -UZ3 + UZ3
0 = -X2 + X1
0 = -Y2 + Y1
0 = -Z2 + Z1
Slide 80
Use of MPC to tie GRIDs togetherUse of MPC to tie GRIDs together
• Use CAUTION when tying non-coincident GRIDs together!
• Watch for how those rotations and translations couple!2
1 UX2 = UX1
Z2 = Z1
Slide 81
MPCs for MPCs for RelativeRelative Motion Motion
• What’s the relative motion between GRIDs 1 and 2?
1 2?
Slide 82
MPCs for MPCs for RelativeRelative Motion Motion
• Introduce “placeholder” variable– Good use for SPOINTs
1 2?
• Move dependent term to RHS
0 = - U1000 + UX2 – UX1
• Write out desired relationship as before
U1000 = UX2 – UX1
Slide 83
MPCs for MPCs for RelativeRelative Motion Motion
• Write out MPCs1 2?
0 = -U1000 + UX2 – UX1
SPOINT 1000
MPC 535 1000 1 -1.0 2 1 +1.0
+ 1 1 -1.0
Slide 84
Initial gap
MPCs for Relative MPCs for Relative GAPGAP
• What is the gap between GRIDs 1 and 2?
1 2
Slide 85
MPCs for Relative MPCs for Relative GAPGAP
1 2
UGAP = UINIT + UX2 – UX1
0 = -UGAP + UINIT + UX2 – UX1
• Write equation:– Introduce new placeholder
variable for initial gap
Slide 86
MPCs for Relative MPCs for Relative GAPGAP
• 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
Slide 87
MPC used to Maintain SeparationMPC used to Maintain Separation
• Enforce a separation between GRIDs– Similar to using a gap– Changes which DOF are
dependent/independent
• Example:– Initially 1” apart– Keep separation = 0.25”
1
2
0.25
Slide 88
MPC used to Maintain SeparationMPC used to Maintain Separation1
20.25
U1 = U2 + (desired – initial)
0 = -U1 + U2 + U1000
SPOINT,1000
MPC, 535, 1, 2, -1.0, 2, 2, +1.0
+, , 1000, 1, +1.0
SPC, 2002, 1000, 1, -.75
1.00
Slide 89
Use of MPCs for AVERAGE MotionUse of MPCs for AVERAGE Motion
• Determine average motion of DOFs
U1000 = (U1+ U2 + U3 + U4 +U5 +U6)/6
0 = -6*U1000 + U1+ U2 + U3 + U4 +U5 +U6
Z
4
5
2
3
6
1
Slide 90
MPCs as Bell-crank or Control SystemMPCs as Bell-crank or Control System
• Output of 1 DOF scales another
U2 = U1/1.65
0 = -1.65*U2 + U1
2
1
1 +1.0-1.65 12 1MPC 535
C2 A2A1 G2G1 C1MPC SID
1.6
5
1.00
Slide 91
Units ConversionUnits Conversion
• Somewhat frivolous application, but why not?
– Convert radians to degrees
2 = 1 * 57.29578
– Convert inches to meters
39.37 * X2 = X1
Slide 92
Rigid Element OutputRigid Element Output
• Since Rigid elements are a specialized input of MPC equations, the output is requested by MPCFORCE case control command.– COMMON ERROR
• The MPCFORCEs are associated with GRID IDs, not Element IDs. So when selecting a SET for output, be sure the set is for GRID IDs, not Element IDs.
Slide 93
Guidelines for “Rigid” ElementsGuidelines for “Rigid” Elements
• Linear ONLY– Relationships calculated based on initial
geometry
• Can cause internal constraints for thermal conditions
• Be careful that independent GRID has 6 DOF