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1/94

RBEs and MPCs in MSC.NastranRBEs and MPCs in MSC.Nastran

A Rip-Roarin Review of

Rigid Elements


2/94

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


3/94

Slide 3

Motion at one GRID drives anotherMotion at one GRID drives another

Simple Translation

X motion ofGreen Grid drives X motion

ofRed Grid


4/94

Slide 4

Motion at one GRID drives anotherMotion at one GRID drives another

Simple Rotation

Rotation ofGreen Grid drives X translation

and Z rotation ofRed Grid


5/94

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 DOF

transferred to independent DOF(s)


6/94

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


7/94Slide 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


8/94Slide 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 oneGRID, and dependent DOF

at an arbitrary number of

GRIDs.


9/94Slide 9

The RBARThe RBAR

The RBAR is a rigid link between twoGRID points


10/94Slide 10

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 at

the other

B

A


11/94Slide 11

RBAR Example: FastenerRBAR Example: Fastener

Use of RBAR to weld two parts of amodel together:

1234561234561 2RBAR 535


B

A


12/94Slide 12

RBAR Example: Pin-JointRBAR Example: Pin-Joint

Use of RBAR to form pin-jointedattachment

1231234561 2RBAR 535


B

A


13/94Slide 13

The RBE2The RBE2

One independent GRID (all 6 DOF) Multiple dependent GRID/DOFs


14/94

Slide 14

RBE2 ExampleRBE2 Example

Rigidly weld multiple GRIDs to oneother GRID:

32RBE2 4110199 123456

GM5GM3GM2RBE2 GM4GM1GNEID CM

13

2

101

4


15/94

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


16/94

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


17/94

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 dependentGRID is the weighted

average of the motion(s) at

a set of master(independent) GRIDs


18/94

Slide 18

RBE3 DescriptionRBE3 Description


19/94

Slide 19


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


20/94

Slide 20

U99 = (U1 + U2 + U3) / 3

3 * U99

= U1

+ U2

+ U3

-U1 = + U2 + U3 - 3 * U99


UM fields can be used to move thedependent DOF away from the

reference grid

For Example (in 1-D):


21/94

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


22/94

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 the

CG of the weighted grid group using anequivalent Force/Moment

Step 2: Applied loads at CG transferred tomaster grids according to each gridsweighting factor


23/94

Slide 23


Step 1: Transform force/moment atreference 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


24/94

Slide 24


Step 2: Move loads at CG to mastergrids according to their weighting

values.

Force at CG divided amongst master gridsaccording to weighting factors Wi

Moment at CG mapped as equivalent force

couples on master grids according to

weighting factors Wi


25/94

Slide 25


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

F3

mF2m

Plus Forces derived from moment at CG:

Fim = {McgWiri/(W1r12+W2r2

2+W3r32)}


26/94

Slide 26


Masses on reference grid are smearedto the master grids similar to how forces

are distributed

Mass is distributed to the master grids accordingto their weighting factors

Motion of reference mass results in inertial force

that gets transferred to master grids

Reference node inertial force is distributed insame manner as when static force is applied to

the reference grid.


27/94

Slide 27

Example 1Example 1

RBE3 distribution of loads when force at

reference grid at CG passes through

CG of master grids


28/94

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 onreference grid 99


29/94

Slide 29


Load through CG with uniform weighting

factors results in uniform load distribution


30/94

Slide 30


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


31/94

Slide 31

Example 2Example 2

How does the RBE3 distribute loadswhen force on reference grid does not

pass through CG of master grids?


32/94

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 side

of the beam.

Upward loads on left

side of beam result

from moment caused

by movement ofapplied load to the CG

of master grids.


33/94

Slide 33

Example 3Example 3

Use of weighting factors to generaterealistic load distribution: 100 LB.

transverse load on 3D beam.


34/94

Slide 34

Example 3: Transverse Load on BeamExample 3: Transverse Load on Beam

If uniformweighting

factors are

used, the loadis equally

distributed to all

grids.


35/94

Slide 35


Displacement Contour

The uniform load distribution results intoo much transverse load in flanges

causing them to droop.


36/94

Slide 36


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


37/94

Slide 37

Displacements with quadratic weightingfactors virtually equivalent to those from

RBE2 (Beam Theory), but do not

impose plane sections remain planaras does RBE2.



38/94

Slide 38


RBE3 Displacement Contour

Max Y disp=.00685


39/94

Slide 39


RBE2 Displacement contour

Max Y disp=.00685


40/94

Slide 40

Example 4Example 4

Use RBE3 to getunconstrained

motion

Cylinder under

pressure

Which Grid(s) do you

pick to constrain out

Rigid body motion, butstill allow for free

expansion due to

pressure?

Example 4: Use RBE3 forExample 4: Use RBE3 for


41/94

Slide 41


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 SPCd)

Apply SPC to reference grid



42/94

Slide 42



Since reference grid has 6 DOF, wemust assign 6 UM DOF to a set ofmaster grids Pick 3 points, forming a nice triangle for

best 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



43/94

Slide 43



UM Grids



44/94

Slide 44



For circular geometry, its convenient touse a cylindrical coordinate system for

the master grids.

Put THETA and Z DOF in UM set for each of thethree UM grids to determine RBE3 rigid body

motion



45/94

Slide 45



Result is free expansion due to internalpressure. (note: poisson effect causes shortening)



46/94

Slide 46



ResultingMPC Forces

are numeric

zeroesverifying that

no stiffness

has been

added.


47/94

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


48/94

Slide 48


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



49/94

Slide 49





50/94

Slide 50



Undeformed/Deformed plot showscontinuity in motion of 3D and Beam

model



51/94

Slide 51



MPC forces atinterface show

effect of both the

tip shear and

interfacemoment.



52/94

Slide 52



Shell outer fiberstresses at interface

slightly higher than

beam bending

stresses

3D effects

Shell model under

internal pressure and

not bound by beam

theory assumptions

E l 6E l 6


53/94

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


54/94

Slide 54

Example 6: Using RBE3 to Visualizep g

Beam ModesBeam Modes

Generic engine courtesy of Pratt &Whitney



55/94

Slide 55

a p e 6 Us g 3 to sua ep g


RBE3s used toconnect various

components to

centerline.

Each componentscenterline grids

connected by its

own set of PLOTELs



56/94

Slide 56

p gp g


ComplexMode

Animation



57/94

Slide 57

p gp g


Animation of the

PLOTEL

segments

shows that this

is a whirl mode Relative motion

of various

components

more clearlyseen

E l 7Example 7


58/94

Slide 58

Example 7Example 7

Use RBE3 to connect incompatibleelements

Beam to plate

Beam to solid Plate to solid

Alternative to RSSCON

Example 7: RBE3 Connection ofExample 7: RBE3 Connection of


59/94

Slide 59

pp

Incompatible ElementsIncompatible Elements



60/94

Slide 60

pp


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



61/94

Slide 61

pp


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



62/94

Slide 62

pp


RBE3 connection ofbeams to solids

Map 6 DOF of beam into

solid translation DOF

For best results, beamfootprint should be

similar to RBE3 footprint,

otherwise joint will be too

stiff



63/94

Slide 63

p


RBE3 connectionof plates to solids Coupling of plate

drilling rotation to solid

not recommended

Plate and solid grids

can be equivalent,

coincident, or disjoint

(as shown)



64/94

Slide 64

p


Deformation contours show continuity atRBE3 interfaces



65/94

Slide 65


Bending stress contours consistentacross RBE3 interface

RBE3 Usage GuidelinesRBE3 Usage Guidelines


66/94

Slide 66


Do not specify rotational DOF formaster 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)



67/94

Slide 67


Example: What can happen if masterrotations included?

Modified RBE3 from Example 5

Displacements clearly incorrect when all 6DOF listed for master grids (next page)



68/94

Slide 68


Deformation withall 6 DOF

specified for

master grids at

interface Deformation with

3 translation DOF

specified for

master grids

(same loads/BCs)



69/94

Slide 69


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

Rg

mmand Rm

mmmatrices (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


70/94

Slide 70


Much RBE3 information has been posted onMSCs Knowledge Base http://www.mechsolutions.com/support/knowbase/index.html

http://www.mechsolutions.com/support/knowbase/index.html


71/94

Slide 71


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

User-Input based Rigid ElementsUser-Input based Rigid Elements
http://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.html


72/94

Slide 72

User-Input based Rigid ElementsUser-Input based Rigid Elements

MPCs Most 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


73/94

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

General Approach For Use of MPCsGeneral Approach For Use of MPCs


74/94

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


75/94

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


76/94

Slide 76

General Approach to MPCsGeneral Approach to MPCs

Write down relationship you want toimpose on a per DOF level:

a

j

X

i

= a

1

X

1

+ a

2

X

2

++ a

n

X

n

0 = -aiXi + a1X1 + a2X2++anXn

Move dependent term to 1st term on

right hand side:

Why would I want to use an MPC?Why would I want to use an MPC?


77/94

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


78/94

Slide 78


Write down relationship you want toimpose on a per DOF level:

UX2 = UX1

UY2 = UY2

UZ3 = UZ3

X2

=

X1Y2 = Y1

Z2 = Z1

1

2



79/94

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


Move dependent term to 1st

term onright hand side:

0 = -UX2 + UX1

0 = -UY2 + UY20 = -UZ3 + UZ3

0 = -X2 + X1

0 = -Y2 + Y1

0 = -Z2 + Z1



80/94

Slide 80


Use CAUTION when tying non-coincidentGRIDs together!

Watch for how those

rotations and

translations couple!2

1 UX2 = UX1

Z2 = Z1

MPCs forMPCs for RelativeRelative MotionMotion


81/94

Slide 81

MPCs forMPCs forRelativeRelative MotionMotion

Whats the relative motion betweenGRIDs 1 and 2?

1 2?



82/94

Slide 82

MPCs forRelative Motion

Introduce placeholder variable Good use for SPOINTs

1 2?

Move dependent term to RHS0 = - U1000 + UX2 UX1

Write out desired

relationship as beforeU1000 = UX2 UX1



83/94

Slide 83

MPCs forRelative 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

MPCs for RelativeMPCs for Relative GAPGAP


84/94

Slide 84

Initial

gap

What is the gap between GRIDs 1 and 2?

1 2



85/94

Slide 85

1 2

UGAP= UINIT + UX2

UX1

0 = -UGAP+ UINIT + UX2

UX1

Write equation: Introduce new placeholder

variable for initial gap



86/94

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


87/94

Slide 87

pp

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

MPC used to Maintain SeparationMPC used to Maintain Separation


88/94

Slide 88

pp

1

2

0.25

U1

= U2

+ (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


89/94

Slide 89

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

MPCs as Bell-crank or Control SystemMPCs as Bell-crank or Control System


90/94

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


91/94

Slide 91

Somewhat frivolous application, but whynot?

Convert radians

to degrees 2 = 1* 57.29578 Convert inches

to meters39.37 * X2 = X1

Rigid Element OutputRigid Element Output


92/94

Slide 92

g p

Since Rigid elements are a specializedinput 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.

Guidelines for Rigid ElementsGuidelines for Rigid Elements


93/94

Slide 93

Linear ONLY Relationships calculated based on initial

geometry

Can cause internal constraints forthermal conditions

Be careful that independent GRID has 6

DOF

MPCs and RBEsMPCs and RBEs


94/94

Off the shelf RBAR

RBE2

Customizable RBE3

Handmade

MPC

Add them toyour

modelingarsenal

today!

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