RBEs and MPCs in MSC.Nastran2

• • • • • • 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 8
The RBAR • The RBAR is a rigid link between two GRID pointsSlideΒιβλιοθήκη 9The RBARB
– Most common to have all the dependent DOFs at one GRID, and all the independent DOFs at A the other – 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
Slide 12
The RBE2 • One independent GRID (all 6 DOF) • Multiple dependent GRID/DOFs
Slide 13
RBE2 Example • Rigidly “weld” multiple GRIDs to one other GRID:
Slide 25
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.
• Note: No relative motion between GRIDs 1-4 ! 3
– No deformation of element(s) between these GRIDs
101 4
1 2
Slide 15
Common RBE2/RBAR Uses • RBE2 or RBAR between 2 GRIDs
– MPC
Slide 7
Common 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 2
Motion at one GRID drives another • Simple Translation
X motion of Green Grid drives X motion of Red Grid
Slide 3
Motion at one GRID drives another • Simple Rotation
RBE2 RBE2 EID 99 GN CM GM1 GM2 GM3 GM4 GM5 101 123456 1 2 3 4
3 4 1 2
101
Slide 14
RBE2 Example
RBE2 EID RBE2 99 GN CM GM1 GM2 GM3 GM4 GM5 101 123456 1 2 3 4
Slide 19
RBE3 Description • UM fields can be used to move the dependent DOF away from the reference grid – For Example (in 1-D):
U99 = (U1 + U2 + U3) / 3
– 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 24
RBE3: How it Works? • Step 2: Continued…
FCG
F1m
CG
MCG
F2m
F3m
Total force at each master node is sum of... Forces derived from force at CG: Fif = FCG{Wi/Wi} Plus Forces derived from moment at CG: Fim = {McgWiri/(W1r12+W2r22+W3r32)}
Slide 5
Small Displacement Theory & Rotations • Small displacement theory:
sin() = tan() = cos() = 1
Y
TxB
• For Rz @ A
RzB = RzA= TxB = (-)*LAB TyB = 0
RBE3
RBE2
Slide 21
RBE3: How it Works? • Forces/moments applied at reference grid are distributed to the master grids in same manner as classical bolt pattern analysis
RBAR RBAR EID 535 GA 1 GB 2 CNA CNB 123456 CMA CMB 123456
Slide 10
RBAR Example: Fastener • Use of RBAR to “weld” two parts of a model together:
RBAR EID GA GB CNA CNB CMA CMB
Rotation of Green Grid drives X translation and Z rotation of Red Grid
Slide 4
RBEs and MPCs
The motion of a DOF is dependent on the motion of at least one other DOF
B
-
A
X
Slide 6
Typical “Rigid” Elements in MSC.Nastran • Geometry-based
– RBAR – RBE2
– RBE3
} Really-rigid “rigid” elements
• Geometry- & User-input based • User-input based
Slide 16
RBE3 Elements • Motion at a dependent GRID is the weighted average of the motion(s) at a set of master (independent) GRIDs
– NOT a “rigid” element – IS an interpolation element – Does not add stiffness to the structure (if used correctly)
3 * U99 = U1 + U2 + U3
-U1 = + U2 + U3 - 3 * U99
Slide 20
RBE3 Is Not Rigid! • RBE3 vs. RBE2
– RBE3 allows warping and 3D effects – In this example, RBE2 enforces beam theory (plane sections remain planar)
– “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
FCG
MA
CG
MCG
e
FCG=FA MCG=MA+FA*e
Slide 23
RBE3: How it Works? • Step 2: Move loads at CG to master grids according to their weighting values.