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RBEs and MPCs in MSC.Nastran

RBEs and MPCs in MSC.Nastran. A Rip-Roarin’ Review of Rigid Elements. RBEs and MPCs. Not necessarily “rigid” elements Working Definition:. The motion of a DOF is dependent on the motion of at least one other DOF. Motion at one GRID drives another. Simple Translation.

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RBEs and MPCs in MSC.Nastran

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  1. RBEs and MPCs in MSC.Nastran A Rip-Roarin’ Review of Rigid Elements

  2. RBEs 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. Motion at one GRID drives another • Simple Translation X motion of Green Grid drives X motion of Red Grid

  4. Motion at one GRID drives another • Simple Rotation Rotation of Green Grid drives X translation and Z rotation of Red Grid

  5. RBEs 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)

  6. Small Displacement Theory & Rotations • Small displacement theory: sin() = tan() =  cos() = 1 • For Rz @ A RzB = RzA= TxB = (-)*LAB TyB = 0 Y TxB B - A X

  7. Typical “Rigid” Elements in MSC.Nastran • Geometry-based • RBAR • RBE2 • Geometry- & User-input based • RBE3 • User-input based • MPC } Really-rigid “rigid” elements

  8. 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.

  9. The RBAR • The RBAR is a rigid link between two GRID points

  10. RBAR EID GA GB CNA CNB CMA CMB RBAR 535 1 2 123456 123456 The RBAR B • Most common to have all the dependent DOFs at one GRID, and all the independent DOFs at 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 A

  11. RBAR EID GA GB CNA CNB CMA CMB RBAR 535 1 2 123456 123456 RBAR Example: Fastener • Use of RBAR to “weld” two parts of a model together: B A

  12. RBAR EID GA GB CNA CNB CMA CMB RBAR 535 1 2 123456 123 RBAR Example: Pin-Joint • Use of RBAR to form pin-jointed attachment B A

  13. The RBE2 • One independent GRID (all 6 DOF) • Multiple dependent GRID/DOFs

  14. RBE2 EID GN CM GM1 GM2 GM3 GM4 GM5 RBE2 99 101 123456 1 2 3 4 1 3 4 2 101 RBE2 Example • Rigidly “weld” multiple GRIDs to one other GRID:

  15. RBE2 EID GN CM GM1 GM2 GM3 GM4 GM5 RBE2 99 101 123456 1 2 3 4 1 3 4 2 101 RBE2 Example • Note: No relative motion between GRIDs 1-4 ! • No deformation of element(s) between these GRIDs

  16. Common 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. RBE3 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

  18. RBE3 Description

  19. RBE3 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

  20. 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 3 * U99 = U1 + U2 + U3 -U1 = + U2 + U3 - 3 * U99

  21. RBE3 Is Not Rigid! • RBE3 vs. RBE2 • RBE3 allows warpingand 3D effects • In this example, RBE2 enforces beamtheory (plane sections remain planar) RBE2 RBE3

  22. 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

  23. CG CG FCG Reference Grid FA MA MCG e RBE3: How it Works? • Step 1: Transform force/moment at reference grid to equivalent force/moment at weighted CG of master grids. FCG=FA MCG=MA+FA*e

  24. 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

  25. F1m FCG CG F3m MCG F2m RBE3: How it Works? • Step 2: Continued… 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)}

  26. 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.

  27. Example 1 • RBE3 distribution of loads when force at reference grid at CG passes through CG of master grids

  28. Example 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

  29. Example 1: Force Through CG • Load through CG with uniform weighting factors results in uniform load distribution

  30. 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

  31. Example 2 • How does the RBE3 distribute loads when force on reference grid does not pass through CG of master grids?

  32. Example 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.

  33. Example 3 • Use of weighting factors to generate realistic load distribution: 100 LB. transverse load on 3D beam.

  34. Example 3: Transverse Load on Beam • If uniform weighting factors are used, the load is equally distributed to all grids.

  35. Example 3: Transverse Load on Beam • The uniform load distribution results in too much transverse load in flanges causing them to droop. Displacement Contour

  36. Example 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

  37. Example 3: Transverse Load on Beam • Displacements with quadratic weighting factors virtually equivalent to those from RBE2 (Beam Theory), but do not impose “plane sections remain planar” as does RBE2.

  38. Example 3: Transverse Load on Beam • RBE3 Displacement Contour • Max Y disp=.00685

  39. Example 3: Transverse Load on Beam • RBE2 Displacement contour • Max Y disp=.00685

  40. Example 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?

  41. Example 4: Use RBE3 for Unconstrained 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

  42. Example 4: Use RBE3 for Unconstrained 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

  43. Example 4: Use RBE3 for Unconstrained Motion “UM” Grids

  44. Example 4: Use RBE3 for Unconstrained 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

  45. Example 4: Use RBE3 for Unconstrained Motion • Result is free expansion due to internal pressure. (note: poisson effect causes shortening)

  46. Example 4: Use RBE3 for Unconstrained Motion • Resulting MPC Forces are numeric zeroes verifying that no stiffness has been added.

  47. Example 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.

  48. Example 5: 3D to Stick Model Connection • 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. Example 5: 3D to Stick Model Connection

  50. Example 5: 3D to Stick Model Connection • Undeformed/Deformed plot shows continuity in motion of 3D and Beam model

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