Introduction to MPC Equations and Rigid Elements Glenn Grassi, MSC Software May 2010
Oct 22, 2014
Introduction to MPC Equations and Rigid
Elements
Glenn Grassi, MSC Software
May 2010
2
Agenda
• MSC.Nastran Set Definitions
• What are MPC Equations
• Forming and using MPC Equations
• Rigid Elements in MSC.Nastran
• Q & A
3
Special thanks to
Lance Proctor
Jim Swan
Jack Castro
for their contributions to this presentation.
MSC/MD Nastran Set Definitions
• Each degree of freedom of an MSC/MD Nastran analysis
model is defined as being a member of a “user-set”
• These set notations, such a G-set, M-set, S-set, etc are
identifications and classifications of how each degree of
freedom (dof) in the analysis participates in the solution
sequence
4
MSC/MD Nastran Set Definitions
• When a GRID entry is place in the bulk data section there
are (6) dof’s added into the model
• Other entries such as SPOINT or EPOINT, for example, will
add (1) dof in the model
• The collection of all dof’s that are entered into the model will
initially be label as belonging to the G-set
5
MD Nastran Set Definitions
• The dof’s that are developed are initially placed into the
G-set (Global set) in numerical order according to their ID
number
• If the follow bulk data entries were defined the G-set would
be defined as containing 13 dof’s
– GRID,1,,0.,0.,0.
– GRID,20,,1.,0.,0.
– SPOINT,2
6
MD Nastran Set Definitions
• As the solution proceeds these dof’s may be relabeled and
transferred to other sets.
• If dof’s are constrained using multipoint constraint (MPC)
entries or rigid elements (RBAR, RBE2, RBE3, etc) then
some dof’s are relabeled as now belonging to the M-set
(Dependent Set)
7
MD Nastran Set Definitions
• The remaining dof’s that are not defined in the M-set would
then be relabeled as belonging to the N-set (Independent
Set)
8
• Once a dof is labeled a belong to the M-set it cannot be
relabeled again. This is know as a “mutually exclusive” set
definition. In this example dof’s 7 and 9 belong to the M-set
and cannot be redefined.
MD Nastran Set Definitions
• The dof’s in the N-set can be further reduced by adding
single point constraints (SPC, AUTOSPC, PS) into the
model.
9
• Dof’s 3 and 8 now joint dof’s 7 and 9 as being “mutually
exclusive”
MD Nastran Set Definitions
• If a dof was incorrectly specified in the M-set and the S-set
then a Fatal Message (2101) would occur.
10
MD Nastran Set Definitions
• The dof’s that are not constrained will be relabeled as
belonging to the F-set (Free).
11
MD Nastran Set Definitions
• As the analysis progresses, further set reductions and
relabeling are possible
12
• The original 13 dof problem has been trimmed down to a 5
dof problem
MD Nastran Set Definitions
• A complete description of user sets can be found in the
MSC/MD Nastran Reference Manual and Dynamic User
Guide.
13
MD Nastran Set Definitions
14
• A printout of the user set definitions can be obtained by
including PARAM,USETPRT,2 in the analysis.
MPC Equations
15
• A MultiplePointConstraint Equation (MPC) is a linear
relationship between two or more degrees of freedom that
are expressed in the form
Σj Rj uj = 0
Where
• uj = any degree of freedom defined by a grid point
or an spoint
• Rj = user-defined scale factor
MPC Equations
16
• Multipoint constraints have many important practical
applications and can be used to Tie GRIDs together
• Determine relative motion between GRIDs
• Maintain separation between GRIDs
• Determine average motion between GRIDs
• Model bell-crank or control system
• Units conversion
UY6 = UY7
MPC Equations
17
Σj Rj uj = 0
= 0+
+
M-set
N-set
MPC Equations
18
• Simple example of an MPC Equation.
Y6 = Y7
MPC Equations
19
• Y6 = Y7
• 0 = Y7 - Y6 or 0 = - Y6 + Y7
Independent dof
Dependent dof (first one listed)
• Add coefficients
0 = 1.0 * Y7 – 1.0 * Y6
MPC 1 7 2 1.0 6 2 -1.0
MPC Equations
20
MPC Equations
21
MPC Equations
22
• By including MPCFORCE=ALL the MPC forces acting on the
grids can be printed.
MPC Equations
23
Angle ?
MPC Equations
24
• SPOINT has an ID for a single dof
• ID must be unique (cannot conflict with grids, epoints, etc)
• There are no directions associated with the SPOINT
– dof 0 is usually used in MPC equations
– dof 1 can also be used (cannot use 2 thru 6)
SPOINT 100
SPOINT 200 300
SPOINT 401 THRU 430
MPC Equations
25
• Calculate the relative angle in radians between GRID 6 and GRID 7 by
introducing an SPOINT 100
• Calculate the relative angle in degrees between GRID 6 and GRID 7 by
introducing an SPOINT 200
• MPC equation: SPOINT100 = RZ7 - RZ6 {SPOINT100 - RZ7 + RZ6 = 0 }
• MPC equation: SPOINT200 = SPOINT100 x 57.2958
{SPOINT200 - SPOINT100 x 57.2958 = 0 }
MPC 1 100 0 1.0 7 6 -1.0
+ 6 6 1.0
MPC 1 200 0 1.0 100 0 -57.2958
MPC Equations
26
MPC Equations
27
• SPOINT 100 = 7.238917E-03 (radians)
• SPOINT 200 = 4.147595E-01 (degrees)
How to enforce a 5.0 degree angle
MPC Equations
28
MPC = 1
Begin Bulk
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
SPOINT 100 200
MPC 1 7 2 1. 6 2 -1.
MPC 1 100 1 1.0 7 6 -1.0
+ 6 6 1.0
MPC 1 200 0 1.0 100 0 -57.2958
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
MPC Equations
29
MPC = 1
SPC = 1
Begin Bulk
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
SPOINT 100 200
MPC 1 7 2 1. 6 2 -1.
MPC 1 100 1 1.0 7 6 -1.0
+ 6 6 1.0
MPC 1 200 0 1.0 100 0 -57.2958
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
SPC 1 200 0 5.0
MPC Equations
30
MPC = 1
SPC = 1
Begin Bulk
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
SPOINT 100 200
MPC 1 7 2 1. 6 2 -1.
MPC 1 100 1 1.0 7 6 -1.0
+ 6 6 1.0
MPC 1 200 0 1.0 100 0 -57.2958
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
SPC 1 200 0 5.0
MPC Equations
31
MPC = 1
SPC = 1
Begin Bulk
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
SPOINT 100 200
MPC 1 7 2 1. 6 2 -1.
MPC 1 100 1 1.0 7 6 -1.0
+ 6 6 1.0
MPC 1 200 0 1.0 100 0 -57.2958
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
SPC 1 200 0 5.0
MPC Equations
32
MPC = 1
SPC = 1
Begin Bulk
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
SPOINT 100 200
MPC 1 7 2 1. 6 2 -1.
MPC 1 100 1 1.0 7 6 -1.0
+ 6 6 1.0
MPC 1 100 0 -57.2958 200 0 1.0
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
SPC 1 200 0 5.0
MPC Equations
33
MPC = 1
SPC = 1
Begin Bulk
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
SPOINT 100 200
MPC 1 7 2 1. 6 2 -1.
MPC 1 100 1 1.0 7 6 -1.0
+ 6 6 1.0
MPC 1 100 0 -57.2958 200 0 1.0
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
SPC 1 200 0 5.0
MPC Equations
34
MPC = 1
SPC = 1
Begin Bulk
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
SPOINT 100 200
MPC 1 7 2 1. 6 2 -1.
MPC 1 100 1 1.0 7 6 -1.0
+ 6 6 1.0
MPC 1 200 0 1.0 100 0 -57.2958
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
SPC 1 200 0 5.0
MPC Equations
35
MPC = 1
SPC = 1
Begin Bulk
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
SPOINT 100 200
MPC 1 7 2 1. 6 2 -1.
MPC 1 7 6 -1.0 100 0 1.0
+ 6 6 1.0
MPC 1 200 0 1.0 100 0 -57.2958
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
SPC 1 200 0 5.0
MPC Equations
36
MPC = 1
SPC = 1
Begin Bulk
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
SPOINT 100 200
MPC 1 7 2 1. 6 2 -1.
MPC 1 7 6 -1.0 100 0 1.0
+ 6 6 1.0
MPC 1 200 0 1.0 100 0 -57.2958
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
SPC 1 200 0 5.0
MPC Equations
37
MPC = 1
SPC = 1
Begin Bulk
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
SPOINT 100 200
MPC 1 7 2 1. 6 2 -1.
MPC 1 7 6 -1.0 100 0 1.0
+ 6 6 1.0
MPC 1 100 0 -57.2958 200 0 1.0
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
SPC 1 200 0 5.0
MPC Equations
38
MPC = 1
SPC = 1
Begin Bulk
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
SPOINT 100 200
MPC 1 7 2 1. 6 2 -1.
MPC 1 7 6 -1.0 100 0 1.0
+ 6 6 1.0
MPC 1 100 0 -57.2958 200 0 1.0
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
SPC 1 200 0 5.0
MPC Equations
39
Enforced a 5.0 degree angle
MPC Equations
40
MPC = 1
Begin Bulk
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
SPOINT 100 200
MPC 1 7 2 1. 6 2 -1.
MPC 1 100 1 1.0 7 6 -1.0
+ 6 6 1.0
MPC 1 200 0 1.0 100 0 -57.2958
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
MPC Equations
41
MPC = 400
Begin Bulk
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
SPOINT 100 200
MPCADD 400 1 2 3
MPC 1 7 2 1. 6 2 -1.
MPC 2 100 1 1.0 7 6 -1.0
+ 6 6 1.0
MPC 3 200 0 1.0 100 0 -57.2958
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
MPC Equations
42
Dependent DOF coefficient = -1.0
(pre-defined in MSC.Patran)
0 = 1.0 * Y7 - 1.0 * Y6 ( original )
0 = -1.0 * Y7 + 1.0 * Y6 ( modified x -1.0)
Y6 = Y7
MPC Equations
43
MSC.Patran does not define SPOINT’s
– Use Create/Node/Edit
Constrain all dof’s except the dof = 1
MPC Equations
44
MPC = 1
Begin Bulk
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
SPOINT 100 200
MPC 1 7 2 1. 6 2 -1.
MPC 1 100 0 1.0 7 6 -1.0
+ 6 6 1.0
MPC 1 200 0 1.0 100 0 -57.2958
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
MPC = 1
Begin Bulk
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
GRID 100 23456
GRID 200 23456
MPC 1 7 2 1. 6 2 -1.
MPC 1 100 1 1.0 7 6 -1.0
+ 6 6 1.0
MPC 1 200 1 1.0 100 1 -57.2958
$-------2-------3-------4-------5-------6-------7-------8-------9-------0-------
MPC Equations
45
MPC Equations
46
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
0 = -UX2 + UX1
0 = -UY2 + UY2
0 = -UZ2 + UZ2
0 = - X2 + X1
0 = - Y2 + Y1
0 = - Z2 + Z1
Use of MPC to tie GRIDs together
1
2
MPC Equations
47
MPC 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”1.0”
48
MPC used to Maintain Separation
1
2
0.25
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, -0.75
1.00 desired
initial
total shrink =
2.0 x -0.375 = -0.75
Relative motion:
U1000 = U1 – U2
MPC Equations
49
Use 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
4
5
2
3
6
1
MPC Equations
50
MPCs as Bell-crank or Control System
• 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
1.6
5
Rigid Elements
51
• The multipoint constraint, or MPC entry, provides the capability to model rigid
bodies and to represent other relationships which can be treated as rigid
constraints.
• The MPC entry provides considerable generality but lacks user convenience
since the user must supply all of the coefficients in the equations of constraint
• To enhance user convenience, nine rigid body elements (R-Type) are available
in MSC.Nastran.
• These elements require only the specification of the degrees-of-freedom that
are involved in the equations of constraint. All coefficients in these equations of
constraint are calculated internally in MSC.Nastran.
Rigid Elements
52
Not Exactly Rigid
- Averaging element
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
X motion of Green Grid drives X motion
of Red Grid
Motion at one GRID drives another
• Simple Rotation
Rotation of Green Grid drives X translation
and Z rotation of Red Grid
Linear 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)
Small Displacement Theory & Rotations
• Small displacement theory:
sin( ) ≈ tan( ) ≈
cos( ) ≈ 1
• For Rz @ A
RzB = RzA=
TxB = ( )*LAB
TyB = 0
X
Y
A
B
TxB
• Geometry-based– RBAR
– RBE2
• Geometry- & User-input based– RBE3
• User-input based– MPC
• Less Common “Rigid” elements (not covered today)– RBAR1, RJOINT, RROD, RTRPLT, RTRPLT1, RBE1,
RSSCON, RSPLINE
Commonly used “Rigid” Elements in MSC.Nastran
}Really-rigid “rigid” elements
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.
The RBAR
• The RBAR is a rigid link between two GRID points
– Proper rigid body motion is preserved
The 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
RBAR Example: Fastener
• Use of RBAR to “weld” two parts of a model
together:
1234561234561 2RBAR 535
CMA CMBCNA CNBGA GBRBAR EID
B
A
RBAR Example: Pin-Joint
• Use of RBAR to form pin-jointed attachment
1231234561 2RBAR 535
CMA CMBCNA CNBGA GBRBAR EID
B
A
RBAR definition in Patran
The RBE2
• One independent GRID (all 6 DOF)
• Multiple dependent GRID/DOFs
RBE2 Example
• Rigidly “weld” multiple GRIDs to one other GRID:
32RBE2 4110199 123456
GM5GM3GM2RBE2 GM4GM1GNEID CM
13
2
101
4
RBE2 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
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
RBE2 definition in Patran
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
RBE3 Description
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
– PARAM,AUTOMSET,YES can resolve conflicts
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
• 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
RBE3: How it Works? – Applied Forces
RBE3: How it Works? – Applied Forces
• Step 1: Transform force/moment at reference
grid to equivalent force/moment at the weighted
CG of master grids.
MCG=MA+FA*e
FCG=FA
CG
FCG
MCG
FA
MA
Reference Grid
e
CG
RBE3: How it Works? – Applied Forces
• 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
RBE3: How it Works? – Applied Forces
• 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)}
RBE3: How it Works? – Mass Distribution
• Masses smeared to the master grids similar to
forces distribution• Mass is distributed to the master grids with weighting factors
• Rotational inertia is transferred to master grids
• Reference node inertial force is distributed in same manner as when
static force is applied to the reference grid.
Example 1
• RBE3 distribution of loads when force at reference grid at
CG passes through CG of master grids
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
Example 1: Force Through CG
• Load through CG with uniform weighting factors results in
uniform load distribution
Example 1: Force Through CG
• Comments…
• RBE3 Require 6 RBMODES
• x rotation DOF is added to satisfy equilibrium
Example 2
• Force does not pass thru CG of master grids
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.
Example 3
• Use of weighting factors to generate realistic
load distribution: 100 LB. transverse load on 3D
beam.
Example 3: Transverse Load on Beam
• If uniform weighting
factors are used, the
load is equally
distributed to all
grids.
Example 3: Transverse Load on Beam
Displacement Contour
• The uniform load distribution results in too much
transverse load in flanges causing them to droop.
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
• 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 Beam
Example 3: Transverse Load on Beam
• RBE3 Displacement Contour
• Max Y disp=.00685
Example 3: Transverse Load on Beam
• RBE2 Displacement contour
• Max Y disp=.00685
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?
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
• 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
Example 4: Use RBE3 for Unconstrained Motion
How Do I create UM set in Patran?
UX, UY, UZ onlyUy, Uz in cyl coord
sys is determinate
Reassign
Dependant
termsPick 3 nodes @
approx 120
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
Equation (consider avg x disp of grid 99)
Avg motion: U99x = (U1x + U2x + U3x) / 3
Default MPC: -3.*U99x + U1x + U2x + U3x =0
Rearrange UM: U1 + U2 + U3 - 3 * U99 =0
What is the UM?
• UM fields can be used to move the dependent DOF away from the reference grid
• For Example (in 1-D):
First term in MPC equation is dependent; Same equation, different order
99
1 2 3
99
1 2 3
Example 4: Use RBE3 for Unconstrained
Motion
“UM” Grids
Example 4: Use RBE3 for Unconstrained Motion
• Result is free expansion due to internal pressure. (note: poisson effect causes shortening)
Example 4: Use RBE3 for Unconstrained
Motion
• Resulting MPC
Forces are
numeric zeroes
verifying that no
stiffness has
been added.
–PARAM,AUTOMSET,YES can also be
used in many instances instead of UM
RBE3 – Non Uniform Distribution – CHEXA(8)
Coefficients all 1.0
Coefficients 1.0, 0.5 and 0.25
RBE3 – Non Uniform Distribution – CHEXA(8)
Coefficients 1.0, 0.5 and 0.25
Coefficients all 1.0
Stress and Deflection
Correct Stress = 2,500
Correct Disp = 2.5e-3
Max Stress 5,830
Max Disp = 2.86e-3
RBE3 – Non Uniform Distribution – CHEXA(20)
Coefficients all 1.0
Coefficients: 1.0 -2.0 0.5 -1.0 0.25
RBE3 – Non Uniform Distribution – CHEXA(20)
Stress and Deflection
Correct Stress = 2,500
Correct Disp = 2.5e-3
Max Stress 11,600
Max Disp = 3.21e-3Coefficients all 1.0
Coefficients:
1.0 -2.0 0.5 -1.0 0.25
RBE3: 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
http://simcompanion.mscsoftware.com)
–Visit SimCompanion
Thank You