A Constraint Equation Primer:
How to Tie Degrees of Freedom Together
Eric Miller
Co-Owner
Principal, Simulation and
Business Technologies
04/26/2012
PADT, Inc.
DX R13: 02/17/2011
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Agenda
• Note: This presentation is being
recorded
•
•
•
•
•
Introductions
Theory and Basic Info
The CP and CE Commands
Internal CE’s (MPC)
CE’s in Workbench
DX R13: 02/17/2011
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Introductions
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Upcoming Webinars
• Upcoming Webinars
–
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•
Feb 9, 2012 - 12:00 MST
Working Directly with Nodes and Elements in ANSYS Mechanical
Feb 23, 2012 - 12:00 MST
Assembly Meshing in ANSYS R14 CANCELED
March 8, 2012 - 12:00 MST
Intro to Workbench Framework Scripting - Controlling projects, materials, and solution execution with python
March 22, 2012 - 12:00 MST
Mastering the Remote Solver Manager (RSM) at R14
April 12, 2012 – 12:00 MST
A POST26 Primer: Post Processing over Multiple Time/Load Steps in Mechanical APDL
April 27, 2012 – 12:00 MST
A Constraint Equation Primer: How to Tie Degrees of Freedom Together
May 10, 2012 – 12:00 MST
Optimization with ANSYS DesignXplorer at R14
May 24, 2012 – 12:00 MST
Modeling Moisture Diffusion in ANSYS
Summer Break: June & July (maybe August)
Primers are new:
– Oriented towards newer users or Workbench users who may not have experience with
some of the fundamentals in the ANSYS Mechanical APDL solver
•
See upcoming and past webinars at:
– padtincevents.webex.com
• Click on ANSYS Webinar Series
DX R13: 02/17/2011
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About PADT
• PADT is an Engineering Services
Company
– Mechanical Engineering
– 18 Years of Growth and Happy customers
– 70’ish Employees
• 3 Business Areas
– CAE Sales & Services
• Consulting, Training, Sales, Support
– Product Development
– Rapid Prototyping & Manufacturing
• Learn More: www.PADTINC.com
We Make Innovation Work
DX R13: 02/17/2011
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Cube HVPC Systems
• Balance between speed and cost
– Mini-Cluster
96 Cores / 512 GB RAM / 6 TB Disk
Mobile Rack / UPS / Monitor / Keyboard
$34,900
– Compute Server
32 Cores / 256 GB RAM / 3 TB Disk
$14,250
– Simulation Workstation (Intel)
12 Cores / 96 GB RAM / 3 TB Disk
$11,750
– Simulation Workstation (AMD)
12 Cores / 64 GB RAM / 3 TB Disk
$6,300
• www.CUBE-HVPC.com
DX R13: 02/17/2011
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PeDAL – The APDL Editor
•
•
•
•
•
•
•
•
Side-by-side editor and help viewer layout.
Instant help on any documented APDL command by pressing F1.
Full syntax highlighting for ANSYS v12 Mechanical APDL.
Auto-complete drop downs for APDL Commands.
APDL Command argument hints while typing commands.
Search ANSYS help phrases and keywords.
Multiple tabs for the editor and html viewer.
Full capability web browser built in allows for rich web experience and web
searches.
DX R13: 02/17/2011
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Connect with PADT
Facebook:
facebook.com/padtinc
Email Subscriptions:
Twitter:
#padtinc
Web:
www.PADTINC.com
LinkedIn:
Search on PADT, Inc.
ANSYS User Blog:
padtinc.com/focus
www.padtinc.com/epubs
DX R13: 02/17/2011
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Theory and Basic
Info
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What is a Constraint Equation
• Remember you are solving a series of linear equations:
• Structural: (F) = [K](u)
– Every node has a force (F) in each direction and a deflection (u).
– You are solving for (F) and (u)
– The deflections are called the Degrees of Freedom or DOF
• Generalized to solve many types of physics, the meaning of
(F), [K] and (u) change. But (u) is still a DOF
• Constraint equations are equations that tie the value of one
DOF to the value of one or more DOF’s
• Added into set of linear equations before solve
• We will call them CE’s most of the time
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There are Really 3 Types
• Constraint Equations (CE)
– Equations fed to the solver that describe relations between DOF’s
– (what we will mostly talk about)
• Couples (CP)
– All DOF’s are equal
• Multipoint Constraint (MPC)
– Actually internal MPC
– No equations are written by the users, created at runtime in the matrix
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Defined In Terms of a Sum
• Constant =
𝑁
𝐼=1(𝑐𝑜𝑒𝑓𝑖𝑐𝑐𝑖𝑒𝑛𝑡
𝐼 ∗𝑈 𝐼 )
– N = number of terms in the equation
– U(I) = the DOF solution for term I
• You write equations that relate one or more DOF in linear
way:
– After a solve, the sum of the user defined coefficients times their
deflection equals some constant
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Example: Beam to Plane Stress Elements
• (from MAPDL help)
• If you have a beam attached to a block, the ROTZ DOF is
free, and it can spin like a hinge
• So, we know for small deflections and a rigid connection,
that ROTZ in radians is equal to the distance from the
connection to the corner nodes times the rotation in radians.
– So if it was one node, it would be a multiplier of 5, but because there
are two sharing the deflection, one up and one down, it is 10 and the
coefficients on the UY direction are 1 and -1.
– 𝑅𝑂𝑇𝑍2 = 𝑈𝑌3−𝑈𝑌1 10
– 0 = UY3 – UY1 – 10*ROTZ2
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Example: Cyclic Symmetry
• Assumption when a disk shape is made up of a repeated
chunk of geometry.
• The DOF solution at the boundary of the repeatable chunk
are identical
• Enforced with CE’s
– In a cylindrical coordinate system
– Uaxial129 = -1*Uaxial363
Uhoop129 = -1*Uhoop363
Uradial129 = -1*Uradial363
– 0.0 = Uaxial129 + Uaxial363
0.0 = Uhoop129 + Uhoop363
0.0 = Uradial129 + Uradial363
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All Sorts of Uses
• There are many situations where you want to relate DOF’s:
– Coupling: Setting one DOF equal to Another
– Cyclic Symmetry: forcing cyclic (and anti-cyclic) behavior at the
repeatable boundary
– Contact: contacts are CE’s that turn on and off based on proximity
– Joints: Constrain some DOF’s and leave other free
• Pin type stuff that NASTRAN users do all the time
–
–
–
–
Gears and linkages: relate rotational DOF’s or rotation to displacment
Connect mesh regions with more DOF’s to regions with less
Connect Dissimilar Meshes
Represent behavior of rigid elements
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DOF Elimination
• One of the DOF’s in the equation needs to be “set free” and
solved for: eliminated from the equation
• It can not have any DOF value imposed on it with a
displacement, master DOF, or couples.
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Coordinate Systems
• The DOF’s on a node are defined in that nodes coordinate
system
– Each node in an ANSYS model has a unique rotation defined relative
to the global coordinate system
• Make sure that when you define a CP or CE that the nodes
are all rotated in the same Cartesian, radial, or spherical
coordinate system
– Very important if you are using Mechanical, you may not know what
coordinate system nodes are in.
• Critical for cyclic symmetry
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Creation
• MAPDL
– Several commands to define by hand – you enter the equation
– More commands to automatically generate between specified nodes
– Automatically created as part of contacts
• Mechanical
–
–
–
–
Created automatically with contacts
Created automatically with remote points
Created automatically as part of repeatable boundary
Defined by hand between points
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Viewing
• Using the /PBC,ce,1
command turn on CE’s
• Any plots show the
CE’s
• Little arrows show DOF
at each node
– Way to check the
nodal rotation
• Lines connect all the
DOF’s in a CE
• Unselected nodes are
not shown
• If Mechanical is making
CE’s, put a CE plot into
your snippets to check
them.
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The CP and CE
Commands
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Some Background
• Most CE related commands start with CE
• Each CE in a model has a unique number
– You define the number when you create the CE
– You refer to the CE number when you want to look at it, modify it,
delete it, add to it
• All Holds true for CP’s as well
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Couples
•
•
•
•
•
A constraint equation, but not treated as one
DOF1 = DOF2
Can be a CE: 0 = DOF1 – DOF2
But more efficient to substitute DOF2 every place DOF1 was used
Command:
– CP, NSET, Lab, NODE1, NODE2, NODE3, NODE4, NODE5, NODE6, NODE7,
NODE8, NODE9, NODE10, NODE11, NODE12, NODE13, NODE14, NODE15,
NODE16, NODE17
– Every node in the list will have the same value for whatever DOF you specify in Lab
– Repeat with same NSET to add even more nodes
– Supports picking (NODE1= p) and components
– Use –NODEx to remove a node from the set
•
Valid Lab:
–
–
–
–
–
–
–
Structural labels: UX, UY, or UZ (displacements); ROTX, ROTY, or ROTZ (rotations) (in radians); HDSP (hydrostatic
pressure).
Thermal labels: TEMP, TBOT, TE2, TE3, . . ., TTOP (temperature).
Fluid labels: PRES (pressure); VX, VY, or VZ (velocities).
Electric labels: VOLT (voltage); EMF (electromotive force drop); CURR (current).
Magnetic labels: MAG (scalar magnetic potential); AX, AY, or AZ (vector magnetic potentials); CURR (current).
Diffusion label: CONC (concentration).
Explicit analysis labels: UX, UY, or UZ (displacements).
DX R13: 02/17/2011
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Couple Related Commands
•
CPDELE, NSET1, NSET2, NINC, Nsel
– Delete a CP set
– If Nsel = ALL, only delete if all nodes are selected
•
CPINTF, Lab, TOLER
– Puts all the nodes below a certain distance (Toler) from each other in a CP set with
DOF = LAB
– Best used for coincident, or very close to coincident nodes
•
CPLGEN, NSETF, Lab1, Lab2, Lab3, Lab4, Lab5
– Makes copies of an existing couple set (NSETF) using 1 or more new DOF labels
•
CPLIST, NSET1, NSET2, NINC, Nsel
– Lists out coupled sets
– Use this in a Mechanical APDL snippet to set what CP’s were made by workbench
•
CPNGEN, NSET, Lab, NODE1, NODE2, NINC
–
•
Like CP but uses node range to specify nodes
CPSGEN, ITIME, INC, NSET1, NSET2, NINC
–
Makes ITIME copies of existing CP sets, incrementing the nodes by INC
DX R13: 02/17/2011
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Couple Issues
• Only the first DOF value in the set is used in the matrix, all
others are replaced by it
– Called the prime DOF
– Don’t put displacements (D) on DOF’s that are coupled out
• CP’s on Non coincident nodes, or nodes who do not lie on
the DOF that is coupled, will induce moments.
• A DOF should never appear in more than one CP
• The set number in the CP command can be:
–
–
–
–
n: the set number
HIGH: use the highest number currently defined
NEXT: use the highest number + 1 (new)
NOTE: The default is not NEXT!, it is HIGH.
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Making CE’s: The CE Command
• CE, NEQN, CONST, NODE1, Lab1, C1, NODE2, Lab2, C2,
NODE3, Lab3, C3
– NEQN can be: n, HIGH, or NEXT (HIGH is default!)
– CONST = the constant for the equation
– NODEn,Labn,C1 = the node, the DOF, and the multiplier.
• So, our early example:
– 𝑅𝑂𝑇𝑍2 = 𝑈𝑌3−𝑈𝑌1 10 −−→ 0 = UY3 – UY1 – 10*ROTZ2
– CE, next, 0, 3,uy,1, 1,uy,-1, 2,rotz,10
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Making CE’s: The CE Command
• Most hand CE’s are pretty simple
–
–
–
–
–
Often an anti-symmetry
Connecting a remote mass point to your model
Doing your own cyclicsymmetry constraints
Connecting rotation DOF’s to axial based on distances
Defining a joint or “gear”
• Use APDL macro to generate
• Or use Excel for fancy ones (make sure your math is right)
• These days, they are almost always made for you
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Making Cyclic Symmetry Boundaries
• Back in “the day” you had to make your own CE’s for this…
– Kids today have it too easy
• CECYC, Lowname, Highname, Nsector, HIndex, Tolerance, Kmove,
Kpairs
–
–
–
–
Lowname, Highname are the component names of each side of your “wedge”
Nsector is the number of times the sector gets repeated
Hindex is the harmonic index… no time to explain
Tolerance specifies how close in the axial/radial/tangential+sector angle
nodes need to be to be coupled
– Kmove = 1 says you can move the high nodes to match the low (don’t use!)
– Kpairs = 1 prints out a list of pairs when it executes
• It rotates the nodes into CSYS = 1 !!!!!!!!!!
– This may not be the same axis as your model, check
– Do your won CE’s if that is true
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Join Interfaces with CEINTF
• Use this to tie two meshes together at an interface
• Uses weighted averages of distance to smear the constraint equations
• Connects the nodes on the first surface to all the nodes on the surface
elements on the second surface
• CEINTF, TOLER, DOF1, DOF2, DOF3, DOF4, DOF5, DOF6, MoveTol
– Toler: fraction of element size, find all nodes within that fraction from element
– DOF1 – DOF6: DOF’s to write CE’s for
– MoveTo1: if not 0, move the nodes onto the surface of the elements if they
don’t sit exactly on. Value is fraction of element size
• Hints
–
–
–
–
Use components to set up
Nodes should be smaller and denser of the two sides
Don’t use to attach 6DOF elements to 3DOF elements
Use CPEINTF if the nodes line up
DX R13: 02/17/2011
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CEINTF Example: Joining Two Blocks
finish
/clear
/prep7
blc4,-1,-1,2,2,2
vatt,2
blc4,-3,-2,6,4,-2
et,1,185
esize,.9
vmesh,all
vsel,s,,,1
nslv,s,1
nsel,r,loc,z,0
vsel,s,,,2
nslv,s,1
nsel,r,loc,z,0
esln,s
allsel
/pnum,mat,1
/number,1
/view,1,1,1,1
/vup,1,z
/triad,lbot,1
eplot
ceintf,5,ux,uy,uz
nsle,a
/pbc,ce,1
eplot
DX R13: 02/17/2011
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Looking at one CE in our CEITNF
CONSTRAINT EQUATION
CONSTANT= 0.000000
NODE=
2 DIR=
NODE=
141 DIR=
NODE=
145 DIR=
NODE=
146 DIR=
NODE=
142 DIR=
NO.
UX
UX
UX
UX
UX
1 HAS
COEFFICIENT=
COEFFICIENT=
COEFFICIENT=
COEFFICIENT=
COEFFICIENT=
5 TERMS.
-1.000000
0.5000000
0.2500000
0.8333333E-01
0.1666667
• Connects node 2 to
all the corner nodes
of the element it sits
on.
• Coefficients are
distance to node 2
divided by sum of all
the distances.
DX R13: 02/17/2011
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Create Rigid Regions CERIG
• Make a bunch of nodes all have the same DOF response for
connecting 6DOF nodes
• CERIG, MASTE, SLAVE, Ldof, Ldof2, Ldof3, Ldof4, Ldof5
– MASTE is the node that drives the motion. All nodes will move like
MASTE
– SLAVE is the node(s) that will be linked to MASTE.
• Use ALL to slave all selected nodes
– LDOF-LDOF5 are the degrees of freedom to fix
• ALL, UXYZ, RXYZ, UX,UY,UZ,ROTX,ROTY,ROTZ
• Assumes that the master node is a 6DOF node
– Otherwise, just use a CP
• No CE number, it assigns the next number
• Mostly replaced by contact elements
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CERIG Example
nsel,s,,,1000
cmsel,a,nb1
cerig,1000,all,uz
CONSTRAINT EQUATION NO.
0.000000
NODE=
113 DIR= UZ
NODE=
1000 DIR= UZ
NODE=
1000 DIR= ROTX
NODE=
1000 DIR= ROTY
1 HAS
4 TERMS.
CONSTANT=
COEFFICIENT= 1.000000
COEFFICIENT= -1.000000
COEFFICIENT= 2.000000
COEFFICIENT= -3.000000
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NASTRAN Connections: RBE3
• Added for NASTRAN users who wanted their RBE3
• The motion of the master is the average of the motion of the
slaves
• RBE3, Master, DOF, Slaves, Wtfact
–
–
–
–
Master is your 6 DOF node
DOF is what DOF’s you want to connect (usually all)
Slaves is ALL or an array with node numbers (?!?!)
Wtfact is a weighting factor you can apply to any slave node to
“lesson” the effect of that node.
• Does average (1/num_nodes) for translational
• Does distance average for rotational (distn/total_dist)
• Not rigid. Distributes forces and moments
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RBE3 Example
• Connect a beam to 4 nodes
nsel,s,,,1000
cmsel,a,nn1
rbe3,1000,all,all
LIST ALL SETS FOR CONSTRAINT EQUATIONS WITH ANY
NODES SELECTED
CONSTRAINT EQUATION
CONSTANT= 0.000000
NODE=
1000 DIR=
NODE=
146 DIR=
NODE=
147 DIR=
NODE=
150 DIR=
NODE=
151 DIR=
NO.
CONSTRAINT EQUATION
CONSTANT= 0.000000
NODE=
1000 DIR=
NODE=
146 DIR=
NODE=
147 DIR=
NODE=
150 DIR=
NODE=
151 DIR=
NO.
CONSTRAINT EQUATION
CONSTANT= 0.000000
NODE=
1000 DIR=
NODE=
146 DIR=
NODE=
147 DIR=
NODE=
150 DIR=
NODE=
151 DIR=
NO.
CONSTRAINT EQUATION
CONSTANT= 0.000000
NODE=
1000 DIR=
NODE=
146 DIR=
NODE=
147 DIR=
NODE=
150 DIR=
NODE=
151 DIR=
NO.
CONSTRAINT EQUATION
CONSTANT= 0.000000
NODE=
1000 DIR=
NODE=
146 DIR=
NODE=
147 DIR=
NODE=
150 DIR=
NODE=
151 DIR=
NO.
UX
UX
UX
UX
UX
UY
UY
UY
UY
UY
UZ
UZ
UZ
UZ
UZ
ROTX
UZ
UZ
UZ
UZ
ROTY
UZ
UZ
UZ
UZ
1 HAS
5 TERMS.
COEFFICIENT= 1.000000
COEFFICIENT=-0.2500000
COEFFICIENT=-0.2500000
COEFFICIENT=-0.2500000
COEFFICIENT=-0.2500000
2 HAS
5 TERMS.
COEFFICIENT= 1.000000
COEFFICIENT=-0.2500000
COEFFICIENT=-0.2500000
COEFFICIENT=-0.2500000
COEFFICIENT=-0.2500000
3 HAS
5 TERMS.
COEFFICIENT= 1.000000
COEFFICIENT=-0.2500000
COEFFICIENT=-0.2500000
COEFFICIENT=-0.2500000
COEFFICIENT=-0.2500000
4 HAS
5 TERMS.
COEFFICIENT= 1.000000
COEFFICIENT= 0.6250000
COEFFICIENT=-0.6250000
COEFFICIENT= 0.6250000
COEFFICIENT=-0.6250000
5 HAS
5 TERMS.
COEFFICIENT= 1.000000
COEFFICIENT=-0.5833333
COEFFICIENT=-0.5833333
COEFFICIENT= 0.5833333
COEFFICIENT= 0.5833333
CONSTRAINT EQUATION NO.
6 HAS
9 TERMS.
CONSTANT= 0.000000
NODE=
1000 DIR= ROTZ COEFFICIENT= 1.000000
NODE=
146 DIR= UX
COEFFICIENT=-0.2909739
NODE=
146 DIR= UY
COEFFICIENT= 0.3117577
NODE=
147 DIR= UX
COEFFICIENT= 0.2909739
NODE=
147 DIR= UY
COEFFICIENT= 0.3117577
NODE=
150 DIR= UX
COEFFICIENT=-0.2909739
NODE=
150 DIR= UY
COEFFICIENT=-0.3117577
NODE=
151 DIR= UX
COEFFICIENT= 0.2909739
NODE=
151 DIR= UY
COEFFICIENT=-0.3117577
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MAXIMUM CONSTRAINT EQUATION NUMBER=
6
34
CE Utility Commands
• CELIST, NEQN1, NEQN2, NINC, Option
– Lists the CE’s
– Option is:
•
•
•
•
ANY – list if any of the nodes in the CE are selected
ALL – list of all of the nodes in the CE are selected
INTE – List internal CE’s created as MPC’s (solu only)
CONV – conert internal to external (solu only)
• CEDELE, NEQN1, NEQN2, NINC, Nsel
– Deletes CE’s
– Nsel is ANY or ALL
• CESGEN, ITIME, INC, NSET1, NSET2, NINC
– Generates CE’s from a previous set
– Increments node numbers
– (used before automatic meshing…)
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Internal CE’s:
MPC’s
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Bonded Contact
• Use with CONTA171/172/173/174/175/176/177
• Advantages
–
–
–
–
–
No elimination of DOF’s
Works with large deflection
Automatically generates equations at solve
Does force distribution based on shape functions, more accurate
Uses less memory than CE’s
• Does Rigid or Force Distributed
• Very detailed info in
– Mechanical APDL // Contact Technology Guide // 9. Multipoint
Constraints and Assemblies
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Just Like any Contact Definition
• First, you tell it your want MPC: KEYOPT(2) = 2
• Usually you also want bonded always: KEYOPT(12) = 5
– But works with no separation (4) or bonded, initial contact (6)
– So much more flexible then CE’s
• Use KEYOPT(4) to control what DOF’s to use
– 0 is typical, all that make sense
– 1 is no rotational
– 2 is all 6 DOF’s
• Handles connecting Beams/Shells/Solids to each other
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Example: Block on Block
et,11,170
et,12,175
r,11
real,11
keyopt,12,2,2 ! MPC
keyopt,12,12,5 ! Bonded
cmsel,s,nb1
type,11
esln,s,0
Esurf
cmsel,s,nt1
type,12
esln,s,0
Esurf
allsel
DX R13: 02/17/2011
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CELIST,all,,,conv
LIST ALL SETS FOR CONSTRAINT EQUATIONS WITH ANY
NODES SELECTED
CONSTRAINT EQUATION
NODE=
1 DIR=
NODE=
463 DIR=
NODE=
467 DIR=
NODE=
468 DIR=
NODE=
464 DIR=
NO.
UX
UX
UX
UX
UX
1 HAS
5 TERMS. CONSTANT=
COEFFICIENT= 1.000000
COEFFICIENT=-0.1666667
COEFFICIENT=-0.8333333E-01
COEFFICIENT=-0.2500000
COEFFICIENT=-0.5000000
0.000000
CONSTRAINT EQUATION
NODE=
1 DIR=
NODE=
463 DIR=
NODE=
467 DIR=
NODE=
468 DIR=
NODE=
464 DIR=
NO.
UY
UY
UY
UY
UY
2 HAS
5 TERMS. CONSTANT=
COEFFICIENT= 1.000000
COEFFICIENT=-0.1666667
COEFFICIENT=-0.8333333E-01
COEFFICIENT=-0.2500000
COEFFICIENT=-0.5000000
0.000000
CONSTRAINT EQUATION
NODE=
1 DIR=
NODE=
463 DIR=
NODE=
467 DIR=
NODE=
468 DIR=
NODE=
464 DIR=
NO.
UZ
UZ
UZ
UZ
UZ
3 HAS
5 TERMS. CONSTANT=
COEFFICIENT= 1.000000
COEFFICIENT=-0.1666667
COEFFICIENT=-0.8333333E-01
COEFFICIENT=-0.2500000
COEFFICIENT=-0.5000000
0.000000
DX R13: 02/17/2011
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Why Use CE’s?
• For most cases where you are gluing meshes together, use
MPC’s
• Use CE’s:
–
–
–
–
–
If you need to control the equations
Joints, gears, symmetry, etc…
You want to view the connections
Where nodal rotations play a role
You are working with DOF’s other than UXYZ/ROTXYZ
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CE’s In Workbench
DX R13: 02/17/2011
42
Mostly Hidden from User
• When you make MPC bonded contact, it does internal CE’s
• Some commands make CE’s or CP’s
– View the *.inp file to see what it does
– But dominant method is with MPC’s
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Two Ways to Make Your Own
• APDL Commands in Code Snippet
– Use named selections to grab the nodes you need
– You need to know how CE’s work and the APDL commands
• Insert into your model tree
– Considered Loads
– CP’s only available in modal analysis
• Between geometry
– CE’s available between remote points and/or joints
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CE’s in Workbench
• First, make your remote points
• Then RMB on environment object and select Constraint
Equation
• You get a Worksheet
– Define your constant
– Then add lines for each remote point in the equation
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Displaying CE’s in Workbench
• After you solve you can see an CE’s you made, or that
Workbench made
• Click on the Solution Information Object
• Set the FE Connection Visibility to show CE’s
• Also shows beams and springs
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Thoughts
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Understand CE’s
• As time goes by, the need to create your own CE’s goes
down
– That is good
• But you need to understand what the program is doing
– Under/over constraint can screw things up
• As always, read the help!
• If you need to do your own, crawl, walk, run
– Do a single CE, then move up to the whole model.
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