A Constraint Equation Primer - padtinc.compadtinc.com/blog/wp-content/uploads/oldblog/PADT...Mobile...

DX R13: 02/17/2011

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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.

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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

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Introductions

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Upcoming Webinars • Upcoming Webinars

– 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

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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

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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


$14,250

– Simulation Workstation (Intel)


$11,750

– Simulation Workstation (AMD)


$6,300

• www.CUBE-HVPC.com

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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.

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Connect with PADT

Facebook:

facebook.com/padtinc

Twitter:

#padtinc

LinkedIn:

Search on PADT, Inc.

Email Subscriptions: www.padtinc.com/epubs

Web:

www.PADTINC.com

ANSYS User Blog:

padtinc.com/focus

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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 = (𝑐𝑜𝑒𝑓𝑖𝑐𝑐𝑖𝑒𝑛𝑡 𝐼 ∗ 𝑈 𝐼 )𝑁𝐼=1

– 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).

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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

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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

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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

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Looking at one CE in our CEITNF

• 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.

CONSTRAINT EQUATION NO. 1 HAS 5 TERMS.

CONSTANT= 0.000000

NODE= 2 DIR= UX COEFFICIENT= -1.000000

NODE= 141 DIR= UX COEFFICIENT= 0.5000000


NODE= 146 DIR= UX COEFFICIENT= 0.8333333E-01


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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. 1 HAS 4 TERMS. CONSTANT=

0.000000

NODE= 113 DIR= UZ COEFFICIENT= 1.000000

NODE= 1000 DIR= UZ COEFFICIENT= -1.000000

NODE= 1000 DIR= ROTX COEFFICIENT= 2.000000

NODE= 1000 DIR= ROTY 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


CONSTANT= 0.000000


NODE= 146 DIR= UX COEFFICIENT=-0.2500000





CONSTANT= 0.000000

NODE= 1000 DIR= UY COEFFICIENT= 1.000000

NODE= 146 DIR= UY COEFFICIENT=-0.2500000





CONSTANT= 0.000000


NODE= 146 DIR= UZ COEFFICIENT=-0.2500000





CONSTANT= 0.000000

NODE= 1000 DIR= ROTX COEFFICIENT= 1.000000






CONSTANT= 0.000000

NODE= 1000 DIR= ROTY COEFFICIENT= 1.000000






CONSTANT= 0.000000

NODE= 1000 DIR= ROTZ COEFFICIENT= 1.000000









MAXIMUM CONSTRAINT EQUATION NUMBER= 6

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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

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CELIST,all,,,conv

LIST ALL SETS FOR CONSTRAINT EQUATIONS WITH ANY NODES SELECTED

CONSTRAINT EQUATION NO. 1 HAS 5 TERMS. CONSTANT= 0.000000



NODE= 467 DIR= UX COEFFICIENT=-0.8333333E-01






NODE= 467 DIR= UY COEFFICIENT=-0.8333333E-01






NODE= 467 DIR= UZ COEFFICIENT=-0.8333333E-01



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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

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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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Thank You…

• PADT Enjoys doing these webinars…

• Please consider us as your partner

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– SLA, SLS, FDM, PolyJet, CNC, Soft Tooling,

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• Help us by letting us Help you

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