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Convergence Problems: Contact Simulations

Lecture 5

L5.2

Overview

? Unstable Separation of Contacting Surfaces ? Chattering Between Contact Surfaces ? Contact with Quadratic Elements ? Poorly Defined Master Surfaces ? Friction

Obtaining a Converged Solution with Abaqus

129

BEGIN

Solution procedure without contact

Begin new increment Begin new attempt Begin new iteration

L5.3

Begin new step

Form Ktangent Solve for u

Step loop

Increment loop

Attempt loop

Iteration loop

Update u

Compute residuals

Yes Compute new t No Analysis finished? Yes DONE!

Obtaining a Converged Solution with Abaqus

Reduce t

No

Convergence likely?

No

Converged? Yes Output results

No Yes Step finished?

BEGIN

Solution procedure without contact

Begin new increment Begin new attempt Begin new iteration

L5.4

Begin new step

Form Ktangent Solve for u

Step loop

Increment loop

Attempt loop

Iteration loop

Update u

Change contact constraints if necessary

Contact changes?

Compute residuals Yes Compute new t No Analysis finished? Yes DONE!

Obtaining a Converged Solution with Abaqus

Reduce t

No

Convergence likely?

No

Converged? Yes Output results

No Yes Step finished?

130

Unstable Separation of Contacting Surfaces

L5.6

Unstable Separation of Contacting Surfaces

? A large quantity of strain energy can be generated in two contacting bodies. ? Should the two bodies separate suddenly, the release of the elastic strain energy causes unstable response. ? During this unstable phase it is difficult for Abaqus to find a converged solution. ? Usually Abaqus will cut back the increment size because the solution diverges. ? Problems in which contact between two bodies occurs at a single node are especially vulnerable to unstable separation. ? Snap-through or snap-in problems are the most common type of simulations where unstable separation occurs.

Obtaining a Converged Solution with Abaqus

131

L5.7

Unstable Separation of Contacting Surfaces

? Unstable separation of contact surfaces is one of many possible causes of diverging solution warnings in Abaqus. ? The presence of severe discontinuity iterations (SDIs, where a slave node opens) before the diverging solution warnings is one symptom that contact separation is the cause of the problem. ? Another symptom of unstable contact is that the node with the largest displacement correction and the magnitude of the correction does not change as Abaqus cuts back the increment size—this is a typical symptom of unstable behavior regardless of whether contact is involved or not. ? There are two techniques for overcoming unstable contact conditions: ? Adding inertia to the problem (making the problem dynamic).

? Adding viscous damping to the (static) problem.

Obtaining a Converged Solution with Abaqus

L5.8

Unstable Separation of Contacting Surfaces

? Adding inertia ? When inertia is added to an unstable contact problem, the inertial forces counterbalance the forces created by the unstable contact conditions. ? However, the addition of inertia to a contact problem in Abaqus/Standard makes the analysis more complex and more expensive to perform. ? If implicit dynamics is required, use the quasi-static application type (see Lecture 3).

? Alternatively, consider using Abaqus/Explicit.

? This technique, however, is not an ideal option for many practical simulations.

Obtaining a Converged Solution with Abaqus

132

L5.9

Unstable Separation of Contacting Surfaces

? Adding viscous damping ? Viscous damping can be used to control unstable problems, even in a static simulation. ? Abaqus/Standard calculates the nodal velocities as the increment of displacement, u, divided by the increment of time, t . ? The easiest way to include viscous damping in a model is to use the automated stabilization capability available in Abaqus/Standard (see Lecture 3):

*STATIC, STABILIZE

? Local viscous damping can be added to a model by defining DASHPOT1 elements at selected nodes in the model.

Obtaining a Converged Solution with Abaqus

L5.10

Unstable Separation of Contacting Surfaces

? For unstable contact conditions, viscous damping can be added to the behavior of a contact interaction rather than to all the nodes. ? The viscous forces will be applied normal to the master surface and will be proportional to the relative approach velocity of the surfaces. ? The viscous damping coefficient, 0, is defined as a function of the clearance, c, between the surfaces.

? u

slave

? master u

t

n

Vrel ? slave n ( u ? master ) u

Relative approach velocity of two surfaces

Obtaining a Converged Solution with Abaqus

133

L5.11

Unstable Separation of Contacting Surfaces

Viscous surface damping

Obtaining a Converged Solution with Abaqus

L5.12

Unstable Separation of Contacting Surfaces

? Add damping to the behavior of a surface interaction model.

*surface interaction, name=IntProp-1 *contact damping, definition=damping coefficient 0.01, 0.12, 0.5

0

c0

? The following example illustrates a technique to determine appropriate values for the contact damping parameters.

c0 c0

Obtaining a Converged Solution with Abaqus

134

L5.13

Unstable Separation of Contacting Surfaces

? Example: Reinforced medical tubing

? Polymer tube reinforced internally with a series of metallic coils, or filars

? Beam elements ? Tube outer radius = 1.0 ? Tube inner radius = 0.76 ? Spring radius = 0.03 ? Linear elastic material ? ITT elements used to model: ? Filar-to-filar contact ? Filar-to-tube contact ? Lateral load applied to wrap tube around cylinder

filars tube

F

Rigid cylinder Detail of finite element model

Obtaining a Converged Solution with Abaqus

L5.14

Unstable Separation of Contacting Surfaces

? Abaqus begins having trouble finding a converged solution at about 3.5 of the applied load.

? Difficulty determining the contact state

? Filars are long, flexible, curved wires ? Behavior is highly unstable as the tube bends around the cylinder.

SUMMARY OF JOB INFORMATION: STEP INC ATT SEVERE EQUIL TOTAL DISCON ITERS ITERS ITERS 1 1 1 0 2 2 1 2 1 0 1 1 1 3 1 0 1 1 1 4 1U 8 0 8 1 4 2 0 1 1 1 5 1U 7 0 7 1 5 2 1 2 3 1 6 1 11 2 13 : TOTAL TIME/ FREQ 0.00100 0.00200 0.00350 0.00350 0.00406 0.00406 0.00427 0.00459 STEP TIME/LPF 0.00100 0.00200 0.00350 0.00350 0.00406 0.00406 0.00427 0.00459 INC OF TIME/LPF 0.001000 0.001000 0.001500 0.002250 0.0005625 0.0008438 0.0002109 0.0003164

Deformed state in early stages of analysis

Difficulties begin in this increment and continue throughout analysis

Obtaining a Converged Solution with Abaqus

135

L5.15

Unstable Separation of Contacting Surfaces

? The analysis ultimately completes successfully with default controls ? 144 increments, 604 iterations

SUMMARY OF JOB INFORMATION: STEP INC ATT SEVERE EQUIL TOTAL DISCON ITERS ITERS ITERS : 1 142 1U 6 0 6 1 142 2 1 2 3 1 143 1 1 1 2 1 144 1 0 2 2 TOTAL TIME/ FREQ 0.992 0.994 0.997 1.00 STEP TIME/LPF INC OF TIME/LPF

0.992 0.994 0.997 1.00

0.008354 0.002088 0.003133 0.003133

THE ANALYSIS HAS COMPLETED SUCCESSFULLY

ANALYSIS SUMMARY: TOTAL OF

144 39 604 604 604

INCREMENTS CUTBACKS IN AUTOMATIC INCREMENTATION ITERATIONS INCLUDING CONTACT ITERATIONS IF PRESENT PASSES THROUGH THE EQUATION SOLVER OF WHICH INVOLVE MATRIX DECOMPOSITION

? Use contact damping to stabilize the contact and improve convergence.

Obtaining a Converged Solution with Abaqus

L5.16

Unstable Separation of Contacting Surfaces

? Estimating the damping factor

1

In the converged increment immediately prior to the onset of cutbacks it is observed in the Job Diagnostics dialog box (or the message file) that umax 7. 5e 3 for t = 1. 5e 3.

?max Thus, estimate u

2

5.0.

Look at the Job Diagnostics dialog box (or the message file) to estimate the average force in the model. For the converged increment immediately preceding the onset of cutbacks :

CONVERGENCE CHECKS FOR EQUILIBRIUM ITERATION AVERAGE LARGEST LARGEST LARGEST 1

q

2.498E-03 DOF 3 DOF 1 DOF 3

FORCE 4.765E-03 TIME AVG. FORCE RESIDUAL FORCE 1.263E-10 AT NODE 7036 INCREMENT OF DISP. 7.500E-03 AT NODE 7036 CORRECTION TO DISP. -5.852E-06 AT NODE 7036 THE FORCE EQUILIBRIUM EQUATIONS HAVE CONVERGED

Thus, estimate q

0.005.

Obtaining a Converged Solution with Abaqus

136

L5.17

Unstable Separation of Contacting Surfaces

3 The typical contact area (Ac) for this problem is

1.0.

4 The damping forces should reach the same order of magnitude as the

average force, but at a much lower velocity (e.g., 100 slower). ? Therefore, calculate based on q

?max 0.005 , Ac = 1.0, and u

0.05.

q

Ac ?max u

0.1.

Obtaining a Converged Solution with Abaqus

L5.18

Unstable Separation of Contacting Surfaces

5 Estimate the clearance at which damping drops off to zero.

? For filar-to-filar and filar-to-tube contact, set equal to a small fraction (e.g., 5 ) of the minimum clearance between the filars:

c0

0.06 0.05 0.003.

? For tube-to-cylinder contact, set equal to a small fraction (e.g., 1 ) of the tube outer radius:

c0

1.0 0.01 0.01.

6 Assume the damping coefficient drops off linearly:

0.0.

Obtaining a Converged Solution with Abaqus

137

L5.19

Unstable Separation of Contacting Surfaces

? With contact damping convergence is much easier ? 37 increments, 173 iterations

SUMMARY OF JOB INFORMATION: STEP INC ATT SEVERE EQUIL TOTAL DISCON ITERS ITERS ITERS 1 1 1 0 2 2 1 2 1 0 1 1 1 3 1 0 1 1 1 4 1U 4 2 6 1 4 2 0 9 9 1 5 1 0 6 6 1 6 1 0 2 2 : : 1 34 1 1 3 4 1 35 1 3 4 7 1 36 1 2 3 5 1 37 1 0 2 2 TOTAL TIME/ FREQ 0.00100 0.00200 0.00350 0.00350 0.00406 0.00463 0.00519 STEP TIME/LPF 0.00100 0.00200 0.00350 0.00350 0.00406 0.00463 0.00519 INC OF TIME/LPF 0.001000 0.001000 0.001500 0.002250 0.0005625 0.0005625 0.0005625

0.945 0.967 1.00 1.00

0.945 0.967 1.00 1.00

0.01461 0.02192 0.03288 0.0003329

THE ANALYSIS HAS COMPLETED SUCCESSFULLY

Obtaining a Converged Solution with Abaqus

L5.20

Unstable Separation of Contacting Surfaces

? Viscous dissipation energy is small relative to the internal energy. ? Adequate viscous forces were provided during unstable behavior, which had a minimal influence on the model during more stable response.

Final deformed shape

Obtaining a Converged Solution with Abaqus

138

L5.21

Unstable Separation of Contacting Surfaces

? Additional comments on using viscous damping ? When viscous damping is added to a model to control unstable behavior, it is best if damping parameters are specified so that Abaqus immediately obtains a converged solution. ? If the parameters are not sufficient to control the unstable behavior, much time will be spent running simulations that fail to converge.

Obtaining a Converged Solution with Abaqus

L5.22

Unstable Separation of Contacting Surfaces

? Ideally you will perform a simulation that converges with the damping parameters. Then you must ask, “Is the damping too large? Is it influencing the model’s behavior in the stable regime?”

? To answer these questions, you should reduce the damping parameters (for example, by a factor of 10) and run the simulation again.

? If this analysis converges and there is no appreciable difference in the solution obtained by Abaqus (determined by comparing force versus deflection curves), you can have some confidence that the damping is not influencing the model in the stable regime. ? If this second analysis fails to converge, you will know that your first set of damping parameters was close to the minimum values needed in the model.

Obtaining a Converged Solution with Abaqus

139

Chattering Between Contact Surfaces

L5.24

Chattering Between Contact Surfaces

? Chattering is a phenomenon in which Abaqus has difficulty determining which nodes on a slave surface are supposed to be in contact. ? The symptoms of chattering are repeated SDIs that involve the same nodes. ? Without detailed contact diagnostics (Job Diagnostics dialog box or PRINT, CONTACT=YES), it is impossible to detect when and where chattering occurs. ? An example of the output seen in the message (.msg) file when chattering occurs is shown on the next slide.

Obtaining a Converged Solution with Abaqus

140

L5.25

Chattering Between Contact Surfaces

CONTACT PAIR (SLAVE, RIGID1) NODE 2 IS OVERCLOSED BY 2.8232E-06. 1 SEVERE DISCONTINUITY OCCURRED DURING THIS ITERATION. 1 POINT CHANGED FROM OPEN TO CLOSED

same node in most SDIs

CONTACT PAIR (SLAVE, RIGID1) NODE 2 OPENS. CONTACT PRESSURE/FORCE IS -4.0463E-01. 1 SEVERE DISCONTINUITY OCCURRED DURING THIS ITERATION. 1 POINT CHANGED FROM CLOSED TO OPEN

CONTACT PAIR (SLAVE, RIGID1) NODE 2 IS OVERCLOSED BY 2.1232E-04. 1 SEVERE DISCONTINUITY OCCURRED DURING THIS ITERATION. 1 POINT CHANGED FROM OPEN TO CLOSED CONTACT PAIR (SLAVE, RIGID1) NODE 2 OPENS. CONTACT PRESSURE/FORCE IS -9.0463E-01.

1 SEVERE DISCONTINUITY OCCURRED DURING THIS ITERATION. 1 POINT CHANGED FROM CLOSED TO OPEN

Obtaining a Converged Solution with Abaqus

L5.26

Chattering Between Contact Surfaces

? When the (default) node-to-surface contact discretization is used, chattering often occurs at the edge of two bodies that are in contact. ? As the slave node makes contact with the master surface, it slides off the edge of the master surface (1), but it regains contact one or a few iterations later (2).

2

1

trimmed master surface 3 Automatically extended master surface slave node

? For the finite-sliding, node-to-surface contact discretization, Abaqus/Standard automatically extends deformable master surfaces to try to minimize this problem. ? This problem is less likely with the surface-to-surface contact discretization, because each contact constraint is based on a region of the slave surface rather than individual slave nodes.

Obtaining a Converged Solution with Abaqus

141

L5.27

Chattering Between Contact Surfaces

? Chattering can also occur when the normal force between the two contacting bodies is very small. It can be very hard for Abaqus to find an equilibrium configuration for the model in this situation.

? When chattering is caused for this reason, use the automatic contact tolerances feature to help achieve convergence.

Obtaining a Converged Solution with Abaqus

L5.28

Chattering Between Contact Surfaces

? Automatic contact tolerances ? The automated contact tolerances allow some slight penetration at a slave node that was not previously in contact and some slight tensile force at a slave node that is predicted to be in contact without causing a contact iteration.

? The penetration and tensile force tolerances are based on the magnitude of the displacement solution correction and the time-average force at a node.

? These automatic tolerances are generally recommended, especially in cases where chattering is observed.

Obtaining a Converged Solution with Abaqus

142

L5.29

Chattering Between Contact Surfaces

? These contact tolerances are computed as follows: ? The allowable penetration is set to twice the maximum displacement correction. ? During the first two iterations the allowable tensile contact pressure is equal to 10 times the maximum allowable force residual divided by the contact area of a node. ? After the second iteration the allowable tensile contact pressure is equal to the maximum allowable force residual divided by the contact area of a node. ? If convergence occurs during the first two iterations, at least one more iteration is performed with the tighter tolerance.

Obtaining a Converged Solution with Abaqus

L5.30

Chattering Between Contact Surfaces

? The syntax for using these automatic tolerances is:

*CONTACT CONTROLS, AUTOMATIC TOLERANCES

? The SLAVE and MASTER parameters can be used to limit the controls to a specific contact pair.

? The RESET parameter is used to remove the automatic tolerances.

Obtaining a Converged Solution with Abaqus

143

L5.31

Chattering Between Contact Surfaces

? Example: Clip insertion problem

Pipe

ARM2

ARM1

Mesh for clip insertion simulation

Obtaining a Converged Solution with Abaqus

L5.32

Chattering Between Contact Surfaces

? The clip is made out of a pliable polymer material. ? For the purposes of this example, it is modeled as linear elastic. ? The goals of the simulation are to find the rotation of the pipe as it is pushed into the clip (with an applied displacement in the 2-direction) and to find the force-deflection curve for the pipe. ? Fourteen analysis steps in the simulation. ? The pipe is modeled as a rigid surface. The rigid body motions of the pipe, in the 1- and 6-directions, are initially controlled by soft springs attached to the reference node. ? They are removed early in the simulation. ? Dashpot elements in the 1- and 6-directions are used to control the unstable motion of the pipe as it snaps into the clip.

Obtaining a Converged Solution with Abaqus

144

L5.33

Chattering Between Contact Surfaces

? Abaqus has problems finding a converged solution in the later stages of the simulation.

? Abaqus/Standard terminates the analysis prematurely in Step 12 because of chattering.

? The node highlighted in the figure has the most difficulty establishing a stable contact state in the final (failed) increment (# 111) of Step 12.

Node 607

Obtaining a Converged Solution with Abaqus

L5.34

Chattering Between Contact Surfaces

? Focus on SDI history in Step 12 of node 607

Obtaining a Converged Solution with Abaqus

145

L5.35

Chattering Between Contact Surfaces

? An edited summary from the .msg file is shown below:

INCREMENT 111 STARTS. ATTEMPT NUMBER 2, TIME INCREMENT 1.000E-08

SDI #2: CONTACT PAIR (ARM1-B,ARM2-B) NODE 607 IS OVERCLOSED BY 6.75075E-008. SDI #3: CONTACT PAIR (ARM1-B,ARM2-B) NODE 607 OPENS BY 1.10147E-009 WITH A CONTACT PRESSURE/FORCE OF -6.11511E-005. SDI #5: CONTACT PAIR (ARM1-B,ARM2-B) NODE 607 IS OVERCLOSED BY 6.75075E-008. SDI #6: CONTACT PAIR (ARM1-B,ARM2-B) NODE 607 OPENS BY 1.10147E-009 WITH A CONTACT PRESSURE/FORCE OF -6.11511E-005. SDI #8: CONTACT PAIR (ARM1-B,ARM2-B) NODE 607 IS OVERCLOSED BY 6.75075E-008. SDI #9: CONTACT PAIR (ARM1-B,ARM2-B) NODE 607 OPENS BY 1.10147E-009 WITH A CONTACT PRESSURE/FORCE OF -6.11511E-005. : : ***NOTE: A REPETITIVE SDI PATTERN OCCURS. CONVERGENCE IS JUDGED UNLIKELY.

Obtaining a Converged Solution with Abaqus

L5.36

Chattering Between Contact Surfaces

? Using automatic contact tolerances, convergence difficulties are overcome.

Fully inserted pipe

Force vs. deflection curve for the fully inserted clip simulation

Obtaining a Converged Solution with Abaqus

146

L5.37

Chattering Between Contact Surfaces

? Alternatives to automatic contact tolerances ? The following may also be used to control chattering: ? Penalty enforcement of “hard” contact ? Contact stabilization ? The softened contact model

*SURFACE BEHAVIOR, PRESSURE-OVERCLOSURE=[EXPONENTIAL | LINEAR | TABULAR]

Obtaining a Converged Solution with Abaqus

Contact with Quadratic Elements

147

L5.39

Contact with Quadratic Elements

? Transmission of pressure across element faces is basic to contact problems ? Pressure is applied to element faces by using element shape functions to calculate the equivalent consistent nodal loads ? Constant pressure on an element face generates consistent nodal loads which are: q q

p

? equal for linear elements ? 2D example shown

q q ? pA

p

r

r q r 2/3 pA 1/6 pA

? vary across the element face for quadratic elements ? 2D example shown

Obtaining a Converged Solution with Abaqus

L5.40

Contact with Quadratic Elements

? For some element types, consistent nodal loads for a uniform pressure act in opposite directions or are equal to zero at certain nodes

p 3-D, quadratic, serendipity element ? No midface node ? C3D20 q r

q r

1 pA 3 1 pA 12

Forces act in opposite direction at corner nodes

q q q

p

q

1 pA 3

3-D, quadratic, tetrahedral element ? C3D10(I)

Zero force at corner nodes

Obtaining a Converged Solution with Abaqus

148

L5.41

Contact with Quadratic Elements

? Zero or “negative” consistent nodal forces are problematic for traditional contact formulations

q r

q r

1 pA 3

? Not likely to converge, due to difficulty determining contact status (active or inactive) for slave nodes at corners of C3D20 elements ? In the case of slave nodes at corners of C3D10(I) elements, the surface area associated with the constraint is ≈ 0 ? Often results in convergence problems or very noisy contact pressures

1 pA 12

Forces act in opposite direction at corner nodes

q q

q

q

1 pA 3

Zero force at corner nodes

Uniaxial pressure load of 5.0 (large contact pressure noise!)

Obtaining a Converged Solution with Abaqus

L5.42

Contact with Quadratic Elements

? These problems are avoided with the surface-to-surface formulation

Contact pressure on the slave surface

Uniaxial pressure load of 5.0

Slave: C3D10

Node-to-surface formulation:

From previous page

Master: C3D8

Surface-to-surface formulation:

Desired solution!

Obtaining a Converged Solution with Abaqus

149

Poorly Defined Master Surfaces

L5.44

Poorly Defined Master Surfaces

? There are many different ways that a master surface can be poorly defined; some of them include: ? It can be incorrectly oriented. ? It can have a “seam” or “crack.” ? It can be poorly discretized (e.g., it has kinks).

Obtaining a Converged Solution with Abaqus

150

L5.45

Poorly Defined Master Surfaces

? Surface orientations ? Master surfaces must have consistent orientations and must point toward the slave surface. ? For the surface-to-surface contact discretization, slave surfaces must also have consistent orientations and must point toward the master surface.

Obtaining a Converged Solution with Abaqus

L5.46

Poorly Defined Master Surfaces

? Definition of normals for various surfaces: ? Analytical rigid surfaces: defined by the order in which the surface is defined. ? Rigid elements: defined by element connectivity. ? Structural elements: defined by element connectivity. ? Continuum elements: always point out of the element. ? Unique normals cannot be defined for three-dimensional beams. Therefore, they cannot be used as master surfaces.

In Abaqus/CAE, these surfaces are chosen interactively; the element connectivity that is generated will be consistent with your surface selection.

Obtaining a Converged Solution with Abaqus

151

L5.47

Poorly Defined Master Surfaces

? Symptoms of incorrect normals: ? Inconsistent normals from one element to the next:

Invalid Valid

? In the invalid case this error message is printed in the printed output ( .dat) file:

***ERROR: SURFACE TEST HAS FACETS THAT ARE NOT ORIENTED PROPERLY WITH RESPECT TO EACH OTHER. CHECK THE ELEMENT CONNECTIVITIES FOR UNDERLYING ELEMENT 3 AND 6 (SHARING THE COMMON NODE 4), AS WELL AS THE *SURFACE

Obtaining a Converged Solution with Abaqus

L5.48

Poorly Defined Master Surfaces

? Normals pointing in the wrong direction for the entire master surface:

? Data in the printed output file due to *PREPRINT, CONTACT=YES reflects severe initial overclosure:

SLAVE SURFACE ASURF NODE NUMBER MASTER SURFACE BSURF 5.4325 11 INITIALLY OVERCLOSED BY

? Convergence difficulties will usually follow.

Obtaining a Converged Solution with Abaqus

152

L5.49

Poorly Defined Master Surfaces

? To check normals before doing the analysis, use the following procedure: 1. Run a datacheck analysis:

abaqus job=contact datacheck

2. Start an Abaqus/Viewer session. 3. Open the contact.odb output database file.

4. Open the Common Plot Options dialog box.

5. Choose the Normals folder. Toggle on Show normals and select On surfaces. 6. Click Apply.

Obtaining a Converged Solution with Abaqus

L5.50

Poorly Defined Master Surfaces

? ?Seams? in a master surface ? Avoid defining a threedimensional master surface using coincident surface nodes; it results in a crack or seam in the surface. ? The effect of the crack in a finitesliding analysis is that slave nodes can fall through and become “stuck” under the surface, particularly if the surface is concave. ? Another effect is that the surface is not smoothed at the crack, which may also cause convergence problems.

Both vertices have the same coordinates. They are separated to show the crack in the surface.

Obtaining a Converged Solution with Abaqus

153

L5.51

Poorly Defined Master Surfaces

? Perimeter plots in Abaqus/Viewer can help detect such cracks:

? Perimeter plots are wire frame plots in which only element edges belonging to just one element are shown.

? Cracks in the surface will be plotted as “extra” perimeter lines.

crack

A perimeter plot can help identify seams in master surfaces

Obtaining a Converged Solution with Abaqus

L5.52

Poorly Defined Master Surfaces

? Snagging ? Corners or small protrusions of a jagged master surfaces can penetrate the spaces between slave nodes causing them to snag. Simplistic representation of customer model Node-to-surface Surface-to-surface

slave

master

? In general, slave nodes get snagged easily as they transverse a corner. ? The “averaged” penetration alleviates the tendency of slave surface to snag.

Obtaining a Converged Solution with Abaqus

154

L5.53

Poorly Defined Master Surfaces

? Abaqus/Standard automatically smoothes the master surface for contact calculations utilizing the node-to-surface discretization to minimize snagging.

? Master surface smoothing ensures that master surfaces have continuous surface normals at all points.

? This minimizes the tendency of slave nodes to snag. ? Snagging is not a problem for the surface-to-surface contact discretization. ? Abaqus accounts for the spaces between nodes on both the master and slave surfaces. ? Thus, no smoothing of the master surface occurs when using surface-to-surface contact discretization.

Obtaining a Converged Solution with Abaqus

L5.54

Poorly Defined Master Surfaces

? Master surface smoothing ? Abaqus/Standard automatically smoothes the following types of master surfaces for node-to-surface finite sliding: ? Two-dimensional deformable ? Three-dimensional deformable ? Surfaces defined on rigid elements ? Abaqus/Standard does not automatically smooth analytical rigid surfaces. ? Smoothing has no effect on slave surfaces. ? Smoothing is done only when two adjoining surface facets have different normals.

Obtaining a Converged Solution with Abaqus

155

Friction

L5.56

Friction

? Adding friction to a model generally makes convergence more difficult. ? Penalty friction is used by default. ? Approximates ideal stick-slip behavior by allowing a small amount of elastic slip. ? Provides a balance between accuracy and efficiency for most problems (e.g., metal forming). ? Lagrange friction enforces exact stick-slip behavior.

? Much more difficult to obtain convergence.

? Sometimes it is the only way to obtain convergence. YOU MUST FOLLOW RIGID BODY CONSTRAINT RULES!

Obtaining a Converged Solution with Abaqus

156

L5.57

Friction

? Example: Insertion/removal of a metallic press-on clip ? Explore different attachment strategies by: ? Simulating installation of the clip ? Moving the pin sideways and back to center ? Removing the clip ? Study how the removal force decreases with the amount of sideways motion.

? In this example focus on clip insertion and removal.

Obtaining a Converged Solution with Abaqus

L5.58

Friction

? Pin and clip modeled with shell elements ? For efficiency, the pin is assumed rigid. ? Linear elastic material assumed ? Proof-of-concept analysis. ? Expect small strains, large displacements/rotations. ? Rigid-deformable contact ? High friction ( = 0.4) between the clip and the pin ? Three-step analysis ? Insertion ? Reversal ? Snap Away

Move edges of clip

Fix pin reference node

Step 1: Insert clip

Steps 2+3: Remove clip

Obtaining a Converged Solution with Abaqus

157

L5.59

Friction

? Step definitions

*boundary pinRef, 1, 6 handle, 1, 6 *amplitude, name=disp, time=total 0., 0., 1., 9., 2., -5. ** *step, name=insert, nlgeom *static 0.1, 1.0 *boundary, op=mod, amp=disp handle, 3, 3, -1.0 *end step ** *step, name=reverse, nlgeom *static 0.0075, 0.75 *end step ** * step, name=snap, nlgeom *static, stabilize 0.05, 0.25 *end step Break removal into two steps to use appropriate static stabilization in each.

Reversal step: no stabilization necessary

Snap-away step: use stabilization absorb energy release associated with loss of contact

Obtaining a Converged Solution with Abaqus

L5.60

Friction

? Boundary conditions

*boundary pinRef, 1, 6 handle, 1, 6 *amplitude, name=disp, time=total 0., 0., 1., 9., 2., -5. ** *step, name=insert, nlgeom *static 0.1, 1.0 BCs need only be edited *boundary, op=mod, amp=disp in the first step because handle, 3, 3, -1.0 total-time amplitude *end step curve is used. ** *step, name=reverse, nlgeom *static 0.0075, 0.75 *end step Splitting removal phase ** into two steps may require * step, name=snap, nlgeom trial-and-error; total-time *static, stabilize amplitude curve facilitates 0.05, 0.25 this without having to *end step redefine BCs

Obtaining a Converged Solution with Abaqus

158

L5.61

Friction

? Insertion

? Relatively straightforward

? No convergence difficulties

Obtaining a Converged Solution with Abaqus

L5.62

Friction

? Reversal ? High coefficient of friction causes clip to stick upon load reversal. ? Friction-driven snap-through behavior is induced.

? Problem statically stable.

? Global bending due to contact forces. ? Penalty friction: convergence difficulties upon load reversal. ? Lagrange friction: easy resolution of load reversal.

Friction-driven snap-through

End step just prior to snap-away

Obtaining a Converged Solution with Abaqus

159

L5.63

Friction

? Snap away ? Eventually the clip snaps away from the pin ? Dynamic event: large energy release occurs ? Implicit static analysis encounters convergence difficulties ? No surprise! ? Can either simulate as a dynamic step (costly, can be difficult to set parameters) or use automatic stabilization (easy, inexpensive solution)

Obtaining a Converged Solution with Abaqus

L5.64

Friction

? Load–displacement curve

Friction-driven snapthrough: contact points stick, force decreases!

Snapaway

End insertion; begin removal

Begin insertion Sliding begins

Clip sticks to pin

Obtaining a Converged Solution with Abaqus

160

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