Nonlinear Analysis Convergence Practices BUENISIMO

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ANSYS NonlinearConver ence Best

Practices

Peter R. Barrett, P.E.

September 27, 2012

© 2008 CAE Associates


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ANSYS Nonlinear Convergence Best Practices

Nonlinearities Overview: — Large Deflection

— Material Nonlinearities

— Contact

Characterize Convergence Difficulty with Examples

— Relatively Straight Forward (easy) Problems

— Challenging (i.e. really hard) Problems

Ste -b -Ste Conver ence Procedure

1. Rigid body motion

2. Force balance not obtained

3. Material Instabilities and/or Element formulation error

Q&A

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All Products Exhibit Nonlinearities

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Large deflection affects stiffness

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Material Properties Cannot Always BeAssumed to Be Linear

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Contact is the Most Common Source ofNonlinearity and is Often the Most Difficulto o ve

Status

changes,friction,

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,

What is the pressure?


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Characterize Convergence Difficulty

Easier Problems

— e orma ons are re a ve y sma

— Nonlinear strains (plasticity, creep, swelling) are small

— Contact status does not oscillate

— o e s are sma an s mp e , x symme r c

— Symmetric boundary conditions are utilized

— Displacement based loads

— Loads result in tensile member stresses

— Nonlinear buckling to the point of instability (Post buckling not needed)

409 Parts967 Contact Pairs409 Parts967 Contact Pairs409 Parts967 Contact Pairs

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Characterize Convergence Difficulty

Harder Problems

— ery arge e orma on

— Large strains with large distortion

— Contact chatter and/or loose fitting assemblies

— on ac s ng w g r c on coe c en

— Post buckling response

— Large 3D models with complex geometry

— No symmetry boundaries

— Force based loads

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Pin Insert Model

Hard Solution

— Model the entire Pin / socket assembly

— Mesh fine enough to capture local

stress concentrations

— Use a force based analysis to model

pin insertion and removal

— Determine critical locations / load

Easier Solution

— Model a single axi-symmetric

— Create mapped mesh with refinement

on contact surfaces and areas of high

stress

— Use a displacement controlled solution

— Use auto time stepping and smart

output controls since max stress might

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not occur at the final solution step


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Gasket Assembly

— Large model

— Complex loading sequence

—

— Frictional Contact — Nonlinear material response

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Automatic Contact Reduces Modeling Time

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Building Collapse Simulation

— Evaluating the thermal-structural response of the World Trade Center collapse

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Elastomeric Bearing with Lead Plug

Force

Deflection of a

Single Truss

MatchesDetailed 3d

Model

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Clevis Pin Pullout

Springs can be used to imposed loads and/or prevent rigid body motion

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Surgical Staple – Displ. Controlled Example

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ANSYS Nitinol Material Behavior

Complex Material Response requires many substeps for

accuracy an convergence

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Rubber Boot with Self-Contact

Combined Geometric, Material and Contact Nonlinearities

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Vena Cava Filter

IVC filters are used in case of contraindication to anticoagulation

I.e. – it captures clots!

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FSI Example – Vena Cava Filter

Nonlinear structural response coupled with fluid flow

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FSI Example – Vena Cava Filter

Deformation

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My Analysis Did Not converge. Now What?

1. Rigid body motion

2. Force balance not obtained

.

4. Element formulation error 5. Combination of items 1-4 above

We will examine each in detail including:

— identifying the problem — e erm n ng e cause

— providing solutions

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Understanding the Solver Output

,to determine the origin of the non-convergence

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Rigid Body Motion Error Messages

DOF limit exceeded.

Negative main diagonal.

Small/Negative Pivot error.

MAX DOF INC = “A very large number”

*** WARNING *** CP = 11.703 TIME= 16:15:15Smallest negative equation solver pivot term encountered at UX DOF ofnode 98. Check for an insufficiently constrained model.

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Examples of Rigid Body Motion Cont.

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Causes of Rigid Body Motion

— — Individual parts of an assembly are not supported. This is the most common

form that is found in a contact analysis where rigid body motion occurs

in the parts not associated with any supports.

— Insufficiently connected dissimilar element types (i.e. beams to solids, etc.)

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Find the Rigid Body Motion

displacement scaling

— The example below is a converged solution where the rigid body motion is only

restrained b weak s rin s

— Note the unrealistic 10e-6 displacement scaling

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Use Modal Analysis to Find Rigid Body Motion

,modal analysis can be performed.

— A modal analysis determines the vibration modes including rigid body motion.

—

— Animating the zero frequency mode shape illustrates the rigidly moving model.

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Correct the Rigid Body Motion

— Take advantage of symmetries

— Axisymmetry

— Rotational — Planar or reflective

— Repetitive or translational

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– — Make a 2d Sector model

— Delete/Suppress parts or fix DOF until you get an answer

— Adding a rigid region and pushing it with displacements will usually convergebetter than a force loading.

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— If interfaces are all in compression, one might be able to leave as bonded

— Modify to standard contact one pair at a time

— Can use adjust to touch ANSYS option, but be careful since the geometry willbe changed

— Corrects interference fits

Add friction

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Avoid mistakes from wrong assumptions

— Make sure to include large deflections when displacements are significant

• You can never get the wrong answer by adding large displacement effects

— Check Displacement Scaling

Large deflections included!

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near so u on

C t th Ri id B d M ti


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element types

— Example Shells or beams to solids

—

iterations and penalty stiffness dependency

Add/adjust weak spring stiffness

—

error is introduced

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C t th Ri id B d M ti


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Add Contact Stabilization Damping

Rigid body motion often can occur in the beginning of a static analysis dueto the fact that the initial contact condition is not well established.

Ft ud P nndn

Target

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11

ud P

uP

t d

t d

Pd n

P d 1 , d 2

Contact Stabilization introduces a viscous damping traction proportional to

u oppos e o e re a ve pseu o ve oc es e ween e wo sur aces

along contact normal and/or tangential directions.

Where: = damping coefficient in normal directiond n

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= damping coefficient in tangential direction

= pseudo velocityu

t

C t t St bili ti D i


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Contact Stabilization Damping

radial clearance and under a force based load

— Stabilization captures localized stress distribution more accurately because it

does not chan e the sha e of the in

Conventional Adjust to Touch Contact Stabilization Damping

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Buckling Response

— Nonlinear stabilization

• Local instabilities and global

instability.

• se oge er w ne searc an

automatic time stepping

— Arc-length method

• Circumvent lobal instabilit when

forces are applied.

• Simulate the negative slope portion

of a load-vs.-displacement curve. — unn ng a s a c pro em as a

"slow dynamic" analysis in ANSYS

— Running a static problem as a

" "

ANSYS/LS-DYNA

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Connections that Prevent Rigid Body Motion


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Connections that Prevent Rigid Body Motion

Co n s t r a i n t e q u a t i o n s

S p r i n g s

SpotWelds

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B e am c o n n e c t i o n s

Examples of Force Equilibrium not Obtained


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Examples of Force Equilibrium not Obtained

— Convergence value is greater than criterion after min. load increment and max.

number of iterations are solved

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Equilibrium Iterations


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Equilibrium Iterations

approximations, with corrections.

ANSYS uses an iterative process called the Newton-Raphson

Method. Each iteration is known as an equilibrium iteration.

F

Load

4 A full Newton-Raphson

1

2 iterative analysis for oneincrement of load. (Fouriterations are shown.)

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u Displacement

Convergence Procedure


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Convergence Procedure

a nr

, - ,the residual. It is a measure of the force imbalance in the structure.

The goal is to iterate until the residual becomes acceptably small; less

than the criterion, where the solution is then considered converged.

When convergence is achieved, the solution is in equilibrium, within an

.

Fa

{Fa} {Fnr} Fnr

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u

Newton Raphson Residuals


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Newton Raphson Residuals

— Note that these controls need to be activated prior to the solution

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Ideal Load Stepping


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Ideal Load Stepping

— Use more substeps to reduce iterations, use less if only one or two are

needed. (One exception: If contact without friction is the only nonlinearity,

sometimes one subste with lots of iterations can be an efficient solution

method)

Load Step 2

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Substeps

1

equilibrium

iterations

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“Time

”

Causes of Force Balance not Obtained


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Causes o o ce a a ce ot Obta ed

Contact Stiffness is too large

Oscillation of contact status and force balance caused by large contactstiffness.

— A typical range of ANSYS penalty stiffness is .01 to 10 times the ANSYS

n erna s ness va ue w c s a unc on o ma er a an mes u no

geometry F=KU

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Causes of Force Balance not Obtained


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Load is stepped too rapidly

se n, ax an s ar ng su s ep con ro o mprove convergence. oucannot get the wrong answer by adding too many substeps

Load

TimeIncorrect

Strain Energy

tmaxtstart tmin

Rule of Thumb:The more nonlinearities, the

more substeps required

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Overcome the Force Unbalance


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Nonlinear Solution Corrective Action

ANSYS WB Mechanical offers a toolbox of options under the analysis

settings branch for achieving successful convergence.

— Step Control - Load steps and substeps

— Nonlinear Controls - N-R convergence criteria

— Contact Settings

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— General Rule – more nonlinearities – use more substeps

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Change contact stiffness update

• Recommend using iteration based adjustments

Ramp on the interference fit

Use Higher Order Elements• Especially with curved surface contact

Refine the mesh

• The more points in contact the better the convergence

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Increase the MINREF criterion

• If the criterion is very small this will not effect the solution accuracy

Extend the Stress-Strain curve

Adjust the convergence tolerance

• If the unbalance force difference is very small this can increase solution speed

s gn can y

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Review Initial Contact Settings and Eliminate Gaps


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Surface Projection Based Contact


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. Satisfies moment equilibrium when an offset exists between contact and

target surfaces with friction.

w v .

Better handling of sliding contact. KEYOPT,,4 ,3

Default Contact Settings

Surface Projection Contact

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Examples of Material Instabilities


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force unbalance or can be a result of incorrect material properties

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Causes of Material Instabilities


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— Material law cannot handle large load and/or time increment. If the force

unbalance is very large, the material model might not be the problem

— .

mesh, but again with very large force unbalances the material model might not

be the problem

Too large of plastic or creep strain increment

— Max. increment can be adjusted as part of cutback controls, but typically force

balance is the controlling criterion and thus this is rarely changed.

Elements with mixed u-P constraints not satisfied

— Modify the Volumetric Constraint

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Causes of Element Formulation Errors


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Excessive strain

Volumetric locking (PLESOL,NL,HPRES)

Hourglass modes

— Using Higher order elements or change toenhanced strain to eliminate reduced

Buckling

— Reduce rate of loading

ery arge orce un a ance

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Correct Element Formulation Errors


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— Use CHECK command for overall verification including missing elastic

properties, unconstrained model, and element shape checks.

—

cracks.

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Make sure to use the correct material input

Make sure to input True Stress vs. Log Strain — Conversion from engineering data , :

Always extend your material law will beyondex ected strain levels

l

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Element Selection


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,accurate results

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20 node bricks

Solver Type and Tolerance


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iteration

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Add intermediate substeps

Rezoning

— Requires a restart so generally only used for very large strain cases like

forming operations or seals

Adjust the starting mesh shapes – this is the most common solution

Change Element type / formulation

— Faster and more efficient solutions where applicable

Test with 1 Element model

—

— Modify creep law or coefficients

Start mesh shape so that deformed

elements become more square

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Element Type Selection


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quality

Simple is almost always better and definitely easier to debug

Complex 3-Dgeometries

Slender structures

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Shell elements

model)

Remesh the Model Part Way Through the Analysis


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— Note that this requires a restart, but will map existing stresses and strains so

that the solution history is preserved

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Change Material Models


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Hyperelastic Material Models


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The Value of the One Element Test Case

T ti li t i l d l


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Testing nonlinear material models

— Make sure the material converges for all stress / strain levels expected with theone element model before running full model

— Especially critical step for hyperelastic and creep analyses

Testing of macros and user-defined routines

Evaluation of the impact of large aspect ratios, skew angles or warpedelements

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Element Shape


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Mesh Controls


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stress gradients through multiple elements

— Example showing the value of symmetry

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Mesh Refinement


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sometimes speed

— Automated mesh refinement in workbench is generally only used in linear

anal ses

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Element Formulation


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the element order chosen (midside nodes) and the material association.

Workbench uses higher order 2d elements by default

Elastic material ormetal plasticity withhigher orderelements

2D Plane StressElastic material orMetal Plasticity with

lower order elements

2D Plain StrainElastic material orMetal Plasticity with

Fully incompressiblehyperelasticity with

lower order elements Simplified Enhanced Strain

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ig er or owerorder elements

B-Bar with Mixed u-P

You Have a Solution!


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Change the mesh

— Refine areas of steep gradient

— oarsen areas w ere s resses are ow

— Adjust initial element shapes to create better deformed shapes

Change the Substep settings

— Add substeps to reduce bisections

— Reduce substeps where convergence takes 1 or 2 iterations max.

Include Material Nonlinearities?

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Improve Performance in Subsequent Analyses


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substeps would eliminate the 27 iterations performed before the first

bisection. Reducing the starting number of substeps might eliminate this

bisection

Force Residual vs. Iterations

Time vs. Cumulative Iteration

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Thoroughly Investigate Your Results


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intended and that the results make sense

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Check the Quality of Your Results - Forces


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A p p l i e d l o a d s

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Ma t c h i n g r e a c t i o n f o r c es

Check the Quality of Your Stress Results


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. -

mesh error

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Understand the Data Generated


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Stresses and strain component data rotate with the elements

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Need More Information?


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or through taking training classes

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Nonlinear Analysis Convergence Practices BUENISIMO