ansys nonlinear convergence best g practices

ANSYS Nonlinear Convergence Best g

Practices

Peter R. Barrett, P.E.September 27, 2012

Rev. 2/3/2016

© 2016 CAE Associates

Rev. 2/3/2016

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

Step-by-Step Convergence Procedurep y p g1. Rigid body motion2. Force balance not obtained3. Material Instabilities and/or Element formulation error3. Material Instabilities and/or Element formulation error

Q&A

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All Products Exhibit Nonlinearities

Always start with the simplest linear analysis if possible! Always start with the simplest linear analysis if possible!

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Large deflection Affects Stiffness

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Material properties cannot always be assumed to be linear


Contact is the most common source of nonlinearity and often the most difficult to solve! solve!

SStatus changes, friction, pressurepressure

When where?


When, where? What is the pressure?

Characterize Convergence Difficulty Easier Problems

D f ti l ti l ll— Deformations are relatively small— Nonlinear strains (plasticity, creep, swelling) are small— Contact status does not oscillate

M d l ll d i lifi d (2D A i t i )— Models are small and simplified (2D, Axisymmetric)— Symmetric boundary conditions are utilized— Displacement based loads

L d lt i t il b t— 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

V l d f ti— Very large deformation— Large strains with large distortion— Contact chatter and/or loose fitting assemblies

C t t lidi ith hi h f i ti ffi i t— Contact sliding with high friction coefficient— Post buckling response— Large 3D models with complex geometry

N t b d i— 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

stepssteps Easier Solution

— Model a single axi-symmetric Pin/Socket assemblyPin/Socket assembly

— 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

Gasket Assembly

Hard Problem Hard Problem— Large model— Complex loading sequence

Multiple bolt loads— Multiple bolt loads— Frictional Contact— Nonlinear material response

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Automatic contact reduces modeling time


Building Collapse Simulation

Running an analysis dynamically can be used to obtain convergence Running an analysis dynamically can be used to obtain convergence— 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 ElementElement Matches Detailed 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

daccuracy and 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

StreamlinesStreamlines

Deformation

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My analysis did not converge. Now what?

First step is to determine the cause: First step is to determine the cause:1. Rigid body motion2. Force balance not obtained3 Material Instabilities3. Material Instabilities4. Element formulation error5. Combination of items 1-4 above

We will examine each in detail including:— identifying the problem

d t i i th— determining the cause— providing solutions

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Understanding the Solver Output

Whether in WB or Mechanical APDL the first step is to read the output file Whether in WB or Mechanical APDL, the first step is to read the output file 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 of node 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

Insufficient supports— Insufficient supports— 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

Plot the unconverged or last converged displacement solution and verify Plot the unconverged or last converged displacement solution and verify displacement scaling

— The example below is a converged solution where the rigid body motion is only restrained by weak springsrestrained by weak springs

— Note the unrealistic 10e-6 displacement scaling

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Use modal analysis to find Rigid Body Motion

If it is not clear what constraint is required to eliminate rigid body motion a If it is not clear what constraint is required to eliminate rigid body motion, a modal analysis can be performed.

— A modal analysis determines the vibration modes including rigid body motion.Each rigid body mode is predicted as a zero frequency mode— Each rigid body mode is predicted as a zero frequency mode

— 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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Correct the rigid body motion

Isolate the error by creating a smaller simpler model – KISS!Isolate the error by creating a smaller simpler model KISS!— Make a 2d Sector model— Delete/Suppress parts or fix DOF until you get an answer

Add supports and/or use displacement controlled solution Add supports and/or use displacement controlled solution— Adding a rigid region and pushing it with displacements will usually converge

better than a force loading.

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Use bonded contact for debugging Use bonded contact for debugging— If interfaces are all in compression, one might be able to leave as bonded— Modify to standard contact one pair at a time

Adjust the parts to all start in contact Adjust the parts to all start in contact— Can use adjust to touch ANSYS option, but be careful since the geometry will

be changed Increase pinball region Increase pinball region

— Corrects interference fits Add friction

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Correct the rigid body motion 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!

Li l ti

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Linear solution


Use bonded contact to tie dissimilar Use bonded contact to tie dissimilar element types

— Example Shells or beams to solidsUse MPC contact option to eliminate— Use MPC contact option to eliminate iterations and penalty stiffness dependency

Add/adjust weak spring stiffnessBe sure to check reactions to make sure no— Be sure to check reactions to make sure no error is introduced

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Correct the rigid body motion Add Contact Stabilization Damping Rigid body motion often can occur in the beginning of a static analysis due

to the fact that the initial contact condition is not well established.

FnFn

Contact

Ft

dudP nndn

Target

Contact

22

11

udPudP

td

td

Pdn

Pd1,d2

Contact Stabilization introduces a viscous damping traction proportional to b t it t th l ti d l iti b t th t fbut opposite to the relative pseudo velocities between the two surfaces along contact normal and/or tangential directions.

Where: = damping coefficient in normal directiondd n

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= damping coefficient in tangential direction= pseudo velocityu

d t

Contact Stabilization Damping

Example: Consider a fixed pin interfacing with a hole in plate with initial Example: Consider a fixed pin interfacing with a hole in plate with initial radial clearance and under a force based load

— Stabilization captures localized stress distribution more accurately because it does not change the shape of the pindoes not change the shape of the pin

Conventional Adjust to Touch Contact Stabilization Damping

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Buckling Response— Nonlinear stabilization

• Local instabilities and global instability. U d t th ith li h d• Used together with line search and automatic time stepping

— Arc-length method• Circumvent global instability when g y

forces are applied. • Simulate the negative slope portion

of a load-vs.-displacement curve.R nning a static problem as a— Running a static problem as a "slow dynamic" analysis in ANSYS

— Running a static problem as a "slow dynamic" analysis inslow dynamic analysis in ANSYS/LS-DYNA

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Connections that prevent Rigid Body Motion

Automation tools can save a lot of time in tying assemblies together Automation tools can save a lot of time in tying assemblies together

Constraint equations

Springs

Spot Welds

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Beam connections

Examples of Force equilibrium not obtained

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

number of iterations are solved

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Equilibrium Iterations

A nonlinear structure is analyzed using an iterative series of linear A nonlinear structure is analyzed using an iterative series of linear approximations, with corrections.

ANSYS uses an iterative process called the Newton-RaphsonMethod. Each iteration is known as an equilibrium iteration.

F

Load

3 4 A full Newton-Raphson

1

23

iterative analysis for one increment of load. (Four iterations are shown.)

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u Displacement

Convergence Procedure

The difference between external and internal loads {Fa} {Fnr} is called The difference between external and internal loads, {Fa} - {Fnr}, is called 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 acceptable toleranceacceptable tolerance.

Fa

{{Fa} {Fnr}

Fnr{

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u

Newton Raphson Residuals

Plot Newton Raphson Residuals to determine critical contact pair Plot Newton Raphson Residuals to determine critical contact pair— Note that these controls need to be activated prior to the solution

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Causes of Force balance not obtained

Contact Stiffness is too large Contact Stiffness is too large Load is stepped too rapidly For small load increments, MINREF criterion exceeded Material instability Buckling

Definition of non-convergence, sum of R (unbalanced forces)

t b l 5% f thnever gets below .5% of the sum of F (sum of external loads, reactions, etc.))

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Ideal Load Stepping

Convergence after 3 to 5 iterations each substep Convergence after 3 to 5 iterations each substep— 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 substep with lots of iterations can be an efficient solution pmethod)

LoadLoadLoad Step 2

Load Step 123 4

Load Step 1

Substeps1

2 equilibriumiterations

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“Time”

Causes of Force balance not obtained Contact Stiffness is too large. Note: In V16 and beyond default stiffness

h b d d b b t f t f 10 f i ihas been reduced by about a factor of 10x from previous versions. Oscillation of contact status & force balance caused by contact stiffness.

— A typical range of ANSYS penalty stiffness is .01 to 10 times the ANSYS i t l tiff l hi h i f ti f t i l d h b t tinternal stiffness value which is a function of material and mesh but not geometry

F=KU

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Causes of Force balance not obtained Load is stepped too rapidly

U Mi M d t ti b t t l t i Y Use Min, Max and starting substep control to improve convergence. You cannot get the wrong answer by adding too many substepsLoad

TimeIncorrect

Strain Energy

tmaxtstart tmin

Rule of Thumb:The more nonlinearities, the more substeps required

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Overcome the Force Unbalance

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 substepsp p p— Nonlinear Controls - N-R convergence criteria

— Contact Settingsg

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Reduce Normal Stiffness Factor Reduce Normal Stiffness Factor

Increase the number of Substeps Increase the number of Substeps— General Rule – more nonlinearities – use more substeps

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Change contact stiffness update• Recommend using iteration based adjustments• Try Aggressive Update for tough problems

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

i ifi tlsignificantly

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Review Initial Contact Settings and eliminate gaps

See the ANSYS output file or run CNCHECK before solving See the ANSYS output file or run CNCHECK before solving

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Adjust Contact Pinball Region

Default pinball region is different based on analysis type (see below) Default pinball region is different based on analysis type. (see below) — Increase for large initial penetrations

Default PINB*

Contact Classification

Contact Surface Behavior

Initial Penetration Behavior KEYOPT(9)

3 x Depth** Rigid/Flex Standard Default (Include Everything)4 x Depth Rigid or Flex Standard Include Everything/with Ramped effects2 x Depth Flex/Flex Standard Default (Include Everything)

0.50x Depth Flex/Flex Bonded or No Separation Default (Include Everything)0.75x Depth Rigid/Flex Bonded or No Separation Default (Include Everything)p g p ( y g)1.00x Depth Rigid/Flex Bonded or No Separation Include Everything/with Ramped effects

**Depth = Underlying element depth (for solid elements)* Values are for NLGEOM,ON and are reduced by 50% for NLGEOM,OFF

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Depth Underlying element depth (for solid elements)**Depth = 4 x element thickness (for shells and beams)

Surface Projection Based Contact

More accurate distribution of contact stresses More accurate distribution of contact stresses. Satisfies moment equilibrium when an offset exists between contact and

target surfaces with friction. Can help ith contact con ergence Can help with contact convergence.

Better handling of sliding contact. KEYOPT,<contact element type>,4 ,3

Default Contact Settings Surface Projection Contact

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Examples of Material Instabilities

Depending upon the size of the residual these can be caused by large Depending upon the size of the residual these can be caused by large force unbalance or can be a result of incorrect material properties

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Causes of Material Instabilities

Force balance not obtained Force balance not obtained— 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— Element distorted shape results in negative volume calculation Check theElement distorted shape results in negative volume calculation. Check the

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 Constrainty

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Causes of Element Formulation Errors

Element Shape distortion Element Shape distortion Excessive strain Volumetric locking (PLESOL,NL,HPRES) Hourglass modes

— Using Higher order elements or change to enhanced strain to eliminate reduced integration issues in lower order elementsintegration issues in lower order elements

Buckling— Reduce rate of loading

V l f b l Very large force unbalance

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Correct Element Formulation Errors

Mechanical APDL commands Mechanical APDL commands— Use CHECK command for overall verification including missing elastic

properties, unconstrained model, and element shape checks.— MCHECK command can help you identify defects in the mesh such as holes orMCHECK command can help you identify defects in the mesh such as holes or

cracks.

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Correct Element Formulation Errors Make sure to use the correct material input Make sure to input True Stress vs. Log Strain

— Conversion from engineering data , :

11ln Always extend your material law will beyond

expected strain levels

1 1ln l

p

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Element Selection

Use Higher Order elements for curved surface contact for faster more Use Higher Order elements for curved surface contact for faster, more accurate results

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20 node bricks

Solver Type and Tolerance

Suggest using Direct (Sparse) solver unless PCG is significantly faster per Suggest using Direct (Sparse) solver unless PCG is significantly faster per iteration

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Correct Element Formulation Errors

Add intermediate substepsp Rezoning

— Generally only used for very large strain cases like forming operations or seals Adjust the starting mesh shapes – this is the most common solution Adjust the starting mesh shapes this is the most common solution Change Element type / formulation Use shell or beam elements

Faster and more efficient sol tions here applicable— Faster and more efficient solutions where applicable Test with 1 Element model

— Change the HyperElastic material modelf ff— Modify creep law or coefficients

Start mesh shape so that deformed elements become more square

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Element type selection

Select the appropriate element type to maximize results efficiency and Select the appropriate element type to maximize results efficiency and quality

Simple is almost always better and definitely easier to debug

Complex 3-D geometries

Slender structures (twisted pipe

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Shell elements (twisted pipe model)

Remesh the model part way through the analysis

Rezoning Rezoning— Automatically 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

Yeoh is very robust for large strain problems such as seals Yeoh is very robust for large strain problems such as seals

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The value of the one element test case

Testing nonlinear material models— Make sure the material converges for all stress / strain levels expected with the

one 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 warped

elements

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Element Shape

Robust well shaped elements can improve solution convergence and time Robust well shaped elements can improve solution convergence and time

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Mesh Controls

Numerous controls are available to locally modify the mesh to reduce Numerous controls are available to locally modify the mesh to reduce stress gradients through multiple elements

— Example showing the value of symmetry

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Mesh refinement

Automated mesh refinement will increase the solution quality and Automated mesh refinement will increase the solution quality and sometimes speed

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

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Element Formulation

Solver Output records the element technology being activated based on Solver Output records the element technology being activated based on the element order chosen (midside nodes) and the material association. Workbench uses higher order 2d elements by default

Elastic material or Elastic material or metal plasticity with higher order elements

Default URI2D Plane StressElastic material or Metal Plasticity with lower order elements

Default URI

Enhanced Strain2D Plain StrainElastic material or Metal Plasticity with

Enhanced Strain

Fully incompressible hyperelasticity with h h l

lower order elements Simplified Enhanced Strain

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higher or lower order elements B-Bar with Mixed u-P

You have a solution!

How do you make the solution more efficient? How do you make the solution more efficient? Change the mesh

— Refine areas of steep gradientC h t l— Coarsen areas where stresses are low

— 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

The Force Convergence graph clearly indicates that starting with more The Force Convergence graph clearly indicates that starting with more substeps would eliminate the 27 iterations performed before the first bisection. Reducing the starting number of substeps might eliminate this bisectionbisection

Force Residual vs. Iterations

Time vs. Cumulative Iteration

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Thoroughly investigate your results

List and plot results to check to make sure you solved the problem List and plot results to check to make sure you solved the problem intended and that the results make sense

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Check the quality of your results - forces

First check should always be a free body diagram First check should always be a free body diagram

Applied loads

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Matching reaction forces

Check the quality of your stress results

Comparing average vs un-average stresses can provide an estimate of Comparing average vs. un-average stresses can provide an estimate of mesh error

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Understand the data generated

Displacements are based on original coordinate system Displacements are based on original coordinate system Stresses and strain component data rotate with the elements

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Need more information?

Additional Information on all of these topics is available in the ANSYS Help Additional Information on all of these topics is available in the ANSYS Help or through mentoring or training classes

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ansys nonlinear convergence best g practices

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