Mechanical-Nonlin 13.0 Ch02 Procedure

Customer Training Material

ec u r e General Procedures

Structural Nonlinearities

ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

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Release 13.0 December 2010

ANSYS Mech anical – General Nonlinea r Procedur es

Chapter Overview •


In this chapter, general tools and procedures, not specific to a particular source of nonlinearity, but useful for achieving convergence and post process ing results are introduce: A. Building a Nonlinear Model . •

Step Controls

•

Solver Controls

•

Restart Controls

•

Nonlinear Controls

•

Output Controls

•

Analysis Data Management

C. Postprocessing Nonlinear Results


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A. Building a nonlinear model


What is different about building a nonlinear model vs. a linear model?

• In some cases, there will be no difference! –

A model undergoing mildly nonlinear behavior due to large deflection and geometry set up and meshing.

• In other cases –

ou must include s ecial features:

Elements with special properties (such as contact elements) • Covered in Chapter 3 & 4

–

Nonlinear Material data such as lastic strain, cree strain data • Covered in Chapter 5 -7

–

Include geometric features to overcome singularities that cause convergence trouble. (i.e. add radius to sharp corner for example)

• You might also need to give special attention to: –

Mesh control considerations under large deflection

–

Element technology options under large deflection with nonlinear materials

–

Load and boundary condition limitations under large deflection


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... Building a nonlinear model


• With regards to meshing, if large strains are expected, the shape checking option may be changed to “Aggressive” –

–

For lar e-deflection anal ses, if elements ma under o some chan e in shape, this may reduce the fidelity of the solution By using “Aggressive” shape checking, WB-Mechanical will ensure that the element quality is much better prior to solution in order to anticipate distortion of the element in the course of a large-strain analysis. • The quality of the “Standard” shape checking is suitable for linear analyses, so it does not need to be changed in linear analyses

• With “aggressive” shape checking set, some mesh failures may be more likely. See WB-Mechanical - Intro for ways to detect and remedy mesh failures.


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• For any structural element, DOF solution u is solved at nodes • Stresses and strains are calculated at integration points. They are derived from DOF. –

–

For example, we can determine strains from displacements via:

Δε = B Δu

σ, ε

Where B is called the strain-displacement matrix u

• The image on the right shows a 4-node quad element with 2x2 integration, integration points shown in red.

• When stress/strain values at integration pointswe arepost-process extrapolated results, or copied to nodal locations –

linear results are extrapolated

–

Nonlinear results are copied


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• With Element Control set to Manual, users can manually toggle between Full and Reduced Integration Schemes –

This option influences the number of integration points within an element.

–

This switch only applies to higher order elements.

–

It is sometimes helpful to force full integration when only one element exists across the thickness of a part for improved accuracy.


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• By default, WB Mechanical element technology will mesh geometry with higher order elements (with midside nodes). –

Users have the option to drop midside nodes Kept midside nodes (Quadratic shape function) 20-Node Hex

Dro ed midside nodes (Linear shape function) 8-Node Hex –

–

In challenging large deflection, bending dominated problems with nearly or fully compressible nonlinear materials, it can sometimes be advantageous to drop the midside nodes and allow the code to implement enhanced strain Refer to Appendix 2A for a more detailed discussion of element technology.


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• It is important to note the orientation of loads and its effect on the structure in large-deflection analyses: Load

Direction Before Deflection

Direction After Deflection

Acceleration constant direction

Force, Moment, Bolt Load (constant direction)

Pressure (always normal to surface)


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B. Obtaining a nonlinear solution


What is different about obtaining a nonlinear solution? • Multiple matrix solutions: –

–

Linear static re uires onl one ass throu h the matrix e uation solver (Figure on left) Nonlinear performs a new solution with every iteration (Figure on right). F

F

Ki

3

4

1 u

F = Ku


F i = K iu i

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... Obtaining a nonlinear solution


…What is different about obtaining a nonlinear solution? • Anal sis Settin s has man o tions that need to be considered for a nonlinear run. -

– –

Solver Control - Choosing the right Solver type

–

Restart Controls - resuming a solve

–

Nonlinear Controls - N-R convergence criteria

–

Output Controls - controlling what data i s saved

–

Analysis Data Man agement – deleting/keeping file s

• In the following slides, we consider each of these tools


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Step Controls • “Auto Time Stepping” under Step Controls, enables user to define an initia l minimum and maximum number of substeps per loadstep. • If WB-Mechanical has trouble converging, it specifications to bisect the solution. –

“Bisection applies the load in smaller specified range) starting from the last successfully converged substep.


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Step Controls (cont’d) •

Recall that breaking the load into increments im roves conver ence by bringing the start point within the radius of convergence.

F F1

• adjusts the load increment sizes (up and down) throughout the solution. -

ustart

u

Load

Smaller increments when convergence is difficult, larger increments when convergence is .

Time tstart


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tmin

tmax





Step Controls (cont’d) • If no specifications are defined (Auto Time Stepping = Program Controlled), Mechanical will set specifications automatically depending on the nature of the nonlinearity in the model. • If taking the default auto time stepping specs, user should always verify that these values are adequate by checking the Solution Information folder at the e g nn ng o e r u n a n wa c n g o r s e c o n s . –

Discussed in more detail in Chapter 8 “Nonlinear Diagnostics”


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Solver Controls • Solver Type offers two options, ‘Direct’ and ‘Iterative’. –

–

–

–

This is a reference to the way the code builds the stiffness matrix for each Newton-Raphson equilibrium iteration. Direct (Sparse) solver is more robust and is recommended for challenging nonlinear models and with noncontinuum elements (shells and beams). Iterative (PCG) solver is more efficient (in terms of run time) and is recommended for large bulk solid models dominated by linear elastic behavior. The default ‘Program Controlled” will automatically select a solver based on the problem currently in session.


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Solver Controls (cont’d) • By setting “Large Deflection” = ON, in the Solver Control branch of A nal sis Settings: –

Adjustments will be made to the stiffness for changes in the geometry during the course of the analysis.

–

Also stress stiffenin effects will b e included.


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Workshop 2A – Large Deflection


• Please refer to your Workshop Supplement for instructions on: • W2A- Small Deflection Vs. Large Deflection Analysis


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Restart Controls • Restart Controls offer the ability to generate .. –

–

–

Review/correct an unconverged solution with changes to specifications in Details of “Analysis Settings” Interrupt a Solution in progress to review Add “Post” command snippets without erformin a full solve

• Supported by Static & Transient Structural analyses


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Restart Controls (cont’d) • Generate Restart Points - Enables the creatio n of restart poin ts with the following options… –

Program Controlled: Instructs the program to select restart point generation settin s automaticall • The setting is equivalent to Load Step = Last and Substep = Last.

–

–

Manual: Exposes additional options (next slide) Off: Restricts any new restart points from being created.


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With “Generate Restart Points” set to “Manual”… • Load Step: Specifies at what load steps to create restart points (Last or All). • Substep: Specifies how often the restart points are created within a load step. –

–

–

Last: Create a restart point for the last substep of each load step only. All: Creates restart points for all substeps of each load step. Specified: Creates restart points for a user specified number (N) of substeps per load step. • Where N is defined in “Rate of Recurrence” Field

–

restart points at equally spaced time intervals within a load step. • Where N is defined in “Rate of Recurrence” Field


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Restart Control (Cont’d) • Max Points to Save per Step –

–

When the maximum number has been saved for each load step, the first file of that load substeps.


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Restart Control (Cont’d) • For example, to write 3 equally spaced restart files for each load step:

Load

r5 r4

converged)

r3 r

Time LS 1

LS 2

Substeps Restart points ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

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Restart Control (cont’d) • Retain Files After Full Solve: –

Restart files are automatically deleted if a full solve completes successfully (default) • User has the option to keep restart files regardless by setting this field to YES.

–

incomplete solve due to a convergence failure or if solution run is manually interupted.

–

–

Under the Analysis Data Management category, setting Future Analysis to “Prestressed analysis” also forces the restart files to be retained. Similarly, setting Delete Unneeded Files to “ ” retained.


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... Obtaining a nonlinear solution •

At the completion of the run, user can specify the restart point for the subsequent run. –

•

•


If default restart controls were taken, restart will only be available for e as success u y converge su s ep

Restart specifications: –

Restart Type = Manual

–

Restart Point = Load Step 1, Substep 6

Once the restart specifications have been set and the analysis con ro se ngs an or ex s ng oa s ave een a us e as needed, execute a solve to begin the solution restart…


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Nonlinear Controls • Tolerances on Convergence are calculated

Newton-Raphson process to dictate when a model is Converged or “balanced” –

well for most engineering applications. –

For special situations, users can override these tolerance.

–

A tighter tolerance gives better accuracy, but


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Nonlinear Controls (Cont’d) • In addition to force balance, a moment balance will also be included if rotational degrees of freedom (DOF) are present in the model (i.e. when beam and/or shell elements are present for example).


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Nonlinear Controls (cont’d) • Balance checks on displacement and/or rotational DOF values can also be added as a su lement to force/moment balances.

• When contact nonlinearities are present, these a ona c ec sareno ncu e y ea u because they are generally considered overly restrictive and can cause unnecessary divergence.


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• The Force Convergence graph shows what the force criterion and residual forces (“force convergence”) are. When the residual forces are less than the criterion, the substep is assumed to be converged. Additional useful features include the fact that converged substeps and loadste s are also indicated on this Solution Information chart with a green and blue dotted line, respectively.

Residual

Criteria


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Nonlinear Controls (cont’d) • If you change any convergence criteria, the program deletes all the default criteria! –

, adding a displacement convergence check, the force convergence check will be deleted. • Make sure you reestablish the force convergence check.

–

, should always confirm the specifications reported in the Solution Information branch to ensure intended balance checks are active.


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Why must you re-establish a force convergence criterion? •

ecause

sp acemen - ase

checking is a relative measure of convergence, it should only force-based convergence.

l a u id s e R ig B

• Force-based convergence prov es an a so ute measure of convergence, as it is a measure of equilibrium external forces.


Relying on displacement convergence alone can in some cases lead to erroneous results. L2-29





Nonlinear Controls (cont’d) • The Minimum reference value (MINREF) is a safety feature that revents our solution from tr in to conver e to a zero tolerance. –

–

–

If free-body (unconstrained) systems or mechanisms have no external forces th e criterion * F will be zero. If the criterion is zero, the solution will never converge! In such cases, the program redefines the criterion to be ( R * MINREF). Where R is the convergence tolerance value. The default value that WB-Mechanical uses for MINREF depends on the physics of the problem.


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Nonlinear Controls (cont’d) • Line Search is an additional tool intended to enhance convergence behavior. • When active, line search multiplies the displacement increment by a program-calculated scale factor between 0 and 1, whenever a , . –

By default, the program turns Line Search ON when contact elements are present. You can override the default to turn it on or off explicitly.


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Convergence criteria guidelines: • Default convergence criteria work well most of the time. .

–

• To tighten or loosen a criterion, don’t change the default reference value, but instead change the tolerance factor by one or two orders of magn u e. • Do not use a “loose” criterion to eliminate convergence difficulties. –

This sim l allows the solution to “conver e” to an incorrect result!

• Tightening the criterion requires more equilibrium iterations. • Review any MINREF warning messages during solution. Make sure the minimum reference value used makes sense for the problem being solved.


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Nonlinear Controls (cont’d) • Stabilization is an advanced nonlinear control intended to deal with structural instabilit (buckling and/or localized yielding). –

Analogous to adding artificial dampers or .

• Refer to Chapter 8 for detailed discussion.


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C. Reviewing nonlinear results


What is different about reviewing nonlinear results? • The procedure for reviewing nonlinear results is similar to that of a linear roblem. The difference is that there is usuall more information to process – –

multiple results sets . , , penetration, inelastic strains due to plasticity and or creep,...etc).

• A nonlinear analyses produces a response history

Animated response history ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

Response history graph L2-34



... Reviewing nonlinear results


• In large deformation problems, one usually should view the deformation with “Actual” scaling from the Result toolbar • Any of the structural results may be requested, such as Equivalent Stress, shown below

Model shown is from a sample Unigraphics assembly. ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.

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• If contact is defined, a contact tool can be used to postprocess contact related results (pressure, penetration, frictional stress, status,..etc) –

We can explore this tool in greater detail in Chapters 3 and 4


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• If nonlinear material is defined, various stress and strain components can be requested. –

We will explore this in greater detail in Chapters 5 and 6.


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Workshop 2B – Restart Control


• Please refer to your Workshop Supplement for instructions on: • W2B- Restart Control


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Mechanical-Nonlin 13.0 Ch02 Procedure

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