mechanical-nonlin 13.0 ch02 procedure

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Customer Training Material

ec ure

General Procedures

Structural Nonlinearities

L2-1ANSYS, Inc. Proprietary

2010 ANSYS, Inc. All rights reserved.Release 13.0

December 2010


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ANSYS Mechanical General Nonlinear Procedures

Customer Training MaterialChapter Overview

In this chapter, general tools and procedures, not specific to a

particular source of nonlinearity, but useful for achieving

convergence and post processing 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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Customer Training MaterialA. 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



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Element technology options under large deflection with nonlinear materials

Load and boundary condition limitations under large deflection


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Customer Training Material... 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 uis solved at nodes

Stresses and strains are calculated at integration points.

They are derived from DOF.

For example, we can determinestrains from displacements via: , uB =

Where B is called the strain-displacement matrixu

The image on the right shows a 4-node quad element with 2x2integration, integration points shown in red.

When we post-process results, stress/strain values at integrationpoints are extrapolated or copied to nodal locations

linear results are extrapolated



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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 elementexists 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

8-Node Hex

(Linear shape function)

In challenging large deflection, bending dominated problems with nearly orfully compressible nonlinear materials, it can sometimes be advantageous to

drop the midside nodes and allow the code to implement enhanced strain



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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:

Direction Before Direction After

Load

Deflection Deflection

Acceleration

constant direction

Force, Moment,

Bolt Load

(constant direction)

Pressure

(always normal to

surface)



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Customer Training MaterialB. 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

34Ki

1

u

F = Ku Fi = Kiui



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Customer Training Material... 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 is saved

Analysis Data Management deleting/keeping files

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 initial minimum and

maximum number of substeps per loadstep. If WB-Mechanical has trouble converging, it

specifications to bisectthe solution.

Bisection applies the load in smaller

specified range) starting from the last

successfully converged substep.



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Step Controls (contd)

Recall that breaking the load into

increments im roves conver ence

by bringing the start point within theradius of convergence.

F

F1

adjusts the load increment sizes (up

anddown) throughout the solution.

uustart

Load

- Smaller increments when

convergence is difficult, larger

increments when convergence is

.

Time

tmaxtstart tmin



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Step Controls (contd)

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

eg nn ng o e run an wa c ng or sec ons.

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 buildsthe 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 elasticbehavior.

The default Program Controlled will



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automatically select a solver based on the

problem currently in session.


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Solver Controls (contd)

By setting Large Deflection = ON, in the

Solver Control branch of Anal 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 be

included.



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Customer Training MaterialWorkshop 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 (contd)

Generate Restart Points - Enables the creation of restart points with

the following options

Program Controlled: Instructs theprogram to select restart point generation

settin s automaticall

The setting is equivalent to Load Step = Last and

Substep = Last.

Manual: Exposes additional options (nextslide)

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 (Contd)

Max Points to Save per Step

When the maximum number has been savedfor each load step, the first file of that load

substeps.



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Restart Control (Contd)

For example, to write 3 equally spaced restart files for each load step:

Load r5r4

converged)

r3

r

Substeps

Time

LS1 LS2



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Restart

points


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Nonlinear Controls

Tolerances on Convergence are calculated

Newton-Raphson process to dictate when amodel 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 (Contd)

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 (contd)

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, thesea ona c ec s are no nc u e y e au

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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If you change any convergence criteria, theprogram deletes all the default criteria!

,

adding a displacement convergence check, theforce convergence check will be deleted.

Make sure you reestablish the forceconvergence check.

,should always confirm the specificationsreported in the Solution Information branch toensure 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 measureof convergence, it should only

gResidual

force-based convergence.

Force-based convergenceBi

prov es an a so ute measure

of convergence, as it is a

measure of equilibrium

Relying on displacement

convergence alone can in some

external forces.



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cases lead to erroneous results.


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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 the criterion * F will be zero. If the criterion

is zero, the solution will neverconverge!

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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Line Search is an additional tool intended to enhance convergence

behavior.

When active, line search multiplies the displacement increment by aprogram-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, dont change the default referencevalue, 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 problembeing solved.



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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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ANSYS Mechanical General Nonlinear Proced res


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Customer Training Material... 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



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Model shown is from a sample Unigraphics assembly.



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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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Customer Training MaterialWorkshop 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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