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Home > Tips and Guidelines for Nonlinear Analysis

By taking your time and proceeding with reasonable caution, you can avoid many difficultiescommonly associated with nonlinear analyses. The following suggestions should be useful:

1.1 Be Aware of How the Program and Your Structure Behave

If you have not used a particular nonlinear feature before, construct a very simple model(that is, containing only a few elements), and make sure you understand how to handle thisfeature before you use it in a large, complicated model.

Gain preliminary insight into your structure's behavior by analyzing a preliminarysimplified model first. For nonlinear static models, a preliminary linear static analysiscan reveal which regions of your model will first experience nonlinear response, and atwhat load levels these nonlinearities will come into play. For nonlinear transientdynamic analyses, a preliminary model of beams, masses, and springs can provideinsight into the structure's dynamics at minimal cost. Preliminary nonlinear static, lineartransient dynamic, and/or modal analyses can also help you to understand variousaspects of your structure's nonlinear dynamic response before you undertake the finalnonlinear transient dynamic analysis.Read and understand the program's output messages and warnings. At a minimum,before you try to postprocess your results, make sure your problem converged. Forpath-dependent problems, the printout's equilibrium iteration record can be especiallyimportant in helping you to determine if your results are valid or not.

1.2 Keep It Simple

Keep your final model as simple as possible. If you can represent your 3-D structure asa 2-D plane stress, plane strain, or axisymmetric model, do so. If you can reduce yourmodel size through the use of symmetry or antisymmetry surfaces, do so. (However, ifyour model is loaded antisymmetrically, you can generally not take advantage ofantisymmetry to reduce a nonlinear model's size. Antisymmetry can also be renderedinapplicable by large deflections.) If you can omit a nonlinear detail without affectingresults in critical regions of your model, do so.Model transient dynamic loading in terms of static-equivalent loads whenever possible.Consider substructuring the linear portions of your model to reduce the computationaleffort required for intermediate load or time increments and equilibrium iterations.

1.3 Use an Adequate Mesh Density

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Recognize that regions undergoing plastic deformation require a reasonable integrationpoint density. Lower-order elements will provide the same number of integration pointsper element as will higher-order elements, and are thus often preferred for plasticityanalyses. Mesh density becomes especially important in plastic-hinge regions.Provide an adequate mesh density on contact surfaces to allow contact stresses to bedistributed in a smooth fashion.Provide a mesh density adequate for resolving stresses. Areas where stresses orstrains are of interest require a relatively fine mesh compared to that needed fordisplacement or nonlinearity resolution.Use a mesh density adequate to characterize the highest mode shape of interest. Thenumber of elements needed depends on the elements' assumed displacement shapefunctions, as well as on the mode shape itself.Use a mesh density adequate to resolve any transient dynamic wave propagationthrough your structure. If wave propagation is important, then provide at least 20elements to resolve one wavelength.

1.4 Apply the Load Gradually

For nonconservative, path-dependent systems, you need to apply the load in smallenough increments to ensure that your analysis will closely follow the structure'sload-response curve.You can sometimes improve the convergence behavior of conservative systems byapplying the load gradually, so as to minimize the number of Newton-Raphsonequilibrium iterations required.

A convergence failure can indicate a physical instability in the structure, or it can merely bethe result of some numerical problem in the finite element model.

The ANSYS program furnishes you with several tools that you can use to overcomenumerical instabilities in your analysis. If you are modeling a system that is actuallyphysically unstable (that is, having zero or negative stiffness), then you have a much moredifficult problem on your hands. You can sometimes apply one or more modeling tricks toobtain a solution in such situations. Let's examine some of the techniques that you can useto attempt to improve the convergence performance of your analysis.

2.1 Tracking Convergence Graphically

As a nonlinear structural analysis proceeds, ANSYS computes convergence norms withcorresponding convergence criteria each equilibrium iteration. Available in both batch andinteractive sessions, the Graphical Solution Tracking (GST) feature displays the computedconvergence norms and criteria while the solution is in process. By default, GST is ON forinteractive sessions and OFF for batch runs. To turn GST on or off, use either of thefollowing:

Command(s):

/GST


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GUI:

Main Menu>Solution>Output Ctrls>Grph Solu Track

Figure 8-21 below shows a typical GST display:

Figure 8-21 Convergence norms displayed by the Graphical Solution Tracking (GST)feature

2.2 Using Automatic Time Stepping

Be sure to place an upper limit on the time step size ([DELTIM] or [NSUBST]),especially for complicated models. This ensures that all of the modes and behaviors ofinterest will be accurately included. This can be important in the following situations:

Problems that have only localized dynamic behavior (for example, turbine bladeand hub assemblies) in which the low-frequency energy content of the systemcould dominate the high-frequency areas.Problems with short ramp times on some of their loads. If the time step size isallowed to become too large, ramped portions of the load history may beinaccurately characterized.Problems that include structures that are continuously excited over a range offrequencies (for example, seismic problems).

Take care when modeling kinematic structures (systems with rigid-body motions).These guidelines can usually help you obtain a good solution:

Incorporate significant numerical damping (0.05< <0.1 on the TINTP command)into the solution to filter out the high frequency noise, especially if a coarse timestep is used. Do not use -damping (mass matrix multiplier, ALPHAD command)in a dynamic kinematic analysis, as it will dampen the rigid body motion (zerofrequency mode) of the system.Avoid imposed displacement history specifications, because imposeddisplacement input has (theoretically) infinite jumps in acceleration, which causesstability problems for the Newmark time-integration algorithm.

2.3 Using Line Search


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Line search [LNSRCH] can be useful for enhancing convergence, but it can be expensive(especially with plasticity). You might consider setting line search on in the following cases:

When your structure is force-loaded (as opposed to displacement-controlled).If you are analyzing a "flimsy" structure which exhibits increasing stiffness (such as afishing pole).If you notice (from the program output messages) oscillatory convergence patterns.

2.4 Using the Arc-Length Method

You can use the arc-length method [ARCLEN], [ARCTRM] to obtain numerically stablesolutions for many physically unstable structures. When using the arc-length method, pleasekeep in mind the following considerations:

The arc-length method is restricted to static analyses with proportional (ramped) loadsonly.The program calculates the reference arc-length radius from the load (or displacement)increment of the first iteration of the first substep, using the following formula:

where NSBSTP is the number of substeps specified in the NSUBST command.

When choosing the number of substeps, consider that more substeps will result in alonger solution time. Ideally, you want to choose the minimum number of substepsrequired to produce an optimally efficient solution. You might have to take an"educated guess" of the desired number of substeps, and adjust and re-analyze asneeded.

Do not use line search [LNSRCH], the predictor [PRED], adaptive descent[NROPT,,,ON], automatic time stepping [AUTOTS, TIME, DELTIM], or time-integrationeffects [TIMINT] when the arc-length method is active.Do not attempt to base convergence on displacement [CNVTOL,U]. Use the forcecriteria [CNVTOL,F] instead.To help minimize solution time with the arc-length method, the maximum number ofequilibrium iterations in a single substep [NEQIT] should be less than or equal to 15.If an arc-length solution fails to converge within the prescribed maximum number ofiterations [NEQIT], the program will automatically bisect and continue the analysis.Bisection will continue either until a converged solution is obtained, or until theminimum arc-length radius is used (the minimum radius is defined by NSBSTP[NSUBST] and MINARC [ARCLEN]).In general, you cannot use this method to obtain a solution at a specified load ordisplacement value because the value changes (along the spherical arc) as equilibriumis achieved. Note in Figure 8-4 how the specified load is only used as a startingpoint. The actual load at convergence is somewhat less.Similarly, it can be difficult to determine a value of limiting load or deflection withinsome known tolerance when using the arc-length method in a nonlinear bucklinganalysis. You generally have to adjust the reference arc-length radius (using NSUBST)by trial-and-error to obtain a solution at the limit point. It might be more convenient to


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use standard Newton-Raphson iterations with bisection [AUTOTS] to determine valuesof nonlinear buckling loads.You should usually avoid using the JCG solver [EQSLV] in conjunction with thearc-length method, because the arc-length procedure might result in a negative definitestiffness matrix (negative pivot), which can cause a solution failure with this solver.You can freely switch from the Newton-Raphson iteration method to the arc-lengthmethod at the start of any load step. However, to switch from arc-length to Newton-Raphson iterations, you must terminate the analysis and restart, deactivating thearc-length method in the first load step of the restart [ARCLEN,OFF].

An arc-length solution terminates under these conditions:

When limits defined by the ARCTRM or NCNV commands are reachedWhen the solution converges at the applied loadWhen you use an abort file (Jobname.ABT)

See the ANSYS Basic Analysis Procedures Guide for a discussion of termination andrestart procedures.

Use the load-deflection curve as a guide for evaluating and adjusting your analysis tohelp you achieve the desired results. It is usually good practice to graph yourload-deflection curve (using POST26 commands) with every analysis.Often, an unsuccessful arc-length analysis can be traced to an arc-length radius that iseither too large or too small. "Drifting back," in which the analysis retraces its stepsback along the load-deflection curve, is one typical difficulty that is caused by using toolarge or too small an arc-length radius. Study the load-deflection curve to understandthis problem. You can then use the NSUBST and ARCLEN commands to adjust thearc-length radius size and range, as appropriate.The total arc-length load factor (item ALLF on the SOLU command) can be eitherpositive or negative. Similarly, TIME, which in an arc-length analysis is related to thetotal arc-length load factor, can also be either positive or negative. Negative values ofALLF or TIME indicate that the arc-length feature is applying load in the reversedirection, in order to maintain stability in the structure. Negative ALLF or TIME valuescan be commonly encountered in various snap-through analyses.When reading arc-length results into the database for POST1 postprocessing [SET],you should always reference the desired results data set by its load step and substepnumber (LSTEP and SBSTEP) or by its data set number (NSET). Do not referenceresults by a TIME value, because TIME in an arc-length analysis is not alwaysmonotonically increasing. (A single value of TIME might reference more than onesolution.) Additionally, the program cannot correctly interpret negative TIME values(which might be encountered in a snap-through analysis).If TIME becomes negative, remember to define an appropriate variable range([/XRANGE] or [/YRANGE]) before creating any POST26 graphs.

2.5 Artificially Inhibit Divergence in Your Model's Response

If you do not want to use the arc-length method to analyze a force-loaded structure thatstarts at, or passes through, a singular (zero stiffness) configuration, you can sometimes useother techniques to artificially inhibit divergence in your model's response:

In some cases, you can use imposed displacements instead of applied forces. Thisapproach can be used to start a static analysis closer to the equilibrium position, or to


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control displacements through periods of unstable response (for example,snap-through or post-buckling).Another technique that can be effective in circumventing problems due to initialinstability is running a static problem as a "slow dynamic" analysis (that is, usingtime-integration effects in an attempt to prevent the solution from diverging in any oneload step).You can also apply temporary artificial stiffness to unstable DOFs, using controlelements (such as COMBIN37), or using the birth and death option on other elements.The idea here is to artificially restrain the system during intermediate load steps, toprevent unrealistically large displacements from being calculated. As the systemdisplaces into a stable configuration, the artificial stiffness is removed.

2.6 Turn Off Extra Element Shapes

ANSYS provides "incompatible" modes" formulation (also referred to as "extra shapes") formodeling bending applications. If your problem is predominantly bulk deformation, then youmay choose to turn extra shapes off to reduce CPU/storage requirements and enhanceconvergence. However, doing so precludes the ability to model any bending.

2.7 Using Birth and Death Wisely

Realize that any sudden change in your structure's stiffness matrix is likely to causeconvergence problems. When activating or deactivating elements, try to spread the changesout over a number of substeps. (Use a small time step size if necessary to accomplish this.)Also be aware of possible singularities (such as sharp re-entrant corners) that might becreated as you activate or deactivate elements. Such singularities can cause convergenceproblems.

2.8 Read Your Output

Remember that the ANSYS program performs a nonlinear analysis as a series of linearapproximations with corrections. The program printout gives you continuous feedback on theprogress of these approximations and corrections. (Printout either appears directly on yourscreen, is captured on Jobname.OUT, or is written to some other file [/OUTPUT].) You canexamine some of this same information in POST1, using the PRITER command, or inPOST26, using the SOLU and PRVAR commands. You should make sure that youunderstand the iteration history of your analysis before you accept the results. In particular,don't dismiss any program error or warning statements without fully understanding theirmeaning. A typical nonlinear output listing is shown in Figure 8-22

.

Figure 8-22 Typical nonlinear output listing


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2.9 Graph the Load and Response History

This verification technique may be considered to be a graphical combination of two othertechniques: checking for reasonableness, and reviewing the iteration history. POST26graphs of load and response histories should agree with your informed expectations aboutyour structure's behavior. The results of interest (displacements, reaction forces, stresses,etc.) should show relatively smooth response histories. Any non-smoothness may indicatethat too coarse of a time step was used.

Related Content: Modeling Material Nonlinearities [1]

Nonlinear fracture mechanics for Engineers [2]

Using Geometric Nonlinearities [3]

What is Structural Nonlinearity? [4]

ANSYS Tutorial Structural engineering

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