Non-Linear Non-Convergence Troubleshooting

[Anonymous]

Hi all,

I have a complex model which I'm trying to run in a non-linear analysis, but am having convergence problems. (This is an updated version of the same large model I sent a few months ago with different queries - still in Robot 2010 I'm afraid.)

At the moment I get realistic looking results up to about 15% of the ULS loads before non-convergent iterations, although the greater the number of load increments generally the worse this is. For example if I use 10,000 load increments I can only get to 1.4% loading before non-convergence.

The Newton-Raphson analysis has given the best convergence, as expected, and I have tried various permutations of tolerance for residual forces/displacements but these don't help much. Here's a screenshot of some sample settings:

If I delete all of the releases from the model I can get it up to around 60% ULS load before non-convergence (with the settings in the screenshot above), and it wouldn't surprise me if the problems were related to instabilities in the analysis model due to the way elements like stiff links have been modelled. I've run a linear buckling analysis on the load combination in question, and with and without releases and the lowest mode has a critical factor of 7 in the model without releases.

Any general advice would be welcome!

I also have two specific questions:

1. Can anyone explain what the "Relative code tolerance for residual forces" (and displacements) is? I'm familiar with the concept of residual force tolerance from other software, but this seems to be more complex than the absolute maximum residual force value at any node that I've seen before.
2. Does Robot provide any further information to troubleshoot non-convergence? Again previous software I've used provides details of which particular node numbers were giving the critical residual force at each stage of iteration, so the user can find see which area of the structure is unstable.

Thanks!

Rory

[Rafal.Gaweda]

Tolerance for residual forces 0.1 - far too much - you might have wrongly converged results.
Please send us the file

[t.sautierr]

For the parameters try this : tick matrix update after each subdivision -> this will active FULL Newton Raphson -> more chance to converge.

Otherwise, post your model.

[t.sautierr]

Oups, file 🙂 attached now.

By the way, don't go to far with the tolerance, as far as I know 0.001 is a minimum.

[Anonymous]

Thanks guys - I've ticked the matrix update after each subdivision, and reduced the tolerance. Setting the tolerance to the Robot default 0.0001 seems no good as the convergence kept getting down below 0.001 on the first iteration, then bounced back upwards and diverged, even as the increment sizes were reduced. Setting it to 0.001 was better but still couldn't apply much load.

Typical lack of convergence from model with releases:

And without releases:

Can you explain what these relative tolerance numbers actually mean?

I'd prefer to keep the model private, can you give me an email address to send it to? It's 5 Mb zipped without results.

[Rafal.Gaweda]

http://forums.autodesk.com/t5/Robot-Structural-Analysis/Sending-bigger-files/td-p/3795062
and use Private Message

[Artur.Kosakowski]

Try to run this combination as the (second order) non linear analysis (with no P-Delta which in Robot is responsible for the 3rd order effects) and with the multi-threaded solver.

If you find your post answered press the Accept as Solution button please. This will help other users to find solutions much faster. Thank you.

[Anonymous]

Artur,

Thanks for this, I've deselected P-Delta analysis convergence is much better, but can only get up to 50% of the ULS load. Are you saying this worked for the model that I sent you?

I've run this in Robot 2014 so I can use the multi-threaded solver (although this is no quicker than the Sparse Direct Solver for the non-linear analysis in a side-by-side comparison with Robot 2010), here's a sample lack of convergence:

On the plus side Robot 2014 seems to be telling me which nodes have a low stiffness at each iteration (because they're causing type 3 instability warnings), so I will try some troubleshooting when I have time.

But is non-linear analysis without P-Delta correct?

The Robot help states:

• Non-linear analysis - takes account of the second-order effects, such as the change of bending rigidity depending on the longitudinal forces
• P-delta analysis - takes account of the third-order effects, such as the additional lateral rigidity and stresses resulting from deformation.

I want to carry out a geometrically non-linear analysis (often described as P-Delta analysis), where the effect of large structural deformations is taken into account through iterative analysis, with the analysis at each iteration based on the deflected geometry of the structure rather than the initial un-deflected position. That doesn't seem to match either of these descriptions!

What are third order effects? I have read other posts on this forum and am none the wiser. I've also Googled third-order structural analysis and the only relevant results I get are on your Robot forums, so I don't think this is industry standard terminology!

I also do not want any material non-linearity effects taken into account - everything should behave fully elastically.

Which option do I want?

Thanks,

Rory

[Pawel.Pulak]

Rory,

the main property related to the 3rd order effects is discussed in messages 1and 2 or this forum post:

http://forums.autodesk.com/t5/Robot-Structural-Analysis/Non-linear-analysis-P-delta-analysis/m-p/364...

Moreover the message 2 of above post redirects to the post discussing misleading names of analysis used in Robot:

http://forums.augi.com/showthread.php?141487-Assorted-queries-non-linear-analysis-for-part-braced-fr...

Regards,

[Anonymous]

Yes I've just run a model and have replicated the effect of a beam with axially restrained ends picking up catenary tension forces with "P-Delta" analysis but not with "non-linear" analysis. From the "P-Delta" analysis:

However this tension force is a simple effect that would be picked up by any geometrically non-linear analysis. For example if you take the deflected shape of the beam after a linear analysis, then use that as the initial shape for a further linear analysis with the same loading, it would start to pick up tension forces. "Non-linear" is clearly not carrying out a full geometrically non-linear analysis.

In fact your two links above give completely conflicting information. In the first one it says "non-linear" is what would usually be described as second-order or P-Delta analysis (geometrical non-linearity), but in the second Pawel is saying that "non-linear" analysis only covers material non-linearity (tension only bracing) while "P-Delta" analysis is required for geometrical non-linearity.

Please clarify.

[Pawel.Pulak]

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@Anonymous wrote:

Yes I've just run a model and have replicated the effect of a beam with axially restrained ends picking up catenary tension forces with "P-Delta" analysis but not with "non-linear" analysis. From the "P-Delta" analysis:

However this tension force is a simple effect that would be picked up by any geometrically non-linear analysis. For example if you take the deflected shape of the beam after a linear analysis, then use that as the initial shape for a further linear analysis with the same loading, it would start to pick up tension forces. "Non-linear" is clearly not carrying out a full geometrically non-linear analysis. 

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Such effects are not considered by "any geometrically non-linear analysis", considering some more advenced effects is necessary. For instance one sentence earlier you have noticed yourself that they are not considered when only "non-linear" analysis check-box is active in Robot.

As concerns obtaining tension forces when updating the shape of the beam to the deflected one after a linear analysis it will surely not finish with a single iteration of the first assumed deflected shape. It will be necessary to find the deflected shape corresponding to the equilibrium between the applied loads and the internal forces in the beam resulting from its elongation caused by deflection. 

Making such "manual iterations" would be much more difficult than to run the automatic iteration process when "Non-linear analysis" and "P-delta analysis" are activated in Robot.

As concerns ""Non-linear" is clearly not carrying out a full geometrically non-linear analysis." - yes, it is true, as I have written in my post on the AUGI forum (message #4) it considers only the 2nd order effects. To consider the 3rd order effects it is necessary to tick "P-delta analysis". And even in such case big rotations are not fully considered so it is not "a full geometrically non-linear analysis."

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@Anonymous wrote:

In fact your two links above give completely conflicting information. In the first one it says "non-linear" is what would usually be described as second-order or P-Delta analysis (geometrical non-linearity), but in the second Pawel is saying that "non-linear" analysis only covers material non-linearity (tension only bracing) while "P-Delta" analysis is required for geometrical non-linearity.

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Where in the second link have you found the information that ""non-linear" analysis only covers material non-linearity (tension only bracing) while "P-Delta" analysis is required for geometrical non-linearity"?
In the message #4 of the second link (AUGI forum) I have written: "to account for geometrical non-linearity in a structure with tension-only elements it is necessary to tick 'non-linear' box (2nd order effects) or 'non-linear' and 'P delta' boxes (2nd and 3rd order effects)."

And in the message #2, it the answer to point 1.b) I have confirmed that nonlinear analysis reported for structure containing tension-only members is caused only by nonlinear properties of these members.

Your misunderstanding may be related to some ambiguity of Robot as concerns nonlinear settings - in Analysis Type window in is difficult to distinguish non-linearity resulting from non-linear objects (like tension-only members), geometrical non-linear effects and both together. See the screen capture below:

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If this post answers your question please click the "Accept as Solution" button. It will help everyone to find answer more quickly!

Best regards,

[Anonymous]

Thanks Pawel. I agree there are clearly a lot of misunderstandings here - and I'm not surprised because you still haven't actualy said what Robot is doing in a "non-linear" analysis or a "P-Delta" analysis. Please can you just explain once and for all what each of the analyses are? What analysis is Robot doing in each of them? What effects are included in each and how does Robot take account of them?

I still have no idea, except that in my test model the only "P-Delta" analysis carried out what I would describe as geometrically non-linear (also called second-order or P-Delta) analysis. The "non-linear" analysis gave the same results as a linear analysis. I have never heard of third-order analysis before so you will have to explain that too.

On the AUGI forum the question is:

"b) I have a frame which is part tension braced (cross bracing in elevation), but also acts as a part sway frame at higher levels. Obviously I am getting the default switch to non linear analysis (due to the tension members), but does this also automatically account for the geometric non-linearity due to the sway deflection?" 

And the response is:

"ad 1.b)
No, it is considering only the non-linear behavior of tension-only bracings. Higher order geometrical non-linear effects are not taken into account is such case (if "Non-linear" and "P-delta" check-boxes are not active in any load case)"

So you are saying "non-linear" and "P-Delta" check boxes are required in order to account for geometrical non-linearity due to a sway deflection. The "non-linear" analysis only allows analysis of tension-only bracing, which is a material non-linearity. I may have misinterpreted what you meant though, because you're right that you say later on that geometric non-linearity can be achived with either "non-linear" or both "non-linear" and "P-Delta" ticked.

The trouble is that what you go on to describe as second-order and third-order effects are BOTH what I would describe as standard second-order/P-Delta/geometrically non-linear effects.

[t.sautierr]

Pawel wrote : 

"And even in such case big rotations are not fully considered so it is not "a full geometrically non-linear analysis."

Can you detail a bit more where is the limitation and give an example of such effect that Robot can miss enven with 2 and 3rd order effect activated.

Thx

[Artur.Kosakowski]

As wrote: when you get large rotations of nodes e.g. a cantilever that you want to bend into a coil :-).

[t.sautierr]

🙂 ........ "large" do you have let say a ratio of what is large?

[Artur.Kosakowski]

Till the point the analysis stops to converge 

I can't tell what the limit angle is.

[Tuctas]

rushthedj, It will help if you take a look at an older post related to this issue (especially see the attached picture of he 9th post of the link below)
http://forums.autodesk.com/t5/Robot-Structural-Analysis/Geometric-non-linear-analysis/m-p/4434687#M1...

[Anonymous]

Ahh, thanks. I think I might be starting to piece together what's going on - by "stress stiffening" effect in the "non-linear" analysis type, is that actually referring to a geometrically linear analysis with the stiffness matrix adjusted to take account of "geometric stiffness"? (See here for a good description of this for the avoidance of doubt: www.csiamerica.com/system/files/technical-papers/11.pdf)

Cheers, Rory

[Tuctas]

Yes, "stress stiffening effects" is the same thing with taking into account of "geometric stiffness" ("stress stiffening effects" is not only Robot's term,it is generally used). Nice paper that you attached (but who is the author?). You can also read for this subject in a book-reference (among others) in Structural Dynamics: "Dynamics of Structures" by Ray W. Clough and Joseph Penzien

[Anonymous]

Thanks, I think that might explain it. I hadn't heard the term "stress stiffening" to describe this before (it was always called "geometric stiffness" when I was studying it) but both seem to be widely used (and "stress stiffening" describes the effect better I think).

So let me try and re-write the descriptions of the two analyses:

• Non-linear - Linear analysis with stiffness matrix adjusted for stress stiffening (aka. geometric stiffening) effects. Material non-linearity taken into account.
• P-Delta - Geometrically non-linear (aka. P-Delta) analysis. Material non-linearity taken into account.

"Non-linear" approximates second-order effects, while "P-Delta" rigorously calculates them through iteration.

Is that correct? I'm don't think it is because the solution to the "non-linear" analysis is an iterative procedure in Robot, which I assume it would not need to be for a linear analysis with stress stiffening effects?

I don't understand why someone from Autodesk won't just clearly explain what Robot is doing during each analysis type. This guesswork is a real waste of time and I'm getting no closer to running my model successfully.