15 Replies Latest reply on Apr 3, 2017 9:48 AM by John Willett

Example that Requires Nonlinear Capability with Linear Isotropic Material?

Ignorant question from Non-Engineer:  Can somebody give me an example of a simple simulation that cannot be done correctly with the Large-Displacement option in a Linear Static study even though it does not use a non-linear material?

I'm re-reading Paul Kurowski's excellent tutorial, "Engineering Analysis with Solidworks Simulation 20XX," and I have come across the following statement:  "All nonlinear problems presented in this chapter [so far, even the classic flat plate under pressure, which is stiffened under bending by tension] owe their nonlinearity to changes in geometry and contact taking place during the loading process.  They can be solved using a Static study with the Large displacement option selected.  Now we present a problem where nonlinear behavior is caused by nonlinear material.  This example requires Solidworks Simulation Premium..."

I have Solidworks Premium (linear static simulation only, including the large-displacement option).  All of my problems involve linear isotropic materials, and I want to better understand what kinds of problems I cannot solve without purchasing another license that I cannot afford.

Thanks for any guidance! -- John Willett

• Re: Example that Requires Nonlinear Capability with Linear Isotropic Material?

John, there's a LOT to know about simulation, how it works, how it doesn't work, etc.

Non-Euler buckling, such as buckling in short beams, linear analysis falls flat on it's face.  You wouldn't know that, though, because Sim Linear will just give you a pretty answer.  I'm assuming that if the same problem were analyzed in nonlinear, the results would be more accurately represented.  I haven't verified it, though.

Steel springs, be they coil, flat, etc, all need a nonlinear package to analyze.

Nonlinear is not referring to the material properties per say.  It uses an iterative process to apply a load, displace the model based on loads or other inputs, reapply the load and repeat as necessary.  The material does not necessarily need to reach the area of the curve where it exceeds the yield stress to need nonlinear analysis.  As mentioned above, a spring is a great example of this.  A properly used spring doesn't yield.  It does, though, require a nonlinear analysis if one was to want to deflect it much.

The other thing is that nonlinear doesn't necessarily mean that it will do right by nonlinear materials.  I have a buddy that's a bit of an elastomer guru working with silicon's and polyurethane day in and day out.  He won't use Simulation linear or nonlinear as it has steered him wrong in the past.

As I usually say, there's no substitute for a classical understanding of the mechanics of materials to verify what the computer is doing.  All of us get a little lazy and begin to trust the colors.  Also understanding how the software works, mesh issues and such, and how to deal with these know issues.  Understanding what you are looking for, Von Mises stress, or is there more important stresses to evaluate, such as in composites.  Understanding stress concentrations and if what you are seeing in the software is real or not.

Think about it, this software costs thousands of dollars and there really isn't a comprehensive manual on how to run it and what is happening behind the scenes with each selection you make.  I had to dig and dig to find old Cosmos white papers to give me some ideas on the topic.

In the end, though, always finalize your design with real-world testing, especially where safety is concerned.

http://machinedesign.com/news/nonlinear-fea-explained

• Re: Example that Requires Nonlinear Capability with Linear Isotropic Material?

Chris -- Thanks very much for your comprehensive answer and very interesting link.  Yes I realize I cannot blindly trust the software.  I have a physics and math background an a copy of Machinery's Handbook, and I have been making a valiant attempt to find test cases to validate problems "related" to those I'm trying to simulate.  And yes, springs are one of the next examples in the book, although Kurowski is initially talking about bringing in a yield strength and plastic deformation there.  I know that you need full non-linear to have the external forces (e.g., normal to a face) change direction with deformation, which would likely be an issue with a spring, but beyond that I don't yet know what the problem is -- will have to read more.

I have also read that nonlinear is required if the stiffness changes with deformation (in linear the stiffness matrix is apparently only evaluated once at the beginning of the study, not after every load step), but in the absence of nonlinear materials (and outside of "geometric" stiffness changes, like that of the flat plate under pressure mentioned in my OP, which are apparently handled well with the large-displacement flag in a linear static study -- when it runs at all), I'm not sure what kinds of situations would cause that.  This is the kind of fundamental engineering knowledge I'm digging for.

Frequency analysis, buckling, thermal, flow, and the rest think I can do without for the problems I expect to encounter, but of course I could be wrong... -- John Willett

• Re: Example that Requires Nonlinear Capability with Linear Isotropic Material?

The great part is that you are questioning all of this.

Most people just run the software.

As they promoted it one year at SolidWorks World using one of the dumbest guys they could find:  "Red Bad, Blue Good."

I view that attitude as an attack on our profession.  If that's the case, why did I go to college and take all the structural engineering courses?  I even took part of a graduate course that focused on FEA, how it worked, and how to write the code, but couldn't finish due to needing a elective to graduate.  So I had to drop a vital course to my career to take a joke of a philosophy class.  Still sore about that.

I spent months trying to get users manuals and white papers trying to explain what the software is doing for the Simulation product.  I'm apparently the only one who has ever wanted this, or at least it seemed that way!  Silly that a \$10,000 piece of software doesn't really have a users manual.  Especially one this critical, where most of the time it's used, human safety is often at stake.

I've got several thousand hours doing computer analysis work and am still trying to figure it out!

That's why I'm amazed at how almost everybody, with few exceptions, just runs the software without wanting to figure out what it is doing and it's weaknesses.  So good for you.

You've probably see under the SolidWorks Help menu: SOLIDWORKS Simulation->Validation there are two PDF's with some of the necessary background information on the software.  You might find some answers there.

• Re: Example that Requires Nonlinear Capability with Linear Isotropic Material?

>>You've probably see under the SolidWorks Help menu: SOLIDWORKS Simulation->Validation there are two PDF's with some of the necessary background information on the software.<<

I finally found this -- really dense! -- but here's something I was able to promote from my VAR that others might find of interest.  Now if I could just find a more complete description of the test problems (in English)... -- John Willett

• Re: Example that Requires Nonlinear Capability with Linear Isotropic Material?

>>You've probably see under the SolidWorks Help menu: SOLIDWORKS Simulation->Validation<<

Chris -- There are actually quite a few nonlinear examples here (many of those with linear isotropic materials) that I can solve with static large-displacement studies in Solidworks Premium and get the right answers!  This seems to confirm what Bill was telling me.  Thanks again for pointing me at these. -- John Willett

• Re: Example that Requires Nonlinear Capability with Linear Isotropic Material?

Hi John,

There are 3 types on non linearity, which you already know if you read Paul Kurowski's book. The following might provide some additional insight. They are:

1) contact or boundary non linearity - for most contact problems it is really stiff in one direction and zero (or very low) stiffness in the opposite direction. This is by far and away the most difficult NL to handle for almost all programs. Frequently, they are very low stiffness problems at the start and stiffen up as the loads are applied. Failure in the first step is a frequent error for this class of problem.

2) Geometric non-linearty: with small displacements (say less than 1/2 the strucutral depth), say for a flat plate simply supported all round and a normal load, the response is dominated by the bending stiffness and the problem is essentially linear. Once the deflections start to surpass the 1/2 the thickness (structural depth in this case) then the membrane or tensile response grows rapidly and then dominates the response - it gets a lot stiffer than what was the case under pure bending. The general rule of thumb is that any time a deflection grows to over half the structural depth in any direction a non linear response will emerge. This gets tricky when there is a sudden loss of stiffness such as when buckling occurs. I have had reasonable success with SWX Sim Premium as long as any contact conditions can be ignored. Don't take this as an endorsement - it certainly isn't the most robust code in this regard but understanding and some skills can take you a long way - further than one might think. You need to know when you are looking at junk though.

3) Material non-linearity: the stiffness of the material changes with strain. This is typically easier for most codes to handle but you need non linear material models that suit your problem. As Chris mentioned his friend that was modeling hyper elastics with SWX Sim and was unsatisfied. could be the limited hyper elastic models did not model his material very well or it also had contact that needed to be modeled. I have found SWX Sim to be very problematic in any NL analysis that involves contact and any other non-linearity. Most of these issues are self inflicted as they allow the user to set up the problem so it won't solve. Tet's are also not the best element choice for NL contact problems at least in my humble opinion.

On help files and manuals: In my experience at any rate, I find two things to be germane. 1) what the program is doing and 2) how to get the program to do it.  In my opinion SWX Sim is primarily focused on the later and it needs a lot more information in the former. It is also missing some really fundamental components such as robust couplings. they sort of have them in the remote load functions but getting the info out you want is a bit ambiguous in my opinion.

On Chris's remarks about not understanding structural mechanics before under taking FEA. Well, it is hard to argue that one. I would mention though that you can't learn how to ski powder unless you get in it. The same goes for FEA. However, you do need to have an appreciation that you need to be skeptical and you need to convince yourself that the answer indicated is reasonable. Further it should be considered approximate. Everything is approximate in FEA until you can convince yourself a lower uncertainty is warranted. Most of hte time the quality control aspects are provided by more experienced colleagues and corporate processes that prevent a bad analysis being relied upon when anything of significant value is at stake.

• Re: Example that Requires Nonlinear Capability with Linear Isotropic Material?

good points Bill on the contact issues.  Garbage in->Garbage out.

Often a lot of work is spent "tweaking" things to try to realistically mimic what's actually happening.  Because of the difficulty getting the software to do simple, real-world conditions sometimes shortcuts are taken.  And then often you'll run an analysis only to convince yourself that it's junk and have to start over.

FEA is basically a chain that can be broken or weak at any one of a number of links.  Each link requires special attention.

Guys like you, Bill, who's careers are focused on analysis, are the ones who should be keeping us in line!  There is a lot to this, and much of it is beyond what most people are capable of understanding in any significant way.  Consider that one can get a PhD in structural analysis and any of it's various disciplines.

• Re: Example that Requires Nonlinear Capability with Linear Isotropic Material?

>>There are 3 types on non linearity, which you already know if you read Paul Kurowski's book. The following might provide some additional insight. They are:

1) contact or boundary non linearity...

2) Geometric non-linearty...

3) Material non-linearity...<<

Bill -- Always very helpful to get a response from you!

If I understand you (and Kuroski) correctly, this is the answer I was looking for:  Since I'm ignoring material non-linearity (3) and I try to avoid contact conditions (1) -- other than bonded of course -- all that remains is geometric non-linearity (2) of the sort that you and Kuroski describe.  In that case, SW Premium (even with its dumbed down Large Displacement flag) should be able to handle what I'm throwing at it if the LD solution doesn't fail.  Right?

(An example of this would be the thread at Violation of Small-Angle Assumption?, where LD wouldn't run with the shell on the upper boundary, but when I substituted a Remote Displacement/Direct Transfer, it ran reasonably well.)

I never asked you how you obtained a copy of the COSMOS technical manual.  Is that still feasible? -- John Willett

• Re: Example that Requires Nonlinear Capability with Linear Isotropic Material?

Attached is a cosmos/M manual. I just found it on the internet. I am traveling now so I could not search my archive. Hope this helps.

Bill

• Re: Example that Requires Nonlinear Capability with Linear Isotropic Material?

Bill -- Outstanding!  Thanks again. -- John Willett

• Re: Example that Requires Nonlinear Capability with Linear Isotropic Material?

On your remarks about the large displacement solution in the linear static solve. Just preface these remarks with a caution that it may not be a generality but in my experience in using the linear static solution - when you get an answer - that is the solution completes - it tends to be a not bad estimate. The solution is just an automated force controlled solution NL solution that only outputs the last time step. You need to be careful when you look at animations as they may not depict the solution path but rather just an animation from the initial state to the final state with no regard for the solution path actually taken which in many cases might be critical in you knowing you hit what you were aiming at. Given your self admitted lack of back ground don't go making any big bets with life, limb or property without a good risk reduction program on what you are considering.

• Re: Example that Requires Nonlinear Capability with Linear Isotropic Material?

The large displacement solution is a non-linear solution that accounts only for geometry changes.

One obvious and common example of a non-linear solution where this would not be enough would be material yielding. The core assumption of the linear model is that F = Kx, where F = the applied force vector, K is the stiffness matrix and x is the deformation vector. K is related to the geometry and the slope of the stress strain curve. But the slope of the stress strain curve changes dramatically beyond yield and this would be ignored by the large deformation solution. This causes a non-conservative error--the elastic assumption stiffer than the plastic reality. Consequently, you cannot trust linear solutions where yielding takes place through about (makes up a number) 5% of any given section.

• Re: Example that Requires Nonlinear Capability with Linear Isotropic Material?

This stuff is foundational to the understanding of FEA and fascinating at that.  How is it that the college professors make it so dull?

I did have a materials professor that was a blast.  He gave extra credit for bringing in broken parts, such as broken axles, for the class to see and analyze the failure mode.  Having a '69 Bronco and living near Pismo Dunes during college, I got lots of extra credit!

• Re: Example that Requires Nonlinear Capability with Linear Isotropic Material?

To answer your question specifically: "an example of a simple simulation that cannot be done correctly with the Large-Displacement option in a Linear Static study even though it does not use a non-linear material"

In theory if you are using a linear material model with Large Displacement, there should be little difference in the types of problems you can solve. Practically though, there are many differences.

With Linear Static, Large Displacement there is no way to sequence loadings/events. So any studies with multiple steps/events are not possible. Static Large Displacement also stores only the final result. Nonlinear stores full results through the whole solution. Sometimes this is necessary to achieve the desired output such as a Force vs. Response curve or capturing peak stress which may be partway through solution

Another case would be if a normal load/pressure needs to update direction change with the deformation. This is an option that is available in Nonlinear but not in Linear Static.

The biggest practical limitation of the Linear Static, Large Displacement though is in the event the solution fails to converge, in which case there really are very little tools to aid convergence of the solution. While in Nonlinear there is more advanced control over the timestep, internal solver settings, as well as alternate control methods such as Displacement and Arc Length control to help get past instabilities. So you should be able to analyze more complex problems in Nonlinear, although it still has its limits.

It's also common to use 2D Simplification method for some types of problems in Nonlinear, that may be another thing you would be missing out on depending on your current level of simulation.