Preventing RBM when contact is the only restraint

[smyth13]

I am looking to prevent rigid body motion in a contact analysis problem where the contact is the only restraint against an applied load. This is a generic question concerning general procedures used by members of this forum, although I also have a specific example I am concerned with.
I am concerned with a tablet punch being forced into a die at an offset angle causing the punch to bind. From the FEM I am attempting to retrieve the subsequent contact forces so that they can be related to a maximum allowable friction coefficient to prevent binding (for a given offset angle). In addition I am attempting to match this contact force with my FBD calculations. Please see the attached JPEG of the analysis (this is a 2D analysis but I also have a 3D). Thanks for your help.

 

[Elabbasi]

It is tricky to have contact as the only restraint against rigid body motion. If contact is not active at any iteration (whether at the beginning or during solution) the displacement will be very high leading to divergence. Even if contact is active, if is enforced using pure Lagrange Multipliers the model will still be positive semi-definite and there is no guarantee that a direct or iterative solver can handle it. It is even a little more tricky if friction (rather than normal contact) provides the only restraint against rigid body motion, and that is clearly the case in your model.

In dynamic analysis there is no such instability because there are no singularities due to rigid body modes. Damping has the same effect. Switching to dynamic analysis introduces many other problems however. So, most commercial FEA codes (including Ansys that you are using) have developed techniques that borrow from dynamic/damped analysis to help "stabilize" a static problem and make it easier to solve. You should try static analysis with this automatic stabilization. Make sure the stabilization energy remains small compared to the total strain energy in the model, otherwise your result will be overshadowed with this artificial stabilization.

Note that this will only help you when contact and friction are enough to eliminate rigid body modes. When contact is lost, or when friction state is all sliding then stabilization can't help you anymore.

I hope you find this helpful.

Nagi Elabbasi
Veryst Engineering

 

[ESPcomposites]

Perhaps I am missing something, but I would generally add some "soft" springs that are grounded at one end and connected to the part that could have RBM. You would need to add a few to prevent RBM in all 6 DOF.

Just check the spring forces and make sure they do not pick up significant load. This has the effect of holding the part in a similar way as a series of bungee cords would. It will prevent RBM, but not affect the physics of the model.

Brian

http://www.espcomposites.com

 

[crisb]

It's common practice to use weak springs to resist rigid body movement. I find that using a realistic coefficient of friction at contact faces, rather than zero friction much improves the situation, sometimes to the extent that the springs are not needed. If there is any symmetry in the model then appropriate fixities can be placed on the symmetry plane without affecting results.

 

[smyth13]

Thanks for the replies. I have used "weak" springs to prevent the RBM (and checked their reactions) and I always try to take advantage of symmetry if possible. In addition I have been altering the frictional coefficient from 0 to infinity to determine how this changes the contact forces (and how it affects convergence).

The main reason for my posting was to try and get a general idea of what others would do in a similar situation. I wanted to make sure I wasn't missing some simple point or method. For some reason adding the "weak" springs bothers me!

 

[crisb]

Thankyou for an excellent post. I share your dislike of the weak springs, when it feels like an "exact" solution should be possible where there is friction and binding (i.e. no theoretical rigid body movement). Sometimes prescribed displacement instead of force helps. Small first time step, line searches, large number of iterations are also things I find help at times. I tried once to solve a problem with the springs, and then apply birth/death to the spring elements to solve without them, but cant remember the outcome!

 

[ESPcomposites]

There is nothing wrong with adding soft springs. Provided you check the reaction forces and they are small enough to not affect your model, then it is a good method.

Even if the model was "perfectly" balanced and it theoretically did not need the springs, that is not what your FEM is necessarily solving. Your FEM is solving a system of equations, where the discretized geometry is not exact, there is numerical roundoff, etc. So the FEM sees these small imbalances as an ill conditioned matrix (i.e. RBM). The FEM is a mathematical model, whereas your actual installation exists in reality. So treat it as a math model (and not reality) and you will be fine.


Brian

http://www.espcomposites.com

 

[Elabbasi]

You can think of automatic stabilization as distributed weak dashpots with variable coefficients adjusted during analysis, and with additional output that help the user assess their influence on the solution.

If the stabilization algorithm used by the FEA code is good, these dashpots, when needed, would be active but have minimal effect on the solution, and would die out when not needed. Users generally prefer them more than concentrated springs due to the reasons mentioned in the above posts.

If you have to use force loading in a static analysis where contact/friction is the only restraint against rigid body motion, and there are insufficient symmetries, stabilization becomes a very useful tool.

Nagi Elabbasi
Veryst Engineering

 

[ESPcomposites]

Not all users prefer "advanced" approaches, especially when a proven and simple approach exists. "Advanced" can sometimes be translated into "hard to verify by a third party", "if the code works right", "over engineering", "high learning curve", etc.

It will be up to you to decide which approach you want to take with your problem. Do you want to put on your scientist hat or your engineer hat? That may be the better question.

Brian

http://www.espcomposites.com

 

[smyth13]

Thank you all for the very informative responses. I appreciate the different approaches taken and will certainly be cognizant that there are multiple approaches to achieve the (presumably) identical result.

I am most definetly in favor of new technologies and more advanced methodologies that enable the user to achieve a solution, whereas my comment concerning the use of "weak" springs, etc. was meant more to say that if possible I would prefer to obtain my solution without their assistance.

Obviously you need a theoretically feasible problem with the appropraite BCs, etc. and that will always be the most important component of any FEA solution. I sometimes just fear that the technology (any technology really) sometimes encourages my own laziness!

 

[ESPcomposites]

Getting a bit off topic...but talking about simple versus advanced:

Simple:
-Proven
-May have some undesirable effects. It is up to the user to determine if the result is satisfactory.
-Easily translated to other platforms (different software).
-Easily checked by your lead or other party (i.e. FAA, etc.)

Advanced:
-Learning curve
-May yield a better solution. The question is if the value is there.
-May be specific to your software. Not a problem if you only intend to use one software the rest of your life, but limits your flexibility and preparedness if you plan on using other software.
-You will usually have to make a few sample test runs to prove to yourself the technique works as anticipated.
-If you need to prove your results to someone, you may have to create extra documentation. You may also have to convince someone that you are doing it properly, adding burden to yourself and the other party.

These are some of the trades you can consider. Early in my career, I used to adopt advanced methods with vigor. But in time, I have gone more towards the KISS approach, and concentrated my efforts on the engineering (and not messing around with the latest FEM element,etc.). I would also prefer to spend the extra time enhancing my skills in classical engineering. But this is a personal decision and the type of work you are doing will certainly affect your choice. I tend to use ABAQUS, Nastran, etc. and don't want to spend a lot of time learning very specific solutions, especially when I know I can get the job done accurately and quickly without it. I also work in an environment where FAA certification is a consideration. Under these scenarios, you will find most users prefer simpler techniques, provided you can achieve an acceptable engineering solution. When I worked on space applications, advanced FEM techniques seemed to be a little more encouraged though. If you are trying to demonstrate to a client your capabilities, then maybe you want to do more than what is necessary.

In these cases, ask yourself this. Are you are spending a lot of time learning how to use FEM techniques that may not add real value? If so, then you are subtracting efforts towards the actual engineering and/or moving on to the next problem.

Brian

http://www.espcomposites.com

 

[Elabbasi]

A little off topic, but an interesting discussion Brian. I agree with most of what you mentioned when comparing simple vs. advanced.

Just like you, my bias is affected by my experience. Before my current consulting position, I worked in a finite element development company. The users really push for features like stabilization and other similar “advanced” features because these features reduce their modeling effort. In the case of stabilization, they don’t want to figure out where to put the weak springs, what stiffness to use and when to kill/remove them (or even worse some can’t figure out). Many users just want to click on one checkbox and let the FE codes take care of the rest. The problem with that approach in general is that they forget to check the effect of that click on the solution, even though most FE software provide the necessary tools for that. In the end, whether simple or advanced modeling is used, there is no replacement for good engineering. Advanced modeling tools in the hands of knowledgeable engineers/analysts are generally a good thing!

I’ll get a little off topic here, and bring up something else. I don’t really like to call such features “advanced” because they don’t result in more accurate analyses. My perception of advanced in FEA is something (could be element, contact formulation or material model, for example) that is more accurate than its predecessors, more reliable, significantly faster, or solves a problem that could not previously have been solved with FEA.

Nagi Elabbasi
Veryst Engineering

 

[ESPcomposites]

Nagi, thanks for your perspective. I suppose "advanced" can mean many things. I was referring to it as something that is software specific as opposed to something easily incorporated in all FEM software.

Sorry to get so far off topic!

Brian

http://www.espcomposites.com

 

[smyth13]

Very interesting insight into this topic, even if it may have strayed from my original post. Advanced features that appear across the spectrum of FEA codes, in my opinion, are universally a positive advancement. There is no code specific knowledge and any method learned could be easily applied to a different code. I am all for FEA codes increasing the ease of use so that an engineer can spend more time working on the problem at hand as opposed to implementing the problem into the FEA code.

Although I only have a few years of FEA experience, I wish that more codes would "force" the user to review the validity of the results obtained (equilibrium, weak spring reactions, etc.). I know all of these features are included, but sometimes I feel that they should be displayed more prominently (typically you use what is readily visible). It is definetly an irritant to myself when I have to dig around to find the exact results I am looking for. Sorry if I represent the impatience of my generation!