2D vs 3D FEA... 4

[mizzjoey]

Hi everyone..

I just got back from a meeting and there's something discussed in the meeting that I can't resolve. It should be simple but...

Anyway, a colleague was presenting the difference between running a simple cantilever beam deflection using a 2D planar (simplified) and using 3D model. Now, we all know that simplifying a 3D model that has some form of symmetry in 2D can reduce the run time, cost, etc, but when the colleague presented the output of the two different simulations he gave the following unit translations that I do not understand.

For 2D:
Length - mm
RF - N/mm
Stress - N/mm2
Pressure - MPa

For 3D:
Length - mm
RF - N
Stress - N/mm2
Pressure - MPa

What had me confused was the difference of reaction force unit between 2D and 3D. Why shouldn't it be the same for both 2D and 3D? If stress is F/A, and F is really N/mm2 in 2D... then won't it translate to stress being (N/mm)/mm2 for 3D? (My understanding is that the units would all be the same)

I raised my hand to ask and a senior explained that its because the 2D planar model has no thickness and the beam in the model actually has a thickness of 10mm. I still can't reconcile this with the fact that force unit translates differently but stress unit stays the same... I'm just a junior engineer and I'm confused... can anyone explain?

thanks in advance,
jo

 

[GBor]

Your "senior" explained correctly, depending on what type of 2D analysis he was running and what software was being used. If you recall from your various theories, 2D has options for plane stress, plane strain, and axisymmetric and each of these has unique characterics, but for a beam, I'm assuming whoever was doing the analysis was using plane strain.

With a 2D plane strain model, softwares generally assume a unit depth in an infinitely thick plate. Because of this, loads and reaction data are "per unit thickness of 'infinite' plate". As for the units, you still input a force, but it is also per unit thickness and your results generally report standard force units, but because your model assumes a unit thickness, the results must be interpreted as "per unit thickness".

Stress results are already appropriate because they are area-based (per mm^2).

Not sure this is very clear, but hope it helps.

 

[rb1957]

as GBor says the units can be code dependent. however, the final answer has to be N (as we're talking about forces). before the final answer the code can do it's own thing.

example, NASTRAN forece output is force (N) for rods, but running load (N/mm) for shells. there are good reasons for this, but that is another story.

bottom line, from what you presented, the 3D model is outputing directly reaction forces (in N), but the 2D model is providing an intermediate answer (N/mm), and you need to know what length dimension to apply to get the true reaction force (in N).

you are very confused ... stress/pressure is N/mm2 ... always. Force is always N. 2D elements do have thickness (it's on the propert card), it's not expressly modelled like it is in 3D elements, but it is there.

 

[corus]

It also depends on the software. Some will ask for input forces in N/mm thickness and some the total force (similarly for the reaction force output). For a relatively thin beam I'd use plane stress for a given thickness and not plane strain (for infinitely thick) which is usually expressed in force per unit thickness and therfore is numerically the same as the total force anyway. As has been said, the stress is always expressed in the correct units of force/area regardless of the method used.

corus

 

[mizzjoey]

Thanks everyone for your reply!

rb1957 is right..I AM confused. I thought stress is always F/A = N/mm2 too (or MPa etc), and load is always N. Which is why it stumped me yesterday evening. But the way you guys explain it make sense to me now. We use mainly use Abaqus over here, and yesterday we were discussing plane strain models. My area has always been axisymmetric stuff. My colleague was probably talking about what happens while the software 'does its thing'.

Any good books you can point me to so I can understand FEA better? I'm currently working through Schaum's Outlines FEA. I was never exposed to FEA back in uni and had to learn on the job. But I really like what I do now; just want to understand the theory better.. though when I ask questions I usually get cut off at meetings by my impatient boss.

thanks a lot!
jo

 

[rb1957]

welcome to the real world ... i think they're a hard slog, but worth it, try Ribbie Robertson's books, sorry don't have a title. i think your approach, trying to learn the material rather than the application. from that light, Bruhn has a chapter on the FE method, real old school matrix math, but it explains the fundamental foundation quite well.

i agree with your boss, that meetings aren't the time to learn stuff (i'm assuming your questions are about the very basic methodology ones rather than appropriate to the solution). get some time with the gurus (or maybe the lesser-gurus who can talk and think at the same time !!), maybe take a course at a local college or something.

keep grounded ... as long as you remember stress is stress and load is load you won't go too wrong !

"axi-symmetric" = solid rocket fuel ??

 

[prost]

rb1957--who is Ribbie Robertson? The only Ribbie Robertson I have found on the Net is a musician for Dylan and The Band (even then, I am not familiar enough with Dylan and the Band to know for certain the name is properly spelled).

Did you by chance misspell this person's name?

 

[rb1957]

nah, i did ... should've been "robbie" ... probably "robert" as an author ...

actually since i've just been on amazon it's john robertson "understanding finite element stress analysis"

memory ain't what it was ...

 

[prost]

John Robinson? Is this the book?

http://www.biblio.com/details.php?dcx=120395046&aid=frg

 

[rb1957]

yepper

 

[prost]

What do you like about the book compared to say, Zienkiewicz's or Bathe's book?

 

[rb1957]

he taught a class at work, so i got to know the guy behind the book. your refs are just as good too.

 

[bEakerPPK]

Bathe, Reddy and Cooke are all fantastic for getting a fundamental understanding of the theory. Bathe is the top of my list (one of the best treatments of iso-parametric formulation I have ever seen.) Zienkiewicz is also great but somewhat demanding upon the reader.

An excellent primer is Logan's book as well. It is not as in-depth and old-school as the aforementioned but is a great resource to get you started. Some of the older books are a little snobby and not very forgiving when it comes to a beginner but their value is simply unquestionable.

There is also a great text written by Carlos A. Fellipa that you can get for free at the University of Colorado website. It is written in a course format (pdf of the text, including slides used in the classroom) that will take you from basic linear FEM all the way through to non-linear analysis. Not small though, we're talking about 1000 or so pages here.

Glad to hear you'd like to understand the fundamentals. Too many people just blindly apply the method to produce pretty contour plots and don't have the faintest idea what they have done; let alone lucidly interpret the results. FEM is never really wrong but we often ask it the wrong question. The onus is on you, the analyst, not the code.

A detailed look at these references and your days of confusion will be behind you. Good luck.

 

[rb1957]

is this the material you were referring to ? ... "Introduction to Finite Element Methods (ASEN 5007) - Fall 2007"

 

[bEakerPPK]

Indeed it is, but not in the same form as I recall it. As I was pulling this from memory, it seems that the non-linear material is not available in a straight up Google search anymore. It was in 2006 when I was looking for some reference material for an undergraduate course I was teaching. I imagine it is still there but you may have to do something equivalent to a

site:.edu intitle:"index.of" (pdf) title.of.document

style google search to find what you are looking for. Not sure since I haven't checked it out myself yet but I'm sure it will turn up something.

In general, you can search .edu sites for fantastic reference material suited for learning at an appropriate pace, complete with examples and often some working code that can be used to develop and understand simple examples. I know for a fact that MIT posts all of their lecture material for free. This is just the kind of resource I'd have loved about ten years ago.

My opinion is that one will never truly understand FE unless they have sat down and sweated through the development of at least a simple 1-D code themselves; it minimizes the whole "black box" mentality commonly associated to powerful software tools...but that's just what I think....

 

[bEakerPPK]

I found the links I mentioned, turns out fancy footwork was not required:

Linear FEM:

http://www.colorado.edu/engineering/CAS/courses.d/IFEM.d/Home.html

Advanced FEM:

http://www.colorado.edu/engineering/CAS/courses.d/AFEM.d/Home.html

Non-Linear FEM:

http://www.colorado.edu/engineering/CAS/courses.d/NFEM.d/Home.html

While this is not a replacement for the references mentioned before (I think I'm required to say that) and certainly won't get one from zero to hero (only time and patience can do that), it is definitely worthwhile checking it out, whether you are a beginner (mizzjoey) or simply interested (rb1957). I found it to be a good read, presented in a manner not reeking of pretentiousness or solipsism.

Regards.

 

[mizzjoey]

Great links, beaker! They are now added to my list of favorites. A star for you! I'll try to find the book by John Robinson; but knowing how poorly-stocked the bookstores in my country are I have practically zero chance at obtaining it.

rb1957, axisymmetric as in shaft seals and the like. My background is materials engineering, so I always try to understand a problem in terms of forces acting in the body as opposed to a computational approach.

thanks everyone! great help!

 

[prost]

Back to the poster's original question: The most important FE reference here is not mentioned: the user's manual for the particular software, which will tell you all kinds of information about conventions--some FE software makes you input tractions in units Force/Length, and hence outputs stresses as Force/Length rather than Force/Length^2, which is the true stress dimension. I sometimes encounter Force/Length for stress units when I am dealing with Axisymmetric problems.

Other software wants you to input Force/Length^2 as the traction units. Usually FE software is consistent in this regard, not requiring Force/Length and spitting out Force/Length^2. "RTFM" is still good advice here.