Min. angle for axisymmetric with bricks
Min. angle for axisymmetric with bricks
(OP)
Hallo
Using 3D tetrahedral elements, with what minimum wedge or sector (included) angle would you, generally speaking, still feel comfortable to analyse an axisymmetric problem? 15°? I realise it depends..., and might vary; but surely there must be some rule of thumb to generally deliver robust results (almost code-like).
I still very much prefer using proper axisymmetric elements (especially for non-linear) but most "designer" packages does not offer it, and at the same time computing capabilities also got better.
Thanks
Regards
Using 3D tetrahedral elements, with what minimum wedge or sector (included) angle would you, generally speaking, still feel comfortable to analyse an axisymmetric problem? 15°? I realise it depends..., and might vary; but surely there must be some rule of thumb to generally deliver robust results (almost code-like).
I still very much prefer using proper axisymmetric elements (especially for non-linear) but most "designer" packages does not offer it, and at the same time computing capabilities also got better.
Thanks
Regards





RE: Min. angle for axisymmetric with bricks
RE: Min. angle for axisymmetric with bricks
I guess when modelling a very narrow wedge there should theoretically be no real limitation but one could start running into numerical errors.
RE: Min. angle for axisymmetric with bricks
Well, if available I would export your geometry to a full-time FEA system for analysis and use eight node quadrilateral axisymmetric elements.
Otherwise if you have only got the 3D mesh solution of the CAD system then it is imperative that you increase mesh density in areas of high stress until the problem converges (that is an increase in mesh density has little or no effect on results). You will always get some poor shaped tetrahedral elements with any mesher, but with a relatively fine mesh their effect on the average stress is minimal, so don't concern yourself too much with element quality if you have satisfied yourself that you have achieved a mesh convergence.
RE: Min. angle for axisymmetric with bricks
Thanks for your comments.
RE: Min. angle for axisymmetric with bricks
RE: Min. angle for axisymmetric with bricks
I'm happy with the flexibility and properness of my available boundary conditions/restraints.
RE: Min. angle for axisymmetric with bricks
RE: Min. angle for axisymmetric with bricks
GBor was referring to the boundary conditions available with a FEA module of a CAD product, which can be very limiting.
RE: Min. angle for axisymmetric with bricks
RE: Min. angle for axisymmetric with bricks
I was afraid this thread could easily get over-elaborated; that is why I have chosen my words carefully (from there my words like: generally, depends, robust, code, etc.). Knowing it depends on various factors I was simply hoping to get in some "good practice" estimates of the angle to be modelled. Thanks for your number, Johnhors.
We are using Cosmos DStar.
Regards
RE: Min. angle for axisymmetric with bricks
corus
RE: Min. angle for axisymmetric with bricks
I would think that the basic limit would also depend on what sort of machine you are running it on. Machine Epsilon will limit how small of a number the software can deal with. If you divide Machine Epsilon by 2 the answer is ZERO. Same sort of thing with large numbers. Similarly most computational answers are approximations, but accuracy to 20 or 30 significant digits is generally close enough for most of us. ;)
When you start generating very small numbers that are pushing the limits of Machine Epsilon most of the significant digits in your calculations are zeros. So if you get down to where only the last two digits are non-zero and you assume that the last digit is not rounded off you have a potential for about a 9% error.
As an example, using MS-Excel (32bit);
2.5E-308/2 = 0 rather than 1.25E-308
or
SIN(1/(4*10^307))= 2.5E-308
but
SIN(1/(5*10^307) = 0 rather than 2.0E-308
I'm certain that a true numerical math geek could explain it much more accurately but hopefully I didn't corrupt my explanation too badly.
It would be worth running a few test models just for giggles and see what you get. I suspect that a 32-bit machine will not do as well as a 64-bit unless the code truncates the data. I would bet you can get down to less than 1 deg before things start to get squirrley.
RE: Min. angle for axisymmetric with bricks
RE: Min. angle for axisymmetric with bricks
For elements near the center line I tend to agree with Johnhors - 1° sounds a bit small - except if it involves a region of low stress & stress gradients where one might actually get away with it. Not sure about a 1° segment for elements sitting far away at/on some radius...(i.e. modelling a pipe or casing)
Don't have the time right now, but might try it out some day - would be interesting.
RE: Min. angle for axisymmetric with bricks
RE: Min. angle for axisymmetric with bricks
We deal with this situation often in the world of pressure vessel evaluation for the process industries. Picture a vertical cylinder 20' (~7m) diameter x 3" thick shell say 30' tall. I have a conical transition (similar to a piping reducer) which has a 30° off vertical profile and transitions me to a 10' diameter shell. Let's say teh Inspection group has discovered a thin spot (due to corrosion) near the large diameter to cone transition and for simplicity I want to model it as though it is a full band extending 6" on the 20' diameter shell and 6" onto the cone. It has corroded down to 2" thick. As a first pass, I'm only going to include internal pressure. Its full of pressurized hydrocarbons and bad things would happen if it fails to contain the pressure. On the other hand, an immediate unplanned shutdown of the plant is not only costly but carries with it the not-insignificant hazards of taking the process through a shutdown and startup sequence. Keep in mind, BP Texas city http://w
We now enter the world of Fitness For Service, since we are well past the "new design" code limits. http://w
I could go to my trusty old full blown FEA package and use true axisymmetric elements, or I could use my solid modeling package with the same FEA solver, but restricted to solid elements. If I choose (for whatever reasons) to go with the solid modeling package, I will build a profile of the geometry, which looks just like the axisymmetric model, and sweep it one degree for an inside arc length of about one inch. If I use more than one element through the 2" thickness, I can easily have well-conditioned tetrahedral elements. I apply internal pressure, fix the bottom section cut in the vertical direction, and apply the calculated longitudinal stress as a pressure along the top boundary on my small diameter section. I apply symmetrical boundary conditions on the edges of the slice. Within a few hours of the initial phone call I can have some feel for how dire the situation is, and at that point can either recommend an immediate shutdown or move on to a more detailed model incorporating a more realistic degraded area and additional loads.
My perspective is that it depends. Perhaps one way to look at it would be to put at least enough of a swept arc to have several elements through the swept section. If the profile goes all the way to the centerline, then the concerns expressed in prior posts regarding sharp angles become applicable.
jt
RE: Min. angle for axisymmetric with bricks
15° is a sensible choice for the slice, which would yield both quality elements and a well conditioned stiffness model.
RE: Min. angle for axisymmetric with bricks
perhaps I got lost somewhere, but there is a foundamental thing I don't understand.
The OP's model comes from CAD, right? OK, but why not make a section (section, slice, however your CAD may call the intersection of the solid with a datum plane) of the revolution solid, in order to get a 2D axisymmetric surface? I sincerely can't see a CAD unable of doing that, and I don't see many FEA unable to deal with 2D-geometry...
OK, if you have non-axisymmetric loads / restraints then it may become a little harder since you need harmonic formulation, and only in that case I'd agree not going less than 10 - 15° span with a solid 3D sector in order not to have too close BCs on the sector's delimitation faces.
Regards
RE: Min. angle for axisymmetric with bricks
A previous version (4.5) of Cosmos DStar had it (2D)..., but they took it away (bad! - already requested to bring it back - guess it is about priorities). It is still available in the conventional but more cumbersome CosmosM.
RE: Min. angle for axisymmetric with bricks
Gfbotha, sorry, I was sure I had missed something somewhere!
Regards