Element Size v Stresses
Element Size v Stresses
(OP)
I am very rusty with FEA. To check the effects of the mesh size with the accuracy of the results, I analyzed two 1/2"x4"x10" simply supported plates loaded with 10 psi on the local Z axis. The first plate was meshed with 1"x1" elements and the second with 1/4"x1/4". The stresses on the 1/4"x1/4" element are double than the stresses on the 1"x1". Based on my hand calculations the bending stresses are close to the results of the 1"x1" mesh.Can anyone explain the differences?
Note: I always thought that smaller elements produce better or more accurate results.
Thank you
Note: I always thought that smaller elements produce better or more accurate results.
Thank you





RE: Element Size v Stresses
RE: Element Size v Stresses
Can you clarify how your boundary conditions are setup? Are all edges supported or just ends? If ends, the short or long ends?
What element type are you using?
As they say, a picture is worth a thousand words.
TOP
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RE: Element Size v Stresses
Thank you
RE: Element Size v Stresses
RE: Element Size v Stresses
Plate 1 (top) - 1" x 1" elements
Plate 2 (mid) - 1/4" x 1/4" elements
Plate 3 (mid) - Half 1"x1" elements and the other half 1/4"x1/4"
Plate 4 (bot) - Only the middle of the plate with 1/4"x1/4" elements and the remaining 1"x1"
The streses at the midspan of plates 1, 2 & 3 are approximately the same at around 3.0 ksi. The strsses at some of the elements at the midspan of the 4th plate are more than double at 7.47 ksi.
RE: Element Size v Stresses
You need to have the same size subdivision on both meshes where they join.
RE: Element Size v Stresses
Thanks CRISB and everyone else.
RE: Element Size v Stresses
TOP
CSWP, BSSE
www.engtran.com www.niswug.org
www.linkedin.com/in/engineeringtransport
Phenom IIx6 1100T = 8GB = FX1400 = XP64SP2 = SW2009SP3
"Node news is good news."
RE: Element Size v Stresses
Ellas can you post your hand calcs. to compare.
RE: Element Size v Stresses
RE: Element Size v Stresses
RE: Element Size v Stresses
Also, if you have any type of geometry change resulting in a stress concentration and you try to refine the mesh to get more accurate results, you will in fact acheive the opposite. Refining the mesh too much around a stress concentration causes the stress to approach infinity.
O = F/A, as A approaches 0, O approaches infinity.
If you have time in your analysis, you should run the analysis multiple times with different sized meshes. You are looking for a convergence of results. If the results stay fairly consistant between meshes, then you are good to go. If the resutls vary significantly, you need to take a closer look. Remember about the stress concentrations though, you have to go at least 3 to 5 elements away from the stress concentration to get an accurate reporting on the stress in the area.
Anyway, hope this helps.
RE: Element Size v Stresses
!!!
"If your mesh is too fine, you introduce an artificial stiffness into the equation"
Never heard either of those before.
"O = F/A, as A approaches 0, O approaches infinity."
But if A is going to zero, won't F go closer to zero too?
"Remember about the stress concentrations though, you have to go at least 3 to 5 elements away from the stress concentration to get an accurate reporting on the stress in the area."
Unless the stress concentration is real...
RE: Element Size v Stresses
That being said I don't think that in EVERY case a finer mesh gets better results. I can't remember where I read it but I have a book that shows an example of a super fine mesh having some numerical instabilities that were not present in a coarser one. It may have been due to the element formulation just as much as the mesh density. But I think that in vast majority of cases as long as the element types are appropriate a finer mesh will give more accurate results.
Dan
Han primo incensus
RE: Element Size v Stresses
RE: Element Size v Stresses
However, every element should have a point beyond which meshing further will not give better results. I'm not sure that I would call this "artificial stiffness". Rather, I prefer to think of it as meshing to a point where the plates are so think that the assumptions used in the derivation of that element are no longer valid.
RE: Element Size v Stresses
Numerical instability is due to the code being used, not the FE theory, but would be the only plausible reason IMO. If you could modelled steel with elements approaching the grain structure of steel would you not gradually approach an error less model?.. Now there are many variable in play that could could prove this untrue but theoretically many of the 'approximations' made by engineers to simplify a problem to a workable 'model' will be removed.
RE: Element Size v Stresses
Are you referring to 8 node solid element modeling or 4 node plate element modeling?. I cannot see using a plate element with a width equal to the "grain structure" of steel producing a reasonable result... at least not with the plate elements that I've seen used for most structural applications. Not sure what you're getting at there....
RE: Element Size v Stresses
What are you getting at.. you believe mesh refinement will lead to increased errors and unreliable stress results? An interesting view point..
RE: Element Size v Stresses
I was limiting my discussion to plate elements only since that was the nature of the OP's question. With most plate elements there is a thickness to least width ratio beyond which the element formulation begins to degrade and results do not improve with further sub-meshing. In fact, the results are supposed to degrade.
RE: Element Size v Stresses
I don't have any references that support this, perhaps you could list some for my own understanding?
All my testing on plates elements show the stress converging then not increasing any discernible amount, but not degrading..
These stresses at my convergence point match very accurately the hand calculations too.
Therefore I can only conclude that the mesh should be refined until the stress converges, regardless of whether using solid elements or plate elements. Any further refinement will not compromise the results but will only waste computational time.
Maybe the observation of stress degradation is limited to a particular plate element type with a few select codes? Perhaps now outdated with newer code revisions?..
RE: Element Size v Stresses
Also if you are talking about a 20mm thick plate you wouldn't use a 1mm mesh size.