Aspect Ratio 1

[corus]

In an explicit non-linear analysis the large displacements produce very high aspect ratios in the elements, although the variation of stress along the longer side of the element appears small.
Does the aspect ratio of the element, of say greater than 5 to 1, affect the overall accuracy of the element or does it only affect the accuracy of the results in the 'longer' direction of the element?
In this case remeshing, or adaptive meshing, during the time step isn't possible so the problem of the aspect ratio cannot be ignored.

 

[EdR]

corus:

First, You are way beyond my personal experience so the following should be taken with a large grain of salt....only responded to maybe jog your memory or suggest something that may help...

I am assuming since it is an explicit solution that you are using linear elements with single point integration for the internal force computation. If this is the case then I think:

1. The 5 to 1 ratio should not cause a problem if the stress field is linear (as you noted in the post) and if the shear is mimimal...If the shear is large then you may have a problem...Don't know where the L x W ratio becomes a problem but I have used 5 x 1 in local areas and have gotten OK results...

2. Is the distortion mostly extensional as opposed to rotational i.e. it folds to a 90 degree angle, etc....If rotational then probably will cause bad internal force computations...If extensional (either tensile or compressive) the internal force computation should be OK...

3. Did the distortion decrease one direction to get the 5 x 1 ratio....If so is the integration time step reduced to account for the decreased dimension.....Transit time across the element will have decreased..

4. Is the region where this occurred really the region you need accurate results for...If not and you have what otherwise appears to be valid results I would not worry...Remember FEM is fundamentally an approximate method.

Wish I could help more but maybe this will give you some ideas.

Ed.R.

 

[corus]

Ed,
Thanks for the comments. The problem involves forming a thin structure from a solid block using linear elements, and as such the elements are stretched mainly in one direction, though the corners are more of a problem. The argument is that the 'bad' elements would affect the overall results, as well as locally, though I don't agree. Your points 2 and 3 are interesting, and I'll think over them before re-entering the fray.

 

[RockEngineer]

I just attended a training class this weekend put on by REI for STAAD. In our discussion of plates the instructor stated that FEM programs for plates are only able to determine forces at the corner nodes of an element and deflections at the center of the element. The program then averages the forces at a node from the connecting elements and tries to form a smooth deflection curve between centers. Large aspect ratios throw off these interal calculations. The best elements are squares and equalateral triangles. I was always taught not to have an aspect ration greater than 3 on rectangular elements. The closer to 1 the better especially in your critical areas.

 

[ajose]

Like RockEngineer stated the aspect ratio affect the accuracy.
But try the way testing the convergency of the model, use a small mesh on the model (or just on the area with aspect ratio problems) and compare both output. If the difference is small (5%) these stresses could be accuracy enough

 

[VoyageofDiscovery]

Hi corus,

Through my experiences, I was taught to keep aspect ratios to a maximum of 2.

Regards

VOD

 

[brad]

VOD,
That is a rule of thumb which is based purely on heuristics--corus's problem doesn't lend itself to "rule of thumb" approaches. He has no practical choice but to violate such a recommendation.

Corus--what's the status on this? I haven't piped in previously, but I've been waiting patiently for any results. Anything new?

Regards,
Brad

 

[Cmfg]

VOD,

I have worked with elements with aspect ratio of 1:20 in problems of nonlinear fracture mechanics (elements around the crack tip). They worked just fine.
So the limit 5 to 1 as Bradh pointed out is just a "rule of thumb".

cmfg

 

[corus]

Thanks for all the comments.
I think that in general a maximum aspect ratio of 5 to 1 is a reasonable rule of thumb for most cases away rom regions of interest. In this case it isn't general, and as Brad says, there is no choice as the material has deformed so dramatically and remeshing isn't an option. It would be possible to initally bias the mesh so that after deformation the mesh was more evenly shaped but that hasn't been tried yet.
I don't think RockEngineer's teacher is correct in saying that deformations are calculated at the element centre and then averaged out as the displacements (strains) are assumed to vary linearly in a 4 noded element, whereas the element stresses, related to de/dx, are constant, I believe. In that respect I think the aspect ratio isn't so important providing there is little variation in the longer direction.
The question was really aimed at convincing others and the probable best answer is to throw the automatic mesh generator at it, wait a week for the results, and compare results. Still, the weather is nice.

 

[EnglishMuffin]

I think it depends on the type of deformation - if you have a lot of distortion present then the aspect ratio is more important. For example, if a rectangular element remains rectangular, you can get away with very large aspect ratios.