weird behaviour of shell elements

Hi,

in order to check out the new shell elements, I created a simple geometry: rectangular plate, support at the corners, uniform load. The size of the rectangle and the number of elements in each direction are slider parameters.

Now, depending on the slider settings, karamba does or does not calculate a result. For some combinations of values, karamba's "analyse" component goes red, in other cases, it works as expected. You can observe this by playing around with the 4 sliders on the left side of the canvas.

Does anyone have an idea to

a) explain this

b) get the thing working?

See attached file...

Best regards,

Stefan

Attachments:

121029_shelltest.gh, 12 KB

Replies to This Discussion

Permalink Reply by Robert Vier on October 29, 2012 at 6:17am

Hey,

this is due to the mathematical model karamba uses for shell-elements. they sometimes are sensitive for rotation in plane, so the stiffness matrix gets badly conditioned and cannot be inverted (=the core FE calculation).

to fix this, just insert a single support that holds the shells around their normal vector...

best,

robert

Attachments:

121029_shelltest.gh, 14 KB

Permalink Reply by Stefan on October 29, 2012 at 6:35am

Thanks a lot for the quick response!

Do I get this right?

-> the behaviour you describe is a peculiarity of karamba's shell elements?

(With horizontal displacements fixed at the supports, I would expect all rigid body modes to be eliminated, and no rotational dof should need to be constrained...)

Now the "but":

the solution you suggest is all right for purely transverse loading (as for a [german] "Platte"), but can lead to unwanted results with loading parallel to the shell middle surface (as for a [german] "Scheibe"):

Do you have an idea for that kind of structure?

Regards,

Stefan

Permalink Reply by Robert Vier on October 29, 2012 at 6:55am

You are right, though I'm sure there's a solution to this - but clemens preisinger (who knows best) is away until the 9th of nov- if it's urgent you can try to contact him directly.

I dont really know right now .. it also helps when you change the cross section properties / the material characteristics.

this is an issue we have to adress with shells, cause it also refuses to calculate e.g. with too little shear modulus as a material in certain cases (below 300 as for wood) .. but we have to wait for clemens i'm afraid.

best,

robert

Permalink Reply by Stefan on October 29, 2012 at 6:58am

it's not urgent, so I'll wait.

I appreciate your help :)

Stefan

Permalink Reply by Robert Vier on October 29, 2012 at 8:09am

As a first step, it does not seem to make any difference in this case - the deformation, the energy etc stays the same.

Relates to the general problem of how to connect beams and point-supports to shells (singularity) .. I think, at least.

best, robert

Permalink Reply by Stefan on October 30, 2012 at 4:56am

I have to correct myself: what I said ealier about "unwanted results" for parallel loading is not correct. Fixing the drilling dof as you suggested should not and apparently does not affect the result.

Inspired by your recent post, I came up with this explanation:

the dof in question ist the so-called "drilling rotation" that has no physical meaning, but is necessary for compatibility with other elements (such as beams) or shell elements with different orientation. So, fixing this dof should not influence the result (see e.g. Zienkiewicz, Taylor: The Finite Element Method in Solid and Structural Mechanics, chapter 13.5 ‘Drilling’ rotational stiﬀness)

Searching for "fem shell drilling" yields a multitude of publications on the problem. As far as I know, there is no 100% satisfying solution to it.

best regards,

Stefan

Permalink Reply by Robert Vier on October 30, 2012 at 5:06am

thanks, I remember Clemens telling me something about that :)

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