Moment Peaks in Shells/Plates at Point-Supports

Hi all

I've had a mail correspondence with Clemens regarding peak moments at point supports. We've agreed to share our discussion with the rest of you. It will appear pretty fragmented, but here goes:

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Hi Clemens

I've analysed a plate structure using Karamba and wanted to do a convergence analysis on results computed as a function of the number of elements.

Now, when strictly looking at the result magnitudes of internal energy (IE) and maximum displacement (w_max), it's acceptable, that their relative deviations are very small. But I cannot explain the tendencies of their graphs. From what I know, FEM should always compute underestimated results when compared to analytical solutions. So I don't understand why both the IE and w_max seem to be decreasing for an increasing number of elements.

But my main concern is the behaviour of the peak moment, it seems to be simply hill climbing untill suddenly a singularity kicks in.
I initially wanted to use the peak moment as a fitness value for optimisation, but with this behaviour, I don't think that would make sense.

I've attached my GH file as well.

It would be much appreciated if you could enlighten me on these subjects.

Cheers

Daniel Andersen

Hi Daniel,

I could not run your definition because I have not all the plug-ins installed that you use.

You are basically right that the displacement should increase with a finer mesh. However the result of the shell analysis also depends on the shape of the triangles (well formed vs. very distorted). In order to test this, I think it would be interesting to use a very simple example (e.g. rectangular plate with one column) where you can easily control mesh generation. Would you like to start a discussion on this in the karamba group at http://www.grasshopper3d.com/group/karamba?

It is not a good idea to use the bending moment at a singularity for optimization because the result will be heavily mesh dependent. Also real columns do have a certain diameter and modeling them as point supports introduces an error.

Best,

Clemens

oh, and by the way!

Here's some relevant literature on handling peak moments:
https://books.google.dk/books?id=-5TvNxnVMmgC&pg=PA219&lpg=...
(Blaauwendraad, J., 2010. Plates and FEM : Surprises and Pitfalls, see Chapter 14)

It would be great if a feature dealing with peak moments could be incorporated in Karamba. In my work, I ended up exporting my models to Robot in order to verify the moment values.

Best,
Daniel

Hi Daniel,

thank you for your reply and the link to Blaauwendraads excellent book!

At some point I hope to include material nonlinearity in Karamba which will help in dealing with stress singularities.

If you want you could open a discussion with a title like 'moment peaks in shells at point-supports'. Then we could copy and paste the text of our conversation into it.

Best,

Clemens

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