Hi Calc_em,
That’s the Free-Free rotation version ( configuration N=1).
We had a conversation with Xyont about Rigid Body some months ago when talking about Large shell rotations on the forum.
Calculix Rigid Body only constrains midplane nodes of shells after the expansion. From my point of view that wasn’t right as it allows the shell to still rotate around the axis contained in the intersection between the lip surface plane and the shell midplane. The shell is not made fully rigid when defining the Rigid Body. You can look at this as if there is a rigid ring and then the shell lip is connected to it but still free to rotate in the connection.
Note I’,m not unconstraining the reference node (Ring) which is still unable to rotate.
Another point I will consider for progressing in this nonlinear analysis is that we have a very large number of modes very close to each other. That means we should approach the first buckling mode with tiny steps (load or displacement) and assuring not to overpass it during the iterations to avoid the system to accidentally jump from one mode to the next messing the convergence (here the DIRECT option suggested by Victor can help).
If this were not enough, this problem also seems to have two eigen shapes associated to each eigenvalue.
I think your easy tutorial could become a master course in buckling analysis.