I have try the Tower file as it is’s very well documented and difference can be large and noticeble in both, shape and load factor.
To warranty the fixed base you basically need to constrain rotations arround the tangential direction, build previously with a transform card.
Nice, but is there someting more you changed ? I tried it with the file above (Tower2024.pmx) but only got crazy results, so i wonder where is the trick 
The only things i changed in the original file:
removed plasticity
changed to mapped mesh, only quad elements (same size 200x200 / 15120-S4 elements)
removed the bottom rigid body, instead fixed the bottom edge (deleted all RP history outputs).
Yes I realized that the combination of shells and rigid bodies sometimes lead to unexpected results, but in case you replaced them, what have you used instead to apply the loads and moments?
Thank you
My “results” (BF 1 and errors) with different solvers and ccx 2.21
PS
Also with code aster i don’t get close to your perfect BF of 2.9
¿Does the new developer version changed something related with the rigid connections?
My .dat file is empty. ¿Do I have to add something special to get the Buckling modes written there.?
My gravity is outside the Buckle Step. You don’t want to scale the self-weight as a regular load. V should also be outside but I’m not sure if it just comes from the self weight of the head, so I kept it. (There is a small difference - BL=3.028).
I kept RB on top. The flange is probably made 50 mm for that purpose. It’s very stiff and the usage of RB seems reasonable.
Without it one can apply traction directly on that surface and use distributing for moments.
I’m using S8R.
Pardiso Mkl 8 cores. I compiled myself. AMD CPU.
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Okay thanks. I tried further with refined linear elements (S4 and S4R) but it seems it’s not possible with them to produce reasonable results in this case.
No, at least not intentionally. So you requested some history output but got an empty .dat file?