Your post is similar to some old posts I replied to on the Mecway forum. I went back and analyzed those files in more detail. I made a lot of changes to get agreement to classical calculations and to show a true buckling failure.
With the thin shell model that you are trying to solve, it doesn’t agree well to classical calcs. It also doesn’t seem to fail via buckling. I keep seeing stresses way beyond the yield point. This is why I changed things a lot.
In doing the updates I found that having a fixed base and free top gave the best agreement to classical methods. The fea software doesn’t have the right bc to simulate the other constraints. In any event, just as a simple pure buckling example, the attached should suffice for most people. You can shorten the beam and compare to Johnson’s formula. I ended up lengthening the beam and comparing to Euler’s formula for this particular example. I can get good agreement with either type of beam.
I created the entire model in Mecway and solved within the software using the ccx solver and intel pardiso. To get the buckling mode to appear I deleted some elements from the column. This would simulate something like corrosion or damage of some kind.
You can see that the displacement is nonlinear even though the stress is well below yield. So this is what buckling is about.
You are right, mine was a raw validation of Calc-em proposal. More rigorous approach can be found in ANNEX D of EN1993-1-6 where characteristic imperfection amplitudes are provided as a function of the fabrication quality parameter. DNV-RP-C208 Non-linear FE analysis Methods also provides guidance in this sense at Table 5-7 . Equivalent imperfections .
What you show is global, Euler’s buckling. In this case, I’m interested in the local buckling. When it comes to yielding, sometimes it happens after elastic buckling (in postbuckling regime) but sometimes it happens earlier - plastic buckling is also a thing. Fully (geometrically and materially) nonlinear analysis can account for this.
it seems not comparable in CalculiX and Abaqus shell element, except using continuum ones not classical.
at Abaqus the shell element need to be changed to SC6R (6-node wedge) or SC8R (8-node hexahedron)
the documentation shown, boundary condition for continuum shell element also needed additional definition of node local axes. not as usual and simple as in classical shell element.
