How to Model Flexural-Torsional Buckling of a Ring?

Hello all;

I have been working with rings that have a uniform inward radial force applied. The inward force causes the ring to go into compression, which introduces a flexural-torsional buckling mode. This mode results in large axial displacements; the 1st mode can be visualized as the perimiter of a pringles chip. The generic version of the case I am trying to solve is illustrated on the left, with the pink arrows representing the distributed radial load, and the orange arrows representing the resulting compression forces internal to the ring. A model of the typical experimental result is on the right, with the characteristic 4-node "potato chip" shape shown in light blue, and the initial undeformed shape in transparent gray.

Has anyone had experience modeling a buckling scenario such as this? I know the non-linear buckling solver in Solidworks can accurately capture the behavior of linear beams, but haven't yet found any forum posts or other information on ring buckling. I need a way to predict how stiff the ring needs to be in order to prevent the buckling. I have found sytems of analytical equations for this, but in addition to being atrocious, they make too many assumptions that don't apply to our geometry. I would just try the FEA, but I currently only have access to the basic solver, and would love to know if the more advanced one can handle this before I pursue this further.

Any help or tips will be much appreciated. Thanks!