Sorry about the delay.
Havn't quite found what your looking for i'm afraid. The concept of the interaction formula is generally the way it has been resolved. The generalised interaction formula i believe comes from General Dynamic Structures Manual. RB1957 gave in hos first reply the general assumption.
Anyway, there are many ways of skinning a cat, and one method is to use ESDU81047 which has an accompanying program A814V40, which provides a method for calculating elastic buckling loads of flat rectangular plates under combinations of uniform in-plane biaxial and shear loads. I think the "black-box" methodolgy within it stems form the BAE stress office report data regarding the elastic buckling ratio's etc.
When you have a hole within a panel you have to use a bit of judgement regarding its effect. If its a small hole at the centre your not really going to see much in the way of bending. Panels with holes (reinforced or flanged) can be regarded into 2 classifications: large cut-outa and small cut-outs. In the case of a large cut-out with a reinforcement that extends the width of the panel, the featrue can be considered to act as a panel breaker, reducing the panel aspect ratio of the analysed panel. For a panel with smaller cut-outs, the feature can be accounted for by assuming a plain panel of reduced thickness. the equivalent thickness can be determined by discounting the thickness by a factor of area of the hole to that of the plain panel, (see ESDU 84042).
The panel edge fixity i think is more critical to the overall instability of the panel. The compressive loads will therefroe tend towards the edge members leaving the shear in the web. Towards the cente of the panel shear dominates, but at the corners you can see the combinations of bending, shear and compression, though if you reach an overall panel critical buckling load based upon a (say) Von-mises stress at a corner how do the 2 relate to each other??
I think its more of a black art than a science, because of the effects of the differing perameters involved.
Not much help to you i'm afraid. You could create a detailed NLFE for the elastic buckling, and even maybe NIKE3D for the post-bukling effects. And validate them against various previous methodologies for simple inputs (i.e pure shear etc).
