How to perform a honeycomb structural verification?

Bruhn has analysis of honeycomb panels. I'm sure NACA, NASA, USAF, etc (ESDU?) also do. there are probably dedicated texts as well, probably for your specific application.

A google for "analysis of spacecraft honeycomb sandwich panels" returned many promising hits.

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

Hexcel has a series of excellent engineering manuals. I found them still on their website a couple of years ago - you might find them still there.

Typically, use core shear strength alone for all out-of-plane shear stress. It ignores the shear strength of the facing, but since they will bend and deform with much less stiffness than the core, that's not unreasonable to ignore them.

Ah, what FEM code and element type are you using?
2D shell elements can output thru thickness shear stresses (as far back as 40 years ago).

Is this for the spacecraft... or for the launch vehicle/fairings? Huge difference and one You seem a bit unprepared to deal with.

Launch/throwaway rated composites and sandwich panel... not a big deal... one and done.

Long-term space rated composites and sandwich panels are a VERY big deal. Long-term space exposure is hard on all materials... especially composites... and especially in planetary orbit.

Check NASA publications libraries.

Regards, Wil Taylor
o Trust - But Verify!
o For those who believe, no proof is required; for those who cannot believe, no proof is possible. [variation, Stuart Chase]
o Unfortunately, in science what You 'believe' is irrelevant. ["Orion", HBA forum]
o Only fools and charlatans know everything and understand everything." -Anton Chekhov