I doubt that honeycomb will help you there. Vacuum vessels, if I understand this correctly, are dominated by hoop and longitudinal stresses, not bending. Honeycomb is excellent for applications that need to spread the top and bottom (tension and compression) fibers apart, but useless for single loads.

Terry Drinkard
terrydrinkard@yahoo.com

I partially disagree with terrydrinkard: vacuum vessels may be dominated by the elastic buckling of the wall, and this one is mainly related to the inertia, so that a sandwich may be a good choice. It will depend however on the actual thickness to diameter ratio: for high ratios the plastic buckling should be dominating and there the inertia will help much less.
The problem is not very simple, as, to some extent, the formulas used in pressure vessel calculations contain practical coefficients based on experiment.
As a starting point you can take the formula for the critical external pressure of a long thin cylinder (elastic buckling only!) and adapt it as follows (all the symbols have their commonest meanings, r is some average radius):

p=3*D/r^3

where

D=E*t^3/12(1-ni^2) for a solid wall

Now I suppose (but this is only my opinion!) that for a sandwich one can take for E and ni (Poisson) their equivalent values (ni=0 is a safe choice) and for t^3/12 the moment of inertia of the sandwich per unit length.

The result is a theoretical pressure and a safety coefficient of at least 3 is normally taken for practical applications. Of course it is also essential that the cylinder has uniform bending resistance around the circumference (the longitudinal joint, if any, is a critical point).
This may only be a starting point. The actual length of the cylinder need be accounted for (but a shorter cylinder has of course a higher buckling pressure): the formula is more complicated, but the procedure is exactly the same. Also plastic collapse conditions need be examined: a rough check is obviously that the hoop load (p*r) is not higher than the allowable load in the sandwich. Finally one should examine the heads and perhaps other special points.
You should also consider that in pressure vessel technology a normal solution is to use stiffening rings welded to the vessel wall: this might offer a safer, simpler and already available way to your mass optimization problem!

prex
motori@xcalcs.com
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