hts-
One approach commonly used on for example vessel skirt access holes is simply area replacement. If the cross section (looking down) of the cutout is say 24" x 1" thk then add a collar on the hole which supplies 12 sq.in. on each side. Simplistic but logical and effective: You are looking to maintain the moment of inertia of the original section. By replacing the removed area the A*D^2 term remains the same. This, of course, is applicable when the cutout is not in such a small diameter vessel such that the centroid of the cutout is significantly larger than the centroid of the collar (reinforcement). I ran into this issue with a small diameter vessel which needed a part of its shell replaced.
For a tank, a similar approach should work. One additional issue for tanks which have a relatively larger radius:thickness ratio would be local buckling effects. All in all, doorsheet cutouts on large vessels and tanks are done relatively often, and I've never heard of a failure...
jt