If you're designing a Div.1 vessel AND there are no specific rules in Div 1 (check out Appendix 13...), then you can activate paragraph U-2(g). Good engineering practise says (at least for jurisdictions that have adopted the ASME Code as law - where is this vessel going to be installed??) that you should use ASME Section VIII, Division 2, Appendix 4 (for 2006 and earlier) or Part 5 (2007 Edition). Either way, the answer is that it's very complicated to translate FEA stresses into ASME allowable stresses (stress linearization, membrane, bending, peak stress, etc...).
In your case, I would highly recommend that, if this is a one-of design, you should hire a consultant with years of expertise in this field. If this is something that you are going to be doing a lot of, let me know, and I'll recommend a number of books and papers to start you reading. Oh, and you'll want to find a mentor to help you along. When I train an engineer who knows ASME pressure vessels and then teach them FEA for pressure vessels, I usually plan on at least 6 months of training time.