I think there are other considerations for FRP pipe than the stiffness of the flanges, although John L. is surely right that the FRP flanges are "rigids" when compared to the FRP pipe itself.
1. Steel and Cast Iron valves are going to be more rigid than FRP "rigids." This may or may not be a significant factor in your analysis. It may be sufficient to change the material for the valves and then change back to FRP to continue.
2. Mechanical joints are going to have some inherent flexibility due to their construction, although the joints themselves may well be modeled as "rigids." The FRP vendor should be able to provide guidance.
3. Wrapped butt joints will be more rigid than the pipe, but perhaps not enough to consider them to be "rigids." Again, the FRRP vendor should be able to help.
4. FRP tees and elbows may well be best modeled as "rigids." I hate to repeat myself, but the FRP vendor should be able to give you good advice here too.
Summary:
Call your FRP vendor, or several of the vendors on the bidders' list. If they are prospective bidders, they are going to be eager to help for the good will (you, after all, are going to be doing the tech eval). If there is a supply contract in place, the successful bidder still has self-interest in helping you - if you call and ask for advice, and document the phone call, he will be up a tree if something goes wrong later.
Most of the major FRP vendors have different construction details for a lot of their pieces and parts. It's not really possible for someone to give specific advice on how to model "FRP pipe" without knowing who the vendor is and what particular resins, joints, and winding details are specified. For some vendors, such as Ameron, even the nominal pipe diameter is relevant to the issue. You may have to model 4" flanged joints differently than 24" ones.
As has been repeated may times by the grizzled veterans here, there are many possible answers to most piping problems. I would expect you to have to spend several hours with a phone at your ear to get the details you need. It would scare hell out of me if someone like me gave you specific answers to these questions as you have posed them AND I KNEW YOU TOOK THAT ADVICE AND RAN WITH IT.
Since you have posed your problem in intelligent terms, I suspect you will be able to do the right thing with the information you eventually assemble. But your taking generic advice for FRP piping is a hell of a lot more hazardous to your professional health than my taking generic prescription drugs is to my physical health.
Sorry if my answer makes you overrun your budget.
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CraigB