Thanks for the responses. I suppose the only way we can correct our errors in thinking is by presenting our thoughts for critique...

To summarize my misgivings from above, for bellows, F=P*A' where A' is approximately based on the average of the convolutions' largest inner diameter and the pipes' inner diameter, which may be approximately that of pipe's inner diameter.

We also must be mindful whether our fabric expansion joint is actually under pressure, or if we have some arbitrary design point for selection of wall thickness. I.E. A process or project engineer doesn't know the ramifications of what they're asking for.

One final concern (that probably isn't one), regarding the modeling of fabric expansion joints.

The only way it can have 0 stiffness is if it is installed in compression, and the supports prevent it from extending beyond neutral.

This is also the only way F=PA can apply to your supports. Once your fabric expansion joint becomes taut, whether it's due to pressure or temperature, it is absorbing part of the load that would otherwise be transmitting to the supports in the 0 stiffness scenario.

Understandably, your position as provider for the fabric expansion joint is that you would design for it to never be in tension, and therefore, it should be modeled as 0 stiffness.

However, such an expansion joint installed in neither compression nor tension will have no choice to see tension as a result of pressure, and the balance is stored between the supports and the joint at ratio equivalent to that of the ratio of their stiffnesses. But, you could also argue that even in tension, the stiffness of an expansion joint is so low that the lion's share ends up in the supports anyways...