## Pressure Vessel End Cap Deflection

Hey everyone, hoping someone can point me in the right direction with a deflection question.

A pressure vessel I'm working on needs to be pressure tested before it can be shipped out to the customer, so I'm having a large plate cut to match the flange. The opening is about 1500mm in diameter. It's pretty low internal pressure (less than 1MPa).

I've performed FEA and I know the deflection in my plate is next to nothing (AS1210 says it has to be at least 6mm thick), but the client wants to see the calculations to prove this (you'd think the printed FEA results would be enough).

Is there a way of finding maximum end cap deflection based on 'normal' information I'd have or can calculate?

Is there something similar to the standard beam deflection formulae for round discs?

Thanks very much for any pointers!

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 Recognitions: Homework Help Assuming that the end plate is bolted effectively to the cylinder so that the outer edge of the plate can be treated as fixed, the deflection at the center is: w = p * r^4 / (64 * D), where w is deflection, r is the radius (either to the inside wall of the pipe or the axis of the bolt circle) p is the applied pressure on the plate D is the flexural rigidity of an isotropic plate. D = E * t^3 / (12 * (1 - nu^2)) E = Young's modulus nu = Poisson's ratio t = thickness of the plate This is the simplest formula. The deflection for simply supported edges is a little more involved.
 Thank you so much! That's the formula I was looking for. The edges will be treated as fixed (with 48 x 22mm bolts, it's not going far!). It's nowhere near in depth enough that the edge deflection is significant. It just has to prove the deflection is 'small'. Thank you once again.

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