Closed ended cylinder radial expansion

[kobuss]

Good morning guys/girls, hope all of you are well. I have a question - I want to find out the formula to use when calculating the radial expansion of a close ended cylinder under pressure. i have looked around but can only find formulas regarding open ended cylinders.

Your help would be appreciated...

 

[C2it]

An exact formula is complex since it must take into account:
1. Tri-axial pressure stresses and resulting strains.
2. The restraining effect of a closed end.
Thus any radial expansion solution must account for distance from the closed end.

 

[BigInch]

http://laser.cheng.cam.ac.uk/wiki/images/2/2b/SAPV.pdf

"People will work for you with blood and sweat and tears if they work for what they believe in......" - Simon Sinek

 

[kobuss]

thanks for the replies, will have a look at the information!

 

[BigInch]

It's in there.

"People will work for you with blood and sweat and tears if they work for what they believe in......" - Simon Sinek

 

[C2it]

Big Inch,

Unless I missed it, whilst 3D pressurised cylinder strains are addressed, I don't think the Cambridge article covers the closed end.

Radial pressure strain in a cylinder very close to an end plate will be resisted by the plate causing a radial tensile stress in the end plate. This will also cause annular bending at the plate / cylinder junction, and thus it's a difficult one. Clearly the restraining effect of the end plate will reduce to zero some distance away, and a typical vessel end cap would not have a very significant effect. However, Kobuss was I think looking for the general case.

 

[BigInch]

Page 13-14 The longitudinal strain formula on page 13 is the form for closed ends.
I would think that the volumetric strain formula is sufficient for practical purposes, but true it does consider the end plate flat and rigid, which if it was allowed to dish out, may add some small additional volumes there. I'd calculate that deflection with Roark's formulas, estimate volume and add them to this result, if I thought it might make some significant contribution, but if it was truely a rigid, flat end plate design, you would not normally allow all that much dish deflection.

"People will work for you with blood and sweat and tears if they work for what they believe in......" - Simon Sinek

 

[C2it]

I would have expected to see a relationship where (εh = δR/R) and (εr = δt/t) varies with respect to end distance, which is not addressed.

 

[BigInch]

page 13, no?

"People will work for you with blood and sweat and tears if they work for what they believe in......" - Simon Sinek

 

[kobuss]

thanks for the responces guys, very good to see that so many people are willing to help out!