# Calculate or approximate force required to expand a thin-walled elastic cylinder held rigidly at both ends?

How might one calculate or approximate the negative pressure applied to the outer surface of a cylinder required to expand it a certain distance, when held open rigidly at each end?

The cylinder ID = 20*the wall thickness and the material is very elastic.

Oli

• This is one of the more interesting aspects in engineering. There's an old model, but it doesn't work. Turns out defects (such as a pipe not being perfectly circular) in the pipe will make the pipe buckle significantly earlier than the model predicts. And estimating defects is ... difficult. As a result, we've got the result of a good model, with a big conservative fudge factor on top. May or may not be useful to you.
– Mark
May 18, 2018 at 21:47
• @Mark OK anything's definitely better than nothing! what is this model you're talking about? Cheers May 18, 2018 at 22:35
• Is this a fairly stiff material that only deflects a couple % before rupturing, or is it more elastic, where the axial radius of curvature is less than 100 times greater than the nominal cylinder diameter? For steel and other materials that deform only slightly, see this NASA report on tank stresses and deformations May 19, 2018 at 2:12
• You still haven't adequately described the end constraint. Is there a thick band at the ends that is much stiffer than the middle? Or is there and end plate? and what is their thickness and strength compared to the cylinder? The cylinder's shape depends on both the edge axial shear and edge bending moments. Those usually have to be calculated as well based on the actual physics of the situation. May 19, 2018 at 2:20
• When it inflates, the ends can't slide closer together, the distance between the ends is fixed as well? As in tubing hose-clamped around a two barbs fixed to a base? This is a pretty mean version of the calculus of variations. You first need to verify the modulus and poison's values over the range of stresses in the problem. Hopefully, you can confine the problem to where modulus and poison's ratio are constant. otherwise, you may find yourself looking at a carnival balloon the begins to inflate dramatically at one place, and then the zone of inflation stretches down the length of the balloon. May 19, 2018 at 13:22