# Pressure-volume relation of thin-walled shell [closed]

Attempt to edit into a more specific question as suggested by moderator:

I would like define the shape and material properties of a 3D thin-walled shell/membrane-like structure (for instance a baloon). Then I would like to approximate the pressure volume-relation (PVR) of this structure - what pressure will we obtain when increasing the internal volume?

I'm planning to create a mesh of 2D triangular elements for a 3D shell with volume V0 and internal pressure zero. After defining the stiffness matrix for the material I should be able to compute the nodal forces, geometric configuration and internal volume for a certain internal pressure (the plan is to use an iterative approach searching for a configuration where all resulting nodal forces equals zero, that is where expanding forces arising from the internal pressure equals constricting forces arising from displacement).

To do this I need to calculate the nodal forces created by 1) displacement from the original V0 configuration and 2) from the internal pressure. I think I can figure out the first one, but I do not know how to transform the internal pressure (acting perpendicular on the triangular elements) into nodal forces. Any ideas?

• For spherical vessel, will be more simple than for shell+head vessel. May 19 '17 at 10:34
• For spherical vessel, the pressure can be approximated from shell stress. First, when we add more volume the spherical wall will elongate to new length by ratio of volume0^0.333 and volume1^0.333. then Second: calculate elastic stress due to that elongation. Third: return back the value of stress to thickness calculation to get Pressure. THE POINT IS: Pressure or stress is due to material elongation. May 19 '17 at 10:40
• Resource-finding questions and discussion questions aren't on topic here. I would suggest you start working on the problem and then come back if you have any questions about a specific engineering concept related to your work. May 19 '17 at 12:44
• This doesn't really make it any less broad. "Any ideas?" isn't really an addressable question. In the balloon example, you can look up pressure volume relations for real balloons. It's actually pretty complicated; as you start to stress it the higher order effects start to take precedent.
– JMac
May 23 '17 at 16:08