Modelling stresses in concentric cylinders

[bk2]

I am working on a burst calculation on a cylindrical pressure vessel. I have this cylindrical vessel placed concentrically inside another cylindrical vessel which is acting as a reinforcement to the inner part. (The diametral clearance between the two cylinders is .005" approx.)
The thickness of the inner part is such that the standalone busrt calculations generate stresses beyond the yield strength. But being placed inside the other piece (thin cylinder inside a thicker cylinder) helps it from plastically deforming.
How do I model this using COSMOS?

 

[rb1957]

can you show that the outer thicker cyclinder won't burst ? (in the same way as you know the inner thinner one will)

if so why model the interaction of the cyclinders ?

if you have to model it, you're dealing with a contact (non-linear) problem.

 

[bk2]

rb1957,
Thanks for replying. The outer piece is of the same thickness as the inner piece and so would fail by itself as well.
The inner cylinder moves axially inside the outer piece.I want to keep the delflection on the inside cylinder in the elastic zone so that when the pressure on the ID is relieved, the OD of the inner cylinder can still slide inside the outer cylinder.

I am trying to obtain a rating as tests with 10000 psi on the inside cylinder plastically deformed the inner piece and it was hard to get it apart.

 

[rb1957]

if you've got a test result on the geometry you're modeling, i doubt you'll get a different answer.

 

[prex]

If I correctly understand your setup, you need that the two cylinders, acting together, will limit the deformation in the elastic field. As the deformation of the inner cylinder is clearance+deformation of the two together, you only need to calculate the latter assuming a cylinder with a thickness equal to the sum of the inner and the outer one.
Don't know the diameter of your cylinders, but you seem to be playing with a micrometer in a blacksmith cave.

prex

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[GregLocock]

This is a similar problem to interernce fits for concentric thick walled tubes. Analytically that means using Lame's equations.



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[prost]

Something seemed familiar about this, two concentric cylinders under pressure. Sure enough, go back to Timoshenko's derivation equations for a thick cylinder under pressure. The deformation is isotropic, meaning here that the deformation and therefore stresses do not depend on the azimuthal (angle theta) direction. Timoshenko uses a stress function to derive the equations for the stresses in a linearly elastic body. The shear stress tau-RT (shear stress in the R=constant planes, Theta direction) in such a cylinder is zero for all R! This means in principle that if the two concentric cylinders are of the same material, are very closely matched (say 'neat fit', very low clearance), then the shear stress between the two cylinders is zero, and the two cylinders are acting as one--no need to model contact between the cylinders. All within the theory of elasticity, of course. I don't have my Kachanov here, but I would guess that even for plastic deformation, the deformation is isotropic, so that zero shear stress condition holds.