Thick walled cylinder under normal compression against flat surface
Thick walled cylinder under normal compression against flat surface
(OP)
I'm trying to analyse stresse in a metalic tube, which is held in place by a flat bottom lock screw (See figure). In the study, R will remain constant, L is a constant length, and r will vary. We will assume no friction, smooth surface, isotropic linearly elastic material with σy representing the yield stress. The study will investigate the required compressive force (F) at σy. 
I've tried to find a general solution to this problem, but so far it has evaded me. I've also been trying to perform and FEA through ANSYS, however my experience with ANSYS is limited, and I find this non-linear contact problem is not trivial, and I can't seem to get the solution to converge.
Could anyone assist me in tackling this problem either with ANSYS or arithmetically?

I've tried to find a general solution to this problem, but so far it has evaded me. I've also been trying to perform and FEA through ANSYS, however my experience with ANSYS is limited, and I find this non-linear contact problem is not trivial, and I can't seem to get the solution to converge.
Could anyone assist me in tackling this problem either with ANSYS or arithmetically?






RE: Thick walled cylinder under normal compression against flat surface
If the load on the top is essentially a point load or small round load, you have localize bending that might be similar to that found in pressure vessels with loading applied to shell nozzles. Refer to various pressure vessel handbooks or WRC 107 and later versions for approaches to that.
RE: Thick walled cylinder under normal compression against flat surface
The cylinder will compress into a horizontally-flattened "double-8" with the maximum defoliation at top and bottom. depending on which fails first (deflects the most) Since every machined part is slightly different in small ways from its predecessor and its follower in the assembly process, every "real world" cylinder will fail differently.
RE: Thick walled cylinder under normal compression against flat surface
The analytical solution is given by Roark, as suggested by JStephen. With r becoming small with respect to R you'll need a correction for thick curved beams that's also provided by Roark.
prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads
RE: Thick walled cylinder under normal compression against flat surface
RE: Thick walled cylinder under normal compression against flat surface
I think you can do contact between areas (a portion of the plate, a piece of the outside surface of the tube).
"R constant" will be work ... as you push down with the plate it'll get closer than 2R to the ground (unless that's not what you meant). The contact area will flatten (initially it is an infinitely small line area) and then the tube will bow out and become elliptical.
another day in paradise, or is paradise one day closer ?
RE: Thick walled cylinder under normal compression against flat surface
I found the analytical solution in Roark's for a thin walled pipe with a meridian line load, and I'm trying to find the thick walled correction.