Bending of Circular plate 1

[HarleyE30]

Hi everyone,

Just after a bit of advice. The attached images show a circular plate(blue) mounted above a piston (green). There is a force acting over the entire top face.

Obviously the plate shown in blue is going to experience some nasty bending stresses. I'm not 100% sure how to tackle the problem by hand calculations. Should I just treat is a 2-D beam-in-bending issue? Please ignore the vertical drillings above which the blue ring is located.

Any advice much appreciated, thanks.

 

[chicopee]

It seems that you will also extrude the plate as it forms between the die and punch. Back in the heydays, I made rounded copper caps this way and we did the forming on the on a press brake. I think that I still have my notes so I'll do some digging and I'll let you know if I have anything meaningful.

 

[chicopee]

I have two JPEG attachments that may help you out. Terms that I used in the late 60's were "cupping force" for forming and " Ironing force " for extrusion.
First attachment

 

[chicopee]

Second attachent

 

[MikeHalloran]

Force applied to the top plate by a platen shouldn't be a big issue.
Pressue applied to the top plate surface will try to twist it out of plane, which may compromise your fastening (e.g. circular stake).
I think the case is covered in Roark somewhere.



Mike Halloran
Pembroke Pines, FL, USA

 

[HarleyE30]

The plate will attach to the piston by use of countersunk bolts (the number of which is yet to be determined) on the top surface.
Somebody else has recommended Roark, but it appears somebody has hidden it in the library!

 

[MikeHalloran]

It's time to buy your own Roark.
Even an ancient one will do.


Mike Halloran
Pembroke Pines, FL, USA

 

[IRstuff]

Roark's has a bunch of cases covering both annular and circular plates with a variety of loadings. Seems like there ought to be something that's applicable:

Case 1a to Case 1d
Annular plate with uniform annular line load w at radius ro; outer edge simply supported
Case 1e to Case 1h
Annular plate with uniform annular line load w at radius ro; outer edge fixed
Case 1i to Case 1j
Annular plate with uniform annular line load w at radius ro; outer edge guided
Case 1k to Case 1l
Annular plate with uniform annular line load w at radius ro; outer edge free
Case 2a to Case 2d
Annular plate with uniformly distributed pressure q over the portion from ro to a; outer edge simply supported
Case 2e to Case 2h
Annular plate with uniformly distributed pressure q over the portion from ro to a; outer edge fixed
Case 2i to Case 2j
Annular plate with uniformly distributed pressure q over the portion from ro to a; outer edge guided
Case 2k to Case 2l
Annular plate with uniformly distributed pressure q over the portion from ro to a; outer edge free
Case 3a to Case 3d
Annular plate with a distributed pressure increasing linearly from zero at ro to q at a; outer edge simply supported
Case 3e to Case 3h
Annular plate with a distributed pressure increasing linearly from zero at ro to q at a; outer edge fixed
Case 3i to Case 3j
Annular plate with a distributed pressure increasing linearly from zero at ro to q at a; outer edge guided
Case 3k to Case 3l
Annular plate with a distributed pressure increasing linearly from zero at ro to q at a; outer edge free
Case 4a to Case 4d
Annular plate with a distributed pressure increasing parabolically from zero at ro to q at a; outer edge simply supported
Case 4e to Case 4h
Annular plate with a distributed pressure increasing parabolically from zero at ro to q at a; outer edge fixed
Case 4i to Case 4j
Annular plate with a distributed pressure increasing parabolically from zero at ro to q at a; outer edge guided
Case 4k to Case 4l
Annular plate with a distributed pressure increasing parabolically from zero at ro to q at a; outer edge free
Case 5a to Case 5d
Annular plate with a uniform line moment Mo at a radius ro; outer edge simply supported
Case 5e to Case 5h
Annular plate with a uniform line moment Mo at a radius ro; outer edge fixed
Case 6a to Case 6d
Annular plate with externally applied change in slope; outer edge simply supported
Case 6e to Case 6h
Annular plate with externally applied change in slope; outer edge fixed
Case 7c to Case 7d
Annular plate with externally applied vertical deformation at a radius ro; outer edge simply supported
Case 7g to Case 7h
Annular plate with externally applied vertical deformation at a radius ro; outer edge fixed
Case 8a to Case 8d
Annular plate with uniform temperature differential between bottom and top surface; outer edge simply supported
Case 8e to Case 8h
Annular plate with uniform temperature differential between bottom and top surface; outer edge fixed
Case 9a
Solid circular plate simply supported; uniform annular line load
Case 9b
Solid circular plate fixed; uniform annular line load
Case 10a
Solid circular plate simply supported; uniformly distributed pressure from ro to a
Case 10b
Solid circular plate fixed; uniformly distributed pressure from ro to a
Case 11a
Solid circular plate simply supported; linearly increasing pressure from ro to a
Case 11b
Solid circular plate fixed; linearly increasing pressure from ro to a
Case 12a
Solid circular plate simply supported; parabolically increasing pressure from ro to a
Case 12b
Solid circular plate fixed; parabolically increasing pressure from ro to a
Case 13a
Solid circular plate simply supported; uniform line moment at ro
Case 13b
Solid circular plate fixed; uniform line moment at ro
Case 14a
Solid circular plate simply supported; externally applied change in slope at ro
Case 14b
Solid circular plate fixed; externally applied change in slope at ro
Case 15a
Solid circular plate simply supported; uniform temperature differential between the bottom and top surface from ro to a
Case 15b
Solid circular plate fixed; uniform temperature differential between the bottom and top surface from ro to a
Case 16
Uniform load over a very small central circular area of radius ro; edge simply supported
Case 17
Uniform load over a very small central circular area of radius ro; edge fixed


TTFN
faq731-376

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[rb1957]

i'm sure timoshenko "plates and shells" solves this loading ... circular plates lend themselves to mathematical solutions ... rectangular ones don't.

is the loading really going to be uniform over the overlapped area ? reality might be closer to a linearly increasing load, towards the (outer) edge of the overlap (the blue plate will tend to deform away from the contact face).

Quando Omni Flunkus Moritati