deformation of a circular plate 1

[winterfell99]

Hi all, I have a circular plate with a diameter of 100mm and thickness of 10mm. One face of the plate has a 8mm deep hole with 20mm diameter at its center. The edge of the plate is clamped and a uniformly distributed load of 50Pa is applied to the face without hole. How can I calculate the deformation of this plate?

 

[Tunalover]

For the worst-case deflection assume the plate is only 2mm thick and has no hole in it. Then use Roark's Formulas for Stress and Strain. That book will have the deflection formula for a uniformly clamped circular plate with a uniform pressure applied normal to the surface. Otherwise use FEA and a cylindrical coordinate system. The stress along the bottom perimeter of the 20mm hole will be high so that will probably need to be checked!

Tunalover

 

[IRstuff]

Roark has annular plate equations, and one could probably take a similar approach as above, but use the default annular ring with the entire load as a line load at the edge of the hole, and vary the load al the way up to fully distributed

TTFN
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[prex]

If it is really clamped, you can calculate it as a solid plate, as the maximum stress not at center.
However I can't visualize how such a beast (t/R=0.2!) can be effectively clamped.


prex
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[Tunalover]

I think you can calculate the relative deflection of the 2mm thick "plate" by assuming it's rigidly clamped by the annulus. This design does not look good with only a 2mm thick membrane in the middle!


Tunalover

 

[JStephen]

You should be able to combine two or more load cases from Roark- equate the outside moment and rotation angle from one with the inside moment and rotation angle from the other. It'll be kind of a mess, but doable.