From: "Good, Donald" 
To: 'Mel Bartels' , atm{at}shore.net
Reply-To: "Good, Donald" 


The book reference is
Stresses in Plates and Shells
A. C. Ugural, PhD
McGraw-Hill
1981
ISBN 0-07-065730-0

Unfortunately, this problem does not fit the assumptions of the Kirchhoff
hypotheses which simplifies the problem by assuming bending only.  The
thinness of the glass implies that the deformation will likely be greater
than the thickness, and therefore, stretching (as in the case of an
inflated balloon) cannot be ignored.

-----Original Message-----
From: Mel Bartels [mailto:mbartels{at}efn.org]
Sent: Thursday, January 30, 2003 10:14 PM To: atm{at}shore.net
Subject: ATM deformed mirror shape



I was asked in a private email the derivation of the deformed shape where:

1. glass considered thin meniscus of constant thickness (ex. 12 inch
diameter, 1/4 inch thick)

2. glass supported at extreme edge (supported inward better???)

3. glass facing upward towards zenith

What is the resulting shape?

Years ago Tom Lum and I derived this - and I cannot remember for certainty
if the shape is parabolic or spherical.

Can anyone take a stab or point to articles?

TIA Mel Bartels

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