This paper shows how exact, closed-form expressions can be determined for the deflections under its own weight of a thick, horizontally oriented, circular mirror on a ring support. A theory developed by Reissner for thick plates that includes shear deformations is used, and the results are reduced to those of classical plate theory. An optimum support radius is obtained, for which the center deflection is equal to the deflection of the outer edge. For mirrors having thickness-to-diameter ratios greater than approximately one-tenth, shearing deformations can contribute significantly to the total deflection and hence should not be neglected.
L. A. Selke, "Theoretical Elastic Deflections of a Thick Horizontal Circular Mirror on a Ring Support," Appl. Opt. 9, 149-153 (1970)