Theoretical Elastic Deformations of Solid and Cored Horizontal Circular Mirrors Having a Central Hole on a Ring Support

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Abstract
This paper gives exact, closed-form expressions for the deflection under its own weight, moments, and shears, in a thick, solid, horizontally oriented, circular mirror having a central hole on a ring support. A theory, developed by Reissner for thick plates, that includes shear deformations is used, and it is shown how the results for the solid mirror can be reduced to obtain results for cored, or sandwich, mirrors. It is found that 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. Numerical results are presented and interpreted in detail.