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On the self-weight sag of plate-like structures with application to mirror substrate design Talapatra, Dipak Chandra

Abstract

The thesis investigates the self-weight sag of plate-like structures with application to astronomical mirrors. The exact analytical solution for the self-weight deflection of a circular disc is obtained by superposition of various elementary solutions due to Love, and the validity of the existing approximate procedures is examined. Guided by the concept of arch-like structures for optimum design, a finite element formulation for an axi-symmetrical solid is developed from first principles in terms of triangular ring-elements. Solutions are obtained for various structural configurations constructed within the enevlope of the disc. The superiority of arch-type designs over solid discs with respect to deflection and weight is established and their attractive potential demonstrated. The extensive experimental programme involving frozen stress photoelasticity in conjunction with immersion analogy of gravitational stress and fringe multiplication, clearly emphasizes some of the limitations of this approach. It establishes that a success of the method is dependent upon the availability of a sufficiently stress free araldite. Although not generally followed by stress analysts, a direct measurement of frozen body-force induced displacements is attempted. The phenomenon of continuous polymerization of the model material, hitherto overlooked by photoelasticians, appears to play a decisive role in the measurement of minute self-weight induced deformations. The direct use of silicone rubber models successfully determines the displacements in mirrors, in the form of solid disc and arched dome, and establishes the superiority of the latter.

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