Stress and Strain in Spinning Paraboloid Dishes—2

Abstract

Solutions for the stress and strain systems in spinning paraboloid dishes, both holed and whole, are presented. They are applicable to all such dishes of aperture small enough to justify the usual approximation for small angles of cos θ ≈ 1, sin θ ≈ 0. The direct stress p, the hoop stress f, the shear stress s, the bending moments Mθ and Mφ , and the radial displacement Δ are obtained as power series in θ, the angular distance of any point of the dish at the center of the sphere of curvature at the dish apex. These series in θ are expressed in terms of tabulated coefficients which are essentially functions of a single basic dish parameter Rα2 /h. The range for Rα2 /h covered is 0 ≤ Rα2 /h ≤ 10.