An Approach to Optimum Shape Determination for a Class of Thin Shells of Revolution

Abstract

A method is presented for the determination of an optimum shape of a convex shell of revolution with respect to volume and weight. The technique depends on selecting a multiparameter equation and varying the parameters to achieve a near optimum shape for prescribed failure criteria. As an illustration of the method, the first quadrant of the meridian (x/a)α + (y/b)β = 1 is selected. Here a, b, α, and β are positive constants not necessarily integers, with α and β equal to or greater than unity. Variations in shape are expressed in terms of the parameters b/a, α and β. The procedure is applied to the selection of a thin shell which will fit within the space defined by a circular cylinder of radius b and length 2a. The shell is optimized, in terms of α and β, with respect to volume and weight. The numerical iteration was performed by means of a digital computer.