Volume Minimization of Thin Plates Subject to Constraints

A thin plate of exponentially varying thickness is loaded axisymmetrically and is minimized for volume satisfying two constraints. In addition, the material is homogeneous and isotropic. Thus, minimum volume yields minimum weight. Only uniform load is considered. Such a combination of constraints may be required for pressure-sensitive devices and where clearances are tight. The state of stress in the plate remains everywehre elastic. A major contention of this paper is that volume minimization of thin plates should be considered in terms of certain classes of diametral shapes. Starting with the differential equation of equilibrium and von Mises' yield equation, the necessary mathematics is developed to effect the minimization process, and the resulting equations, containing infinite power series, are solved on the digital computer. A few representative design curves are plotted for wide ranges of values of the variables for the plate simply supported at the boundary. Sample calculations are given.