Design of equi-strength annular disks made of functionally graded materials

Abstract

This research proposes a robust method for designing functionally graded disks subject to internal and external pressures. The design objective is to find the profile of equi-strength disks. The von Mises yield criterion controls the initiation of plastic yielding. The yield stress and Young’s modulus are entirely arbitrary functions of the polar radius. Poisson’s ratio is constant. The solution is facilitated using the dimensionless yield stress as an independent variable instead of the polar radius. In particular, a numerical technique is only required to solve two ordinary differential equations. Moreover, one of these equations is independent of the other. Therefore, the equations can be solved individually, simplifying the solution method. The limitation imposed by the thickness gradient on the acceptability of plane stress conditions is considered. Particular designs are proposed assuming that the power function describes the radial distribution of material properties. A critical condition that allows for deriving relatively simple design solutions is emphasized. It is shown that this condition is satisfied for many specific material property distributions used in the literature.