Optimum profiles of disks subject to frequency or stress constraints

A numerical procedure has been applied to the optimization of the profiles of stationary or rotating disks in the presence of geometric and frequency or stress constraints. The method utilized the Davidon-Fletcher-Powell routine for optimization, and the frequency and stress calculations were performed with the Finite Element Method using linearly tapered annular elements to mathematically model the disks. The disks in the procedure were axisymmetric, symmetrical about the middle plane, and had constant inner and outer diameters. The assumptions were made that the stresses were within the elastic range and that the disks were thin. Two approaches were used to define a disk profile: by defining the thickness at descrete points along the radius or by using a polynomial to define the thickness as a function of radius. Several numeric a.1 examples have been computed to demonstrate the procedure and to make comparisons with the results obtained by other investigators as well as to compare the two approaches used in defining the disk profile. In addition, a limited study was made with the numerical examples to Investigate the input parameters controlling the Davidon-Fletcher-Powell method.