An optimization method for the design of structures for maximum fundamental frequency.

Abstract

An optimization method to maximize the fundamental frequency of a structure is developed. The procedure uses the stresses due to the mechanical loading and the free-vibration mode shapes to determine design coefficients for the elements. Each element of the structure is assigned a design coefficient rated on a scale of zero to ten. The design coefficients are used to modify an initial design following an iterative procedure. This method of optimal structural design, referred to as the Maximum Stiffness Design (MSD), may be classified as an intuitive optimality criteria method. The MSD method is demonstrated by increasing the fundamental frequency of simple beam structures, truss structures, and complex structures. These examples include a support structure for a telescope, a support structure for a beam collapser, an airplane wing, and a truss railroad bridge. The MSD optimization method is compared to NASTRAN's Design Sensitivity Analysis to provide a benchmark comparison. It is shown that the MSD method compares well to NASTRAN's optimization method. Furthermore, the optimization technique is used to develop optimum contour shapes for single arch, double arch, and edge-supported mirrors.