OPTIMUM DESIGN OF STRUCTURES WITH REGARD TO THEIR VIBRATIONAL CHARACTERISTICS - 1. A GENERAL METHOD OF OPTIMUM DESIGN.

An attempt is made to establish a general method or algorithm for solving optimum structural design problems, in which natural frequencies are involved in objective functions and/or in conditions of constraints. The proposed method has wide adaptability to various geometries of structures, by making use of the large matrix method or the transfer matrix method for vibration analysis, after discretizing structures by finite-element idealization. As Rosen's gradient projection method is also employed for optimization technique, the present method can be applied to structures having a number of constraints and design variables even in the case that constraints and objective functions appear in nonlinear forms. Moreover, it is found that the procedure given here, for evaluating gradients of frequency-involved quantities with respect to the design variables, can be utilized in any eigenvalue problems and for other optimization techniques.