Optimum Design of Structures Subjected to Random Loads : Optimization by Approximate Sensitivity

Abstract

This paper considers a shape determination problem of beams which are subjected to given random, loads. taking into consideration its dynamic responses. The optimum, shape is considered as one which minimizes the expected value of the strain energy that will be induced in the structure for a constant volume. A beam is discretized into finite elements and the method of modal analysis is applied to obtain its stationary response against Gaussian excitation. In the numerical treatment, an approximate method for sensitivity analysis is proposed and it works effectively with the use of a convenient optimization procedure by the "Energy-Ratio-Method". A considerable reduction of the expected value of strain energy is accomplished by several iterations of shape reformation. When the beam is supported symmetrically at both ends and is subjected to a concentrated load, the obtained beam has a symmetric shape with respect to Its central cross section, independently of the location of the load.