Optimum Reliability Based Design Criteria for Elastic Structures Subject To Random Dynamic Loads

In this work a new method for the optimal design of generic elastic structures, subject to random dynamic loads, is proposed. Elastic structures are described as deterministic multi-degree of freedom systems in which the structural failure probability, referred to as a first crossing passage problem, is minimized. The proposed method is here applied to optimize the shape of a vertical column with an extra-mass located at the free top end, subject to a base acceleration modeled as a Gaussian, stationary, filtered stochastic process. The elastic threshold crossing probabilities are determined in a finite number of column sections and the objective function is assumed to be a measure of these probabilities. Finally, this measure is minimized under a constant weight constraint (or even under more general conditions).