Robust tools for prediction of variability and optimization in structural dynamics

The aims of this work were to quantify the effects of uncertainties of design parameters on the variability of linear and non-linear behaviour of mechanical structures that we wish to optimize, and to calculate optimal and robust solutions resulting from numerical simulations. We propose a method that takes into account the propagation of uncertainties in finite-element models in a multi-objective optimization procedure. This method is based on coupling the stochastic response surface method (SRSM) and the non-dominated sorting genetic algorithm (NSGA). SRSM is based on application of the stochastic finite-element method via the polynomial chaos expansion method or the modal perturbation method. This strategy avoids the use of Monte Carlo simulation, in which costs can become prohibitive in optimization problems, especially when the finite-element models are large and have a considerable number of design parameters. The robust design described here has been developed to obtain an optimum value that is insensitive to changes of design variables within a feasible range.