Reduction of the stochastic finite element models using a robust dynamic condensation method

One of the ways in which models of structural dynamics can be improved is by taking the various uncertainties that exist into consideration. This would also increase the reliability of predicted calculation trends in these models. Here, an original, robust, multi-level dynamic condensation method of stochastic models is proposed. The first-level condensation is based on a strategy that combines the stochastic finite element method (SFEM) with the robust condensation model. It is based on a discretization technique of random fields that was established using the Karhunen–Loeve procedure. In addition, the use of dynamic condensation was aided by random residual static responses. The consequent loads are representative of local modifications per zone (or component) of the mechanical structure. For the second-level condensation use of the polynomial chaos (PC) approach allows the presence of uncertainties in the design parameters to be taken into account and, also, the variability of the response can be analysed in a less costly manner than by using the Monte Carlo method. Alternatively, a modal perturbation (MP) approach allows rapid synthesis of the random response. We show how either of these can be used to give an accurate prediction of the condensed model and a considerable reduction of the calculation costs. Two numerical examples are presented to illustrate the performance of the proposed method.