SUBSTRUCTURING: APPLICATION TO UNCERTAINTY ANALYSIS IN STRUCTURAL DYNAMICS

Abstract eng:
Uncertainty analysis in structural dynamics is the subject of active research as it covers a wide range of relevant problems such as reliability analysis, reliability sensitivity analysis, Bayesian finite element model updating, reliability-based design optimization, modal sensitivity analysis, etc. A common aspect of these problems is that their solution demands considerable numerical efforts due to the large number of full model re-analyses to be performed during the corresponding simulation processes. Thus, the associated computational cost may be large or even excessive. To cope with the aforementioned challenge, an efficient model reduction technique based on substructure coupling for dynamic analysis is presented in this talk. The dynamic behavior of the substructures is described by a set of normal modes corresponding to the fixed-interface normal modes of individual substructures plus a set of static vectors that account for the coupling at each interface where the substructures are connected. The internal dynamic behavior of the substructures is enhanced by considering the contribution of residual fixed-interface normal modes. On the other hand, the interface degrees of freedom are reduced by considering a small number of characteristic constraint modes. The method produces highly accurate reduced-order models with relatively few modes. When the method is combined with an effective model parametrization scheme, all matrices involved in the characterization of the reducedorder model are computed and assembled once during the entire simulation processes. This result has important implications from the numerical implementation point of view since it allows carrying out the reanalyses efficiently. Numerical examples, in the context of several applications, are presented to demonstrate the effectiveness of the proposed strategy. Validation calculations show that the computational efforts are decreased by two or three orders of magnitude with respect to full model simulations. The drastic reduction is achieved without compromising the accuracy of the results.

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