Optimization of viscoelastic systems combining robust condensation and metamodeling

Abstract

Passive control is recognized as being advantageous in terms of stability, effectiveness in broader bandwidths and ease of implementation (Nashif et al., 1985). In particular, the use of viscoelastic materials has been regarded as a convenient strategy in many types of industrial applications, where they can be applied either as discrete devices or surface treatments at a relatively low cost (Samali and Kwok, 1995;Rao, 2001;de Lima et al., 2009; Espíndola et al., 2005). However, viscoelastic materials present some inherent drawbacks such as the influence of operational and environmental factors (frequency, temperature, pre-loads, moisture, etc.). Also, viscoelastic damping systems (specially, surface treatments) are prone to induce considerable mass additions. This last feature leads to the necessity of performing optimization aiming at achieving the desired performance and, at the same time, complying with design and construction constraints.In the last decades, much effort has been devoted to the development of finite element (FE) models capable of accounting for the typical dependence of the viscoelastic behavior with respect to frequency and temperature (Bagley and Torvik, 1983;MacTavish and Hughes, 1993;Lesieutre and Lee, 1996;Galucio et al., 2004). As a result, it is currently possible to model complex real-world engineering structures such as automobiles, airplanes, communication satellites, buildings and space structures (Balmès and Germès, 2002). A natural extension of this modeling capability is the optimization of the viscoelastic devices aiming the reduction of cost and/or the maximization of performance (Hao et al., 2004;Lee et al., 2004). In the quest for optimization, engineers are frequently faced with conflicting objectives. Such situations are conveniently dealt with by the so-called multiobjective or multicriteria optimization approach (Eschenauer et al., 1990). However, multiobjective optimization generally requires a large number of evaluations of the cost functions involved. For large finite element models of viscoelastic systems, typically composed of many thousands of degrees-of-freedom (DOFs), if such evaluations are made based on exact response computations performed on the full FE matrices, computation times can become prohibitive.The work reported herein intends to propose a general strategy for the reduction of the computational burden involved in the optimization of viscoelastic structures by combining Multiobjective Evolutionary Algorithms (MOEAs), robust condensation and Artificial Neural Networks (ANNs). The motivation for the use of (2002) and Masson et al. (2003), which is based on the use of an enriched modal basis for approximate model reduction. A so-named robust basis is constructed to take into account the structural modifications introduced by the inclusion of the viscoelastic treatments into the original system in such a way that updating of the reduction basis by exact re-analysis is avoided, leading to a drastic reduction of the time required to evaluate the cost fun...

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