Nonlinear geometric modeling of uncertain structures through nonintrusive reduced-order modeling

Abstract : Over the last two decades, maximum entropy concepts have been broadly used to model uncertainties in structures directly at the level of reduced order models (ROMs) of their response, see [1] for review. Among these investigations are a few applications of the methodology to structures in the nonlinear geometric range [2-6] in which two approaches have been used to generate the deterministic ROM on which the uncertainty is built. In the first one of these [3-6], the coefficients of the deterministic ROM are determined using a dedicated finite element strategy from which the introduction of uncertainty is then carried out straightforwardly. The second approach, exemplified solely in [2], relies on a well practiced nonintrusive technique [7] to obtain the deterministic ROM from standard/commercial finite element software. This approach faces two key challenges, of decomposition and non-positive definiteness, in transforming this ROM into one that is suitable for the uncertainty analysis. The focus of the present investigation is on efficiently resolving these two challenges and applying them to a representative set of structures in the nonlinear geometric regimes. REFERENCES [1] Soize, C., (2012). Stochastic Models of Uncertainties in Computational Mechanics. American Society of Civil Engineers. [2] Mignolet, M.P., and Soize, C., (2008). Stochastic Reduced Order Models for Uncertain Geometrically Nonlinear Dynamical Systems, Computer Methods in Applied Mechanics and Engineering 197, 3951-3963. [3] Capiez-Lernout, E., Soize, C., and Mignolet, M.P., (2014). Post-buckling nonlinear static and dynamical analyses of uncertain cylindrical shells and experimental validation, Computer Methods in Applied Mechanics and Engineering 271, 210-230. [4] Capiez-Lernout, E., Soize, C., and Mignolet, M.P., (2012). Computational Stochastic Statics of an Uncertain Curved Structure with Geometrical Nonlinearity in Three-Dimensional Elasticity, Computational Mechanics 49, 87-97. [5] Capiez-Lernout, E., and Soize, C., (2015). Uncertainty Quantification for an Industrial Mistuned Bladed Disk with Geometrical Nonlinearities, Proceeding of the ASME Turbo Expo 2015, Montreal, Quebec, Canada, June 15–19. Paper No. GT2015-42471. [6] Capiez-Lernout, E., and Soize, C., (2017). An Improvement of the Uncertainty Quantification in Computational Structural Dynamics with Nonlinear Geometrical Effects, International Journal for Uncertainty Quantification 7, 83-98. [7] Mignolet, M.P., Przekop, A., Rizzi, S.A, and Spottswood, S.M., (2013). A Review of Indirect/Non-Intrusive Reduced Order Modeling of Nonlinear Geometric Structures, Journal of Sound and Vibration, 332, 2437-2460.
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Contributor : Christian Soize <>
Submitted on : Thursday, June 7, 2018 - 10:37:08 PM
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X. Q. Wang, Marc Mignolet, Christian Soize. Nonlinear geometric modeling of uncertain structures through nonintrusive reduced-order modeling. Eighth Conference on Computational Stochastic Mechanics (CSM8), Jun 2018, Paros, Greece. ⟨hal-01810489⟩

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