This work presents a methodology for the construction of an uncertain nonlinear computational model adapted to the static analysis of a complex mechanical system. The deterministic nonlinear computational model is constructed with the finite element method using a total Lagrangian formulation. The finite element nonlinear response is then considered as a reference deterministic solution from which a reduced-order basis is constructed using the POD (Proper Orthogonal Decomposition) methodology. The mean reduced nonlinear computational model is thus obtained by projecting the reference deterministic solution on this basis. The explicit construction of the mean reduced nonlinear computational model is proposed for any type of structure modeled with three-dimensional solid finite elements. A procedure for the robust identification of the uncertain nonlinear computational model with respect to experimental responses is then given. Finally, the methodology is applied to a structure for which simulated experiments are given.
Uncertainty Quantification in Computational Nonlinear Elasticity
Capiez-Lernout, E, Soize, C, & Mignolet, M. "Uncertainty Quantification in Computational Nonlinear Elasticity." Proceedings of the ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis. Volume 1: Advanced Computational Mechanics; Advanced Simulation-Based Engineering Sciences; Virtual and Augmented Reality; Applied Solid Mechanics and Material Processing; Dynamical Systems and Control. Nantes, France. July 2–4, 2012. pp. 123-132. ASME. https://doi.org/10.1115/ESDA2012-82246
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