Coupling finite element and reliability analysis through proper generalized decomposition model reduction

Abstract : The FEM is the main tool used for structural analysis. When the design of the mechanical system involves uncertain parameters, a coupling of the FEM with reliability analysis algorithms allows to compute the failure probability of the system. However, this coupling leads to successive finite element analysis of parametric models involving high computational effort. Over the past years, model reduction techniques have been developed in order to reduce the computational requirements in the numerical simulation of complex models. The objective of this work is to propose an efficient methodology to compute the failure probability for a multi-material elastic structure, where the Young moduli are considered as uncertain variables. A proper generalized decomposition algorithm is developed to compute the solution of parametric multi-material model. This parametrized solution is used in conjunction with a first-order reliability method to compute the failure probability of the structure. Applications to multilayered structures in two-dimensional plane elasticity are presented.
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L. Gallimard, P. Vidal, O. Polit. Coupling finite element and reliability analysis through proper generalized decomposition model reduction. International Journal for Numerical Methods in Engineering, Wiley, 2013, 95 (13), pp.1079-1093. ⟨10.1002/nme.4548⟩. ⟨hal-01366918⟩

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