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Quasi random numbers in stochastic finite element analysis

Published online by Cambridge University Press:  17 August 2007

Géraud Blatman ,
Bruno Sudret  and
Marc Berveiller
Géraud Blatman
Affiliation:
EDF R&D, Département Matériaux et Mécanique des Composants, Site des Renardières, 77818 Moret-sur-Loing, France Institut Français de Mécanique Avancée et Université Blaise Pascal, Laboratoire de Mécanique et d'Ingénieries, Campus des Cézeaux, 63175 Aubière Cedex, France
Bruno Sudret
Affiliation:
EDF R&D, Département Matériaux et Mécanique des Composants, Site des Renardières, 77818 Moret-sur-Loing, France
Marc Berveiller
Affiliation:
EDF R&D, Département Matériaux et Mécanique des Composants, Site des Renardières, 77818 Moret-sur-Loing, France
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Abstract

A non-intrusive stochastic finite-element method is proposed for uncertainty propagation through mechanical systems with uncertain input described by random variables. A polynomial chaos expansion (PCE) of the random response is used. Each PCE coefficient is cast as a multi-dimensional integral when using a projection scheme. Common simulation schemes, e.g. Monte Carlo Sampling (MCS) or Latin Hypercube Sampling (LHS), may be used to estimate these integrals, at a low convergence rate though. As an alternative, quasi-Monte Carlo (QMC) methods, which make use of quasi-random sequences, are proposed to provide rapidly converging estimates. The Sobol' sequence is more specifically used in this paper. The accuracy of the QMC approach is illustrated by the case study of a truss structure with random member properties (Young's modulus and cross section) and random loading. It is shown that QMC outperforms MCS and LHS techniques for moment, sensitivity and reliability analyses.

Keywords

Uncertainty propagationstochastic finite-elementsnon intrusive spectral approachpolynomial chaos expansionquasi-random numbersstructural reliabilityPropagation d'incertitudeséléments-finis stochastiquesapproche non intrusivechaos polynomialnombres quasi-aléatoiresfiabilité des structures
Type
Research Article
Information
Mechanics & Industry , Volume 8 , Issue 3: Congrès Mécanique de Grenoble , May 2007 , pp. 289 - 297
Copyright
© AFM, EDP Sciences, 2007

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