Robust and efficient methods for stochastic finite element analysis using Monte Carlo simulation

Papadrakakis, Manolis; Papadopoulos, Vissarion

doi:10.1016/0045-7825(95)00978-7

Cited by 164 publications

(98 citation statements)

References 20 publications

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“…Spectral representation has also been successfully implemented in the framework of Monte Carlo simulation (MCS) for the solution of realistic problems with the stochastic finite element approach e.g. [4,20,99,133,[135][136][137][138]145,146,173].…”

Section: The Spectral Representation Methodsmentioning

confidence: 99%

The stochastic finite element method: Past, present and future

Stefanou

2009

Computer Methods in Applied Mechanics and Engineering

838

407

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a b s t r a c tA powerful tool in computational stochastic mechanics is the stochastic finite element method (SFEM). SFEM is an extension of the classical deterministic FE approach to the stochastic framework i.e. to the solution of static and dynamic problems with stochastic mechanical, geometric and/or loading properties. The considerable attention that SFEM received over the last decade can be mainly attributed to the spectacular growth of computing power rendering possible the efficient treatment of large-scale problems. This article aims at providing a state-of-the-art review of past and recent developments in the SFEM area and indicating future directions as well as some open issues to be examined by the computational mechanics community in the future.

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Section: The Spectral Representation Methodsmentioning

confidence: 99%

The stochastic finite element method: Past, present and future

Stefanou

2009

Computer Methods in Applied Mechanics and Engineering

838

407

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“…(1) or (2) is obtained by applying a suitable preconditioner at each iteration to accelerate PCG convergence during the successive FE solutions [1,2]. For this purpose, the FE equations (1) are replaced by the equivalent system:…”

Section: The Pcg-k0 Solution Methodsmentioning

confidence: 99%

“…[1,2,[4][5][6][7][8][9][10][11][12]). In the present work, an established PCG-based solution method is overviewed and a new FPI-based solution method is introduced.…”

Section: Reanalysis Problems In MC Simulation-based Stochastic Fe Anamentioning

confidence: 99%

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Efficient Iterative Solution Techniques for Finite Element Reanalyses in the Context of Monte Carlo Simulation

Charmpis¹

2015

Proceedings of the 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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“…Finally, the direct Monte Carlo numerical simulation method (see for instance [117,87,88] is a very effective and efficient method because this method (1) is non-intrusive, (2) is adapted to massively parallel computation without any software developments and (3) is such that its convergence can be controlled during the computation and (4) the speed of convergence is independent of the dimension. The speed of convergence of the Monte Carlo method can be improved using advanced Monte Carlo simulation procedures [118,119,120,121], subset simulation technics [122], important sampling for high dimension problems [123], local domain Monte Carlo Simulation [124].…”

Section: Propagation Of Uncertainties or What Are The Methods To Solvmentioning

confidence: 99%

Stochastic modeling of uncertainties in computational structural dynamics—Recent theoretical advances

Soize

2013

Journal of Sound and Vibration

137

106

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To cite this version:Christian Soize. Stochastic modeling of uncertainties in computational structural dynamics -Recent theoretical advances. Journal of Sound and Vibration, Elsevier, 2013, 332 (10) AbstractThis paper deals with a short overview on stochastic modeling of uncertainties. We introduce the types of uncertainties, the variability of real systems, the types of probabilistic approaches, the representations for the stochastic models of uncertainties, the construction of the stochastic models using the maximum entropy principle, the propagation of uncertainties, the methods to solve the stochastic dynamical equations, the identification of the prior and the posterior stochastic models, the robust updating of the computational models and the robust design with uncertain computational models. We present recent theoretical advances in this field concerning the parametric and the nonparametric probabilistic approaches of uncertainties in computational structural dynamics for the construction of the prior stochastic models of both the uncertainties on the computational model parameters and on the modeling uncertainties, and for their identification with experimental data. We also present the construction of the posterior stochastic model of uncertainties using the Bayesian method when experimental data are available.

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Robust and efficient methods for stochastic finite element analysis using Monte Carlo simulation

Cited by 164 publications

References 20 publications

The stochastic finite element method: Past, present and future

The stochastic finite element method: Past, present and future

Efficient Iterative Solution Techniques for Finite Element Reanalyses in the Context of Monte Carlo Simulation

Stochastic modeling of uncertainties in computational structural dynamics—Recent theoretical advances

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