Developments in stochastic structural mechanics

Schuëller, G.I.

doi:10.1007/s00419-006-0067-z

Cited by 112 publications

(44 citation statements)

References 84 publications

(99 reference statements)

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“…NSIM % 50 permits only a rough approximation of the mean value and variance of the response. With a larger sample size e.g NSIM % 500, it is possible to estimate the CDF of the response [161]. The solution of NSIM deterministic problems has a significant computational cost especially in the combined case of large-scale systems and of considerable stochastic dimension.…”

Section: Direct Mcsmentioning

confidence: 99%

“…A variant of MCS called ''fast MCS" has been recently used for the efficient numerical evaluation of the variability response function [165] needed to calculate spectral-probability distribution-free upper bounds of the response variability of structural systems [134]. Numerous other variants of this approach (importance sampling, subset simulation, line sampling) have been developed in the last decade especially for the efficient solution of reliability problems where the calculation of small failure probabilities requires a very large number of samples [161]. Even a few years ago, the application of the direct MCS to large-scale realistic problems was impossible due to its excessive computational cost.…”

Section: Direct Mcsmentioning

confidence: 99%

“…The most prominent representative of this class of methods is importance sampling (IS), in which the generation of samples is controlled by a sampling distribution concentrated in the ''important" (low-probability) region of the failure domain. The main challenge in the application of IS to physical problems is the determination of the sampling distribution, which depends on the specific system at hand and on the failure domain [161]. The optimal choice of the sampling distribution (for which the variance of the estimator of the probability of failure p F vanishes) is practically infeasible since an a priori knowledge of p F is required for this purpose [163].…”

Section: 32mentioning

confidence: 99%

“…However, for the dynamic reliability analysis of large nonlinear SFE systems in high stochastic dimensions, the computational effort needed to construct a suitable sampling distribution may exceed the effort required by the direct MCS [161].…”

Section: 32mentioning

confidence: 99%

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The stochastic finite element method: Past, present and future

Stefanou

2009

Computer Methods in Applied Mechanics and Engineering

871

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: Direct Mcsmentioning

confidence: 99%

Section: Direct Mcsmentioning

confidence: 99%

Section: 32mentioning

confidence: 99%

Section: 32mentioning

confidence: 99%

See 2 more Smart Citations

The stochastic finite element method: Past, present and future

Stefanou

2009

Computer Methods in Applied Mechanics and Engineering

871

407

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“…Such an approach is very well adapted and very efficient to take into account the uncertainties on the computational model parameters as soon as the probability theory can be used. Many works have been published in this field and a state-of-the-art can be found, for instance, in [1,2,3,4,5,6,7,8,9,10,11]. Nevertheless, the parametric probabilistic approach does not allow the modeling uncertainties to be taken into account (see for instance [12,13]).…”

Section: Types Of Approach For Stochastic Modeling Of Uncertaintiesmentioning

confidence: 99%

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

Soize

2013

Journal of Sound and Vibration

140

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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Probability density evolution method for seismic liquefaction performance analysis of earth dam

Huang

Xiong

2016

Earthq Engng Struct Dyn

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Summary To investigate the seismic liquefaction performance of earth dams under earthquake loading, we present a new methodology for evaluating the seismic response of earth dams based on a performance‐based approach and a stochastic vibration method. This study assesses an earthfill dam located in a high‐intensity seismic region of eastern China. The seismic design levels and corresponding performance indexes are selected according to performance‐based criteria and dam seismic codes. Then, nonlinear constitutive models are used to derive an array of deterministic seismic responses of the earth dam by dynamic time series analysis based on a finite element model. Based on these responses, the stochastic seismic responses and dynamic reliability of the earth dam are obtained using the probability density evolution method. Finally, the seismic performance of the earth dam is assessed by the performance‐based and reliability criteria. Our results demonstrate the accuracy of the seismic response analysis of earth dams using the random vibration method. This new method of dynamic performance analysis of earth dams demonstrates that performance‐based criteria and reliability evaluation can provide more objective indices for decision‐making rather than using deterministic seismic acceleration time series as is the current normal practice. Copyright © 2016 John Wiley & Sons, Ltd.

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Developments in stochastic structural mechanics

Cited by 112 publications

References 84 publications

The stochastic finite element method: Past, present and future

The stochastic finite element method: Past, present and future

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

Probability density evolution method for seismic liquefaction performance analysis of earth dam

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