A stochastic finite element procedure for moment and reliability analysis

Sudret, Bruno; Berveiller, Marc; Lemaire, Maurice

doi:10.3166/remn.15.825-866

Cited by 39 publications

(29 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…SPDEs are useful when one cannot, or does not want to, describe precisely the microstructure. Examples include uncertainty quantification for structures in civil engineering [8,48], for complex flows in fluid dynamics [28], or for multiphase flows in porous media [14].…”

Section: Stochastic Partial Differential Equationsmentioning

confidence: 99%

A reduced basis approach for variational problems with stochastic parameters: Application to heat conduction with variable Robin coefficient

Boyaval

Bris

Maday

et al. 2009

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

In this work, a Reduced Basis (RB) approach is used to solve a large number of boundary value problems parametrized by a stochastic input -expressed as a Karhunen-Loève expansion -in order to compute outputs that are smooth functionals of the random solution fields. The RB method proposed here for variational problems parametrized by stochastic coefficients bears many similarities to the RB approach developed previously for deterministic systems. However, the stochastic framework requires the development of new a posteriori estimates for "statistical" outputs -such as the first two moments of integrals of the random solution fields; these error bounds, in turn, permit efficient sampling of the input stochastic parameters and fast reliable computation of the outputs in particular in the many-query context.

show abstract

Section: Stochastic Partial Differential Equationsmentioning

confidence: 99%

A reduced basis approach for variational problems with stochastic parameters: Application to heat conduction with variable Robin coefficient

Boyaval

Bris

Maday

et al. 2009

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

show abstract

“…The limitation of these approaches is that the available data do not always represent well the full range of variation of the governing parameters. A response-surface methodology combined with the numerical evaluation of the ultimate strength can be an answer to this problem [8]. This approach can have different strategies for covering the relevant range of variation of the parameters.…”

Section: Response-surface Methods For Ultimate Strength Of the T-stubmentioning

confidence: 99%

“…Another advantage is the possibility to perform parametric studies which can give information about importance of various structural elements from which a T-stub is a part. On behalf of this aim a modelling using probabilistic framework often takes place [8].…”

Section: Introductionmentioning

confidence: 99%

A probabilistic approach for a T-stub ultimate strength assessment using response-surface approximation

Kurčik

ir²,

Vičan

2008

Per. Pol. Civil Eng.

View full text Add to dashboard Cite

The main goal of the study is to examine and demonstrate the application of a developed probabilistic framework to the analysis of a chosen general type of steel connection component in order to obtain the basic characteristics of its mechanical behaviour with regard to the chosen type of the input geometry and material properties. Accordingly, as a typical representative of the component method proposed by the Eurocode the equivalent T-stub was chosen as a subject of the study. This type of structural element has the capability to address the behaviour of several parts of the connection: column flange in bending, end plate in bending and flange cleat in bending. A method is proposed to determine the probability density function of the ultimate strength using a response-surface approach coupled with FEM applied to a stochastic structural model. The results of a study were processed by means of sensitivity analysis to determine the importance level of the input variables.Keywords steel connection · T-stub ultimate strength · finite element model · response-surface method · stochastic model · MonteCarlo simulation · sensitivity analysis Acknowledgement

show abstract

“…Often, the form of equations or code used to solve the deterministic equations is complex and it makes the implementation of the PC difficult, if not impossible. Therefore, non-intrusive methods have been proposed based on regression technique [30,31] or on projection method [19,20]. Instead of building prior expansions of uncertainty sources and of finding the coefficients by solving the corresponding equations, these approaches use interpolation methods and project a set of deterministic simulations, which are defined using samples of parameters chosen carefully, with a polynomial basis.…”

Section: Determination Of the Pc Coefficientsmentioning

confidence: 99%

Sensitivity study of dynamic systems using polynomial chaos

Sandoval

Anstett-Collin

Basset

2012

Reliability Engineering & System Safety

View full text Add to dashboard Cite

Global sensitivity has mainly been analyzed in static models, though most physical systems can be described by differential equations. Very few approaches have been proposed for the sensitivity of dynamic models and the only ones are local. Nevertheless, it would be of great interest to consider the entire uncertainty range of parameters since they can vary within large intervals depending on their meaning. Other advantage of global analysis is that the sensitivity indices of a given parameter are evaluated while all the other parameters can be varied. In this way, the relative variability of each parameter is taken into account, revealing any possible interactions. This paper presents the global sensitivity analysis for dynamic models with an original approach based on the polynomial chaos (PC) expansion of the output. The evaluation of the PC expansion of the output is less expensive compared to direct simulations. Moreover, at each time instant, the coefficients of the PC decomposition convey the parameter sensitivity and then a sensitivity function can be obtained. The PC coefficients are determined using non-intrusive methods. The proposed approach is illustrated with some well-known dynamic systems.

show abstract

A stochastic finite element procedure for moment and reliability analysis

Cited by 39 publications

References 38 publications

A reduced basis approach for variational problems with stochastic parameters: Application to heat conduction with variable Robin coefficient

A reduced basis approach for variational problems with stochastic parameters: Application to heat conduction with variable Robin coefficient

A probabilistic approach for a T-stub ultimate strength assessment using response-surface approximation

Sensitivity study of dynamic systems using polynomial chaos

Contact Info

Product

Resources

About