Book2012

Stochastic Models of Uncertainties in Computational Mechanics

112 citations0/0 files storedAmerican Society of Civil Engineers eBooks

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Probabilistic and Robust Engineering Design Geotechnical Engineering and Analysis Structural Health Monitoring Techniques

Abstract

We present an overview concerning the main concepts, formulations and advances, including new results, for the stochastic modeling of uncertainties and random fields in computational mechanics. In a first part, the parametric probabilistic approach, the nonparametric probabilistic approach and the generalized probabilistic approach of uncertainties are presented in the context of linear and nonlinear structural dynamics and in structural acoustics and vibration, including not only the construction of prior probability models but also the identification of posterior probability models. In a second part, a set of recent results is presented and is devoted to the construction of prior probability models and the identification of posterior probability models with an application to the mesoscale modeling of heterogeneous elastic microstructures.

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References

2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations 2003Modeling uncertainty in flow simulations via generalized polynomial chaos 2007A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data 2010Spectral Methods for Uncertainty Quantification 2008A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data 2008Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics 2004Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure 2005An adaptive multi-element generalized polynomial chaos method for stochastic differential equations

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