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Xiu, D.B. and Em Karniadakis, G. (2003) Modeling Uncertainty in Steady State Diffusion Problems via Generalized Polynomial Chaos. Computer Methods in Applied Mechanics and Engineering, 191, 4927-4948.
http://dx.doi.org/10.1016/S0045-7825(02)00421-8

has been cited by the following article:

• TITLE: Elastic Stress Predictor for Stochastic Finite Element Problems

  AUTHORS: Drakos Stefanos

  KEYWORDS: Polynomial Chaos, Stochastic Finite Element, Karhunen-Loeve Expansion, Quantification of Uncertainty

  JOURNAL NAME: World Journal of Mechanics, Vol.5 No.11, November 16, 2015

  ABSTRACT: The paper presents a new algorithm of elastic stress predictor in non linear stochastic finite element method using the Generalized Polynomial Chaos. The statistical moments of strains calculated based on the displacement Polynomial Chaos expansion. To descretise the stochastic process of material the Karhunen-Loeve Expansion was used and it is presented. Using the strains and the material Karhunen-Loeve Expansion the stress components are calculated. A numerical example of shallow foundation was carried out and the results of stress and strain of the new algorithm were compared with those raised from Monte Carlo method which is treated as the exact solution. A great accuracy was presented.