Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Studia Geotechnica et Mechanica

The Journal of Wroclaw University of Technology

4 Issues per year

Open Access
Online
ISSN
2083-831X
See all formats and pricing
More options …

Stochastic Finite Element Analysis using Polynomial Chaos

S. Drakos / G.N. Pande
Published Online: 2016-04-18 | DOI: https://doi.org/10.1515/sgem-2016-0004

Abstract

This paper presents a procedure of conducting Stochastic Finite Element Analysis using Polynomial Chaos. It eliminates the need for a large number of Monte Carlo simulations thus reducing computational time and making stochastic analysis of practical problems feasible. This is achieved by polynomial chaos expansion of the displacement field. An example of a plane-strain strip load on a semi-infinite elastic foundation is presented and results of settlement are compared to those obtained from Random Finite Element Analysis. A close matching of the two is observed.

Keywords: foundation settlements; stochastic finite element; polynomial chaos

REFERENCES

  • [1] Davies R., Harte D., Tests for Hurst effect, Biometrika, 1987, 74(4), 95–101.CrossrefGoogle Scholar

  • [2] Dembo A., Mallows C., Shepp L., Embedding nonnegative definite Toeplitz matrices in nonnegative definite circulant matrices, with applications to covariance estimation, IEEE Transactions on Information Theory, 1989, 35, 1206–1212.CrossrefGoogle Scholar

  • [3] Dietrich C., Newsam G., A fast and exact simulation for multidimensional Gaussian stochastic simulations, Water Resources Research, 1993, 29(8), 2861–2869.CrossrefGoogle Scholar

  • [4] Dietrich C., Newsam G., Fast and exact simulation of stationary Gaussian processes through circulant embedding of the covariance matrix, SIAM Journal on Scientific Computing, 1997, 18(4), 1088–1107.CrossrefGoogle Scholar

  • [5] Gneiting T., Power-law correlations, related models for long-range dependence and their simulation, Journal of Applied Probability, 2000, 37(4), 1104–1109.CrossrefGoogle Scholar

  • [6] Gneiting T., Sevčíková H., Percival D., Schlather M., Jiang Y., Fast and exact simulation of large Gaussian lattice systems in R2: Exploring the limits, Journal of Computational and Graphical Statistics, 2006, 15(3), 483–501.CrossrefGoogle Scholar

  • [7] Stein M., Local stationarity and simulation of self-affine intrinsic random functions, IEEE Transactions on Information Theory, 2001, 47(4), 1385–1390.CrossrefGoogle Scholar

  • [8] Stein M., Fast and exact simulation of fractional Brownian surfaces, Journal of Computational and Graphical Statistics, 2002, 11(3), 587–599.CrossrefGoogle Scholar

  • [9] Stein M., Simulation of Gaussian random fields with one derivative, Journal of Computational and Graphical Statistics, 2012, 21(1), 155–173.CrossrefGoogle Scholar

  • [10] Wood A., Chan G., Simulation of stationary Gaussian processes in [0, 1]d, Journal of Computational and Graphical Statistics, 1994, 3(4), 409–432.Google Scholar

  • [11] Paice G.M., Griffiths D.V., Fenton G.A., Finite element modeling of settlements on spatially random soil, J. Geotech. Eng., 1996, 122(9), 777–779. Smith, I. M., and Griffiths,CrossrefGoogle Scholar

  • [12] Fenton G.A., Griffiths D.V., Statistics of block conductivity through a simple bounded stochastic medium, Water Resour. Res., 1993, 29(6), 1825–1830.CrossrefGoogle Scholar

  • [13] Fenton G.A., Griffiths D.V., Probabilistic foundation settlement on spatially random soil, J. Geotech. Geoenviron. Eng., 2002, 128(5), 381–390.Google Scholar

  • [14] Fenton G.A., Griffiths D.V., Three-dimensional probabilistic foundation settlement, J. Geotech. Geoenviron. Eng., 2005, 131(2), 232–239.Google Scholar

  • [15] Fenton G.A., Griffiths D.V., Risk assessment in geotechnical engineering, Wiley, Hoboken, N.J. 2008.Web of ScienceGoogle Scholar

  • [16] Fenton G.A., Vanmarcke E.H., Simulation of random fields via local average subdivision, J. Eng. Mech., 1990, 116(8), 1733–1749.Google Scholar

  • [17] Ghanem R.G., Spanos P.D., Stochastic finite elements: A spectral approach, Springer-Verlag, New York 1991.Google Scholar

  • [18] Griffiths D.V., Fenton G.A., Seepage beneath water retaining structures founded on spatially random soil, Geotechnique, 1993, 43(4), 577–587.CrossrefGoogle Scholar

  • [19] Xiu D, Karniadakis G.E., Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos, Computer Methods in Applied Mechanics and Engineering, 2003, 191 (43), 4927–4948Google Scholar

  • [20] Gray R.M., Toeplitz and Circulant Matrices: A review, Department of electrical Engineering Stanford University, 2006.Google Scholar

About the article

Published Online: 2016-04-18

Published in Print: 2016-03-01


Citation Information: Studia Geotechnica et Mechanica, ISSN (Online) 2083-831X, ISSN (Print) 0137-6365, DOI: https://doi.org/10.1515/sgem-2016-0004.

Export Citation

© 2016 S. Drakos et al., published by De Gruyter Open. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Comments (0)

Please log in or register to comment.
Log in