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Stochastic Finite Element Analysis using Polynomial Chaos

Studia Geotechnica et Mechanica
Volume 38 (2016): Issue 1 (March 2016)
By:
S. Drakos and  G.N. Pande  
Open Access
|Apr 2016

References

  1. [1] Davies R., Harte D., Tests for Hurst effect, Biometrika, 1987, 74(4), 95–101.10.1093/biomet/74.1.95
    Search in Google Scholar
  2. [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, 1206–1212.10.1109/18.45276
    Search in Google Scholar
  3. [3] Dietrich C., Newsam G., A fast and exact simulation for multidimensional Gaussian stochastic simulations, Water Resources Research, 1993, 29(8), 2861–2869.10.1029/93WR01070
    Search in Google Scholar
  4. [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), 1088–1107.10.1137/S1064827592240555
    Search in Google Scholar
  5. [5] Gneiting T., Power-law correlations, related models for long-range dependence and their simulation, Journal of Applied Probability, 2000, 37(4), 1104–1109.10.1239/jap/1014843088
    Search in Google Scholar
  6. [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), 483–501.10.1198/106186006X128551
    Search in Google Scholar
  7. [7] Stein M., Local stationarity and simulation of self-affine intrinsic random functions, IEEE Transactions on Information Theory, 2001, 47(4), 1385–1390.10.1109/18.923722
    Search in Google Scholar
  8. [8] Stein M., Fast and exact simulation of fractional Brownian surfaces, Journal of Computational and Graphical Statistics, 2002, 11(3), 587–599.10.1198/106186002466
    Search in Google Scholar
  9. [9] Stein M., Simulation of Gaussian random fields with one derivative, Journal of Computational and Graphical Statistics, 2012, 21(1), 155–173.10.1198/jcgs.2010.10069
    Search in Google Scholar
  10. [10] Wood A., Chan G., Simulation of stationary Gaussian processes in [0, 1]d, Journal of Computational and Graphical Statistics, 1994, 3(4), 409–432.10.1080/10618600.1994.10474655
    Search in Google Scholar
  11. [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,10.1061/(ASCE)0733-9410(1996)122:9(777)
    Search in Google Scholar
  12. [12] Fenton G.A., Griffiths D.V., Statistics of block conductivity through a simple bounded stochastic medium, Water Resour. Res., 1993, 29(6), 1825–1830.10.1029/93WR00412
    Search in Google Scholar
  13. [13] Fenton G.A., Griffiths D.V., Probabilistic foundation settlement on spatially random soil, J. Geotech. Geoenviron. Eng., 2002, 128(5), 381–390.10.1061/(ASCE)1090-0241(2002)128:5(381)
    Search in Google Scholar
  14. [14] Fenton G.A., Griffiths D.V., Three-dimensional probabilistic foundation settlement, J. Geotech. Geoenviron. Eng., 2005, 131(2), 232–239.10.1061/(ASCE)1090-0241(2005)131:2(232)
    Search in Google Scholar
  15. [15] Fenton G.A., Griffiths D.V., Risk assessment in geotechnical engineering, Wiley, Hoboken, N.J. 2008.10.1002/9780470284704
    Search in Google Scholar
  16. [16] Fenton G.A., Vanmarcke E.H., Simulation of random fields via local average subdivision, J. Eng. Mech., 1990, 116(8), 1733–1749.10.1061/(ASCE)0733-9399(1990)116:8(1733)
    Search in Google Scholar
  17. [17] Ghanem R.G., Spanos P.D., Stochastic finite elements: A spectral approach, Springer-Verlag, New York 1991.10.1007/978-1-4612-3094-6
    Search in Google Scholar
  18. [18] Griffiths D.V., Fenton G.A., Seepage beneath water retaining structures founded on spatially random soil, Geotechnique, 1993, 43(4), 577–587.10.1680/geot.1993.43.4.577
    Search in Google Scholar
  19. [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), 4927–494810.1016/S0045-7825(02)00421-8
    Search in Google Scholar
  20. [20] Gray R.M., Toeplitz and Circulant Matrices: A review, Department of electrical Engineering Stanford University, 2006.10.1561/9781933019680
    Search in Google Scholar
DOI: https://doi.org/10.1515/sgem-2016-0004 | Journal eISSN: 2083-831X | Journal ISSN: 0137-6365
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Language: English
Page range: 33 - 43
Published on: Apr 18, 2016
Published by: Wroclaw University of Science and Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 4 times per year
Keywords:
foundation settlements,
stochastic finite element,
polynomial chaos
Related subjects:
Geosciences,
Geosciences, other,
Materials sciences,
Composites,
Porous materials,
Physics,
Mechanics and fluid dynamics

© 2016 S. Drakos, G.N. Pande, published by Wroclaw University of Science and Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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