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Analysis of Two-Dimensional Stochastic Systems by the Weighted Integral Method

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Computational Stochastic Mechanics

Abstract

In this paper, the weighted integral method is extended to calculate the response variability of two-dimensional stochastic systems in conjunction with the stochastic finite element method. Plane stress and plane strain problems are examined using the constant stress/strain triangular element. The stochastic stiffness matrix of the structure is calculated in terms of integrals of the stochastic field describing the random material property over the area of each element. These integrals are random variables called weighted integrals. The covariance matrix of these weighted integrals is calculated numerically using Gaussian quadrature formulas. As a consequence, the method is considerably more accurate than the conventional stochastic finite element method that uses the midpoint method to reduce the stochastic field involved in the problem to a series of random variables. Then, a Taylor series expansion is used to calculate the response variability of the response displacements and stresses. Finally, a numerical example involving a stochastic circular plate is examined.

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Author information

Authors and Affiliations

  1. Department of Civil Engineering and Operations Research, Princeton University, Princeton, NJ, 08544, USA

    G. Deodatis, W. Wall & M. Shinozuka

Authors
  1. G. Deodatis
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  2. W. Wall
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  3. M. Shinozuka
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Editor information

Editors and Affiliations

  1. Brown School of Engineering, Rice University, PO Box 1892, Houston, TX, 77251, USA

    P. D. Spanos

  2. Computational Mechanics Institute, Wessex Institute of Technology Ashurst Lodge, Ashurst Southampton, SO4 2AA, UK

    C. A. Brebbia

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© 1991 Computational Mechanics Publications

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Deodatis, G., Wall, W., Shinozuka, M. (1991). Analysis of Two-Dimensional Stochastic Systems by the Weighted Integral Method. In: Spanos, P.D., Brebbia, C.A. (eds) Computational Stochastic Mechanics. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3692-1_34

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  • DOI: https://doi.org/10.1007/978-94-011-3692-1_34

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-85166-698-0

  • Online ISBN: 978-94-011-3692-1

  • eBook Packages: Springer Book Archive

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