Stochastic Finite Elements: A Spectral Approach

Authors: Ghanem, Roger G., Spanos, Pol

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About this book

This monograph considers engineering systems with random parame­ ters. Its context, format, and timing are correlated with the intention of accelerating the evolution of the challenging field of Stochastic Finite Elements. The random system parameters are modeled as second order stochastic processes defined by their mean and covari­ ance functions. Relying on the spectral properties of the covariance function, the Karhunen-Loeve expansion is used' to represent these processes in terms of a countable set of un correlated random vari­ ables. Thus, the problem is cast in a finite dimensional setting. Then, various spectral approximations for the stochastic response of the system are obtained based on different criteria. Implementing the concept of Generalized Inverse as defined by the Neumann Ex­ pansion, leads to an explicit expression for the response process as a multivariate polynomial functional of a set of un correlated random variables. Alternatively, the solution process is treated as an element in the Hilbert space of random functions, in which a spectral repre­ sentation in terms of the Polynomial Chaoses is identified. In this context, the solution process is approximated by its projection onto a finite subspace spanned by these polynomials.

Table of contents (6 chapters)

  • Introduction

    Ghanem, Roger G. (et al.)

    Pages 1-13

  • Representation of Stochastic Processes

    Ghanem, Roger G. (et al.)

    Pages 15-65

  • Stochastic Finite Element Method: Response Representation

    Ghanem, Roger G. (et al.)

    Pages 67-99

  • Stochastic Finite Element Method: Response Statistics

    Ghanem, Roger G. (et al.)

    Pages 101-119

  • Numerical Examples

    Ghanem, Roger G. (et al.)

    Pages 121-183

Buy this book

eBook $89.00
price for USA (gross)
  • ISBN 978-1-4612-3094-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $119.00
price for USA
  • ISBN 978-1-4612-7795-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Stochastic Finite Elements: A Spectral Approach
Authors
Copyright
1991
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York Inc.
eBook ISBN
978-1-4612-3094-6
DOI
10.1007/978-1-4612-3094-6
Softcover ISBN
978-1-4612-7795-8
Edition Number
1
Number of Pages
X, 214
Topics