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portada Stochastic Finite Elements: A Spectral Approach
Type
Physical Book
Publisher
Author
Year
2011
Language
English
Pages
214
Format
Paperback
ISBN
1461277957
ISBN13
9781461277958
Categories

Stochastic Finite Elements: A Spectral Approach

Roger G. Ghanem; Pol D. Spanos (Author) · Springer · Paperback

Stochastic Finite Elements: A Spectral Approach - Roger G. Ghanem; Pol D. Spanos

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Synopsis "Stochastic Finite Elements: A Spectral Approach "

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.

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