Stochastic Finite Elements: A Spectral Approach

Pol D. Spanos

ISBN 10: 1461277957 / ISBN 13: 9781461277958

Published by Springer New York, Springer US, 2011

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9781461277958

Bibliographic Details

• Title: Stochastic Finite Elements: A Spectral Approach
• Publisher: Springer New York, Springer US
• Publication Date: 2011
• Language: English
• ISBN 10: 1461277957
• ISBN 13: 9781461277958
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 13D millimeters 235 millimeters width by 155 millimeters height by 13 millimeters depth
• Weight: 353 grams

About this title

Synopsis

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.

About the Author

Roger G. Ghanem is a Professor at University of Southern California's Department of Aerospace and Mechanical Engineering in Los Angeles.
Pol D. Spanos is the L. B. Ryon Chair in Engineering in the Department of Mechanical Engineering and Materials Science at Rice University.