Stochastic Finite Elements by Roger G Ghanem

Stochastic Finite Elements by Roger G Ghanem

Discrepancies frequently occur between a physical system's responses and predictions obtained from mathematical models. The Spectral Stochastic Finite Element Method (SSFEM) has proven successful at forecasting a variety of uncertainties in calculating system responses. This text analyzes a class of discrete mathematical models of engineering systems, identifying key issues and reviewing relevant theoretical concepts, with particular attention to a spectral approach.
Random system parameters are modeled as second-order stochastic processes, defined by their mean and covariance functions. Relying on the spectral properties of the covariance function, the Karhunen-Loeve expansion is employed to represent these processes in terms of a countable set of uncorrected random variables, casting the problem in a finite dimensional setting. Various spectral approximations for the stochastic response of the system are obtained. Implementing the concept of generalized inverse leads to an explicit expression for the response process as a multivariate polynomial functional of a set of uncorrelated random variables. Alternatively, the solution process is treated as an element in the Hilbert space of random functions, in which a spectral representation is identified in terms of polynomial chaos. In this context, the solution process is approximated by its projection onto a finite subspace spanned by these polynomials.

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.

SKU	Unavailable
ISBN 13	9780486428185
ISBN 10	0486428184
Title	Stochastic Finite Elements
Author	Roger G Ghanem
Series	Dover Civil And Mechanical Engineering
Condition	Unavailable
Binding Type	Paperback
Publisher	Dover Publications Inc.
Year published	2003-06-30
Number of pages	224
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.