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."

Designed for those involved in the analysis and design of random systems, this graduate-level text analyzes a class of discrete mathematical models of engineering systems. It clearly identifies key issues and offers an instructive review of relevant theoretical concepts, with particular attention to a spectral approach. Contents: 1. Introduction. 2. Representation of Stochastic Processes. 3. Stochastic Finite Element Method: Response Representation. 4. Stochastic Finite Elements: Response Statistics. 5. Numerical Examples. 6. Summary and Concluding Remarks. Bibliography. Index. Unabridged republication of the edition published by Springer-Verlag, New York, 1991. 93 Figures. 7 Tables.