Stochastic finite elements : a spectral approach
著者
書誌事項
Stochastic finite elements : a spectral approach
Springer-Verlag, c1991
- : us
- : gw
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注記
Bibliography: p. [193]-209
Includes index
内容説明・目次
- 巻冊次
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: us ISBN 9780387974569
内容説明
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."
- 巻冊次
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: gw ISBN 9783540974567
内容説明
This monograph is dedicated to the field of stochastic finite elements, a rapidly evolving field concerned with the analysis of a class of discrete mathematical models of engineering systems whose properties and excitations can be represented as random processes. The evolution of the field should be viewed in context with the recent growth in availability of computational resources, which has triggered intense interest in developing models for engineering systems that are reliable and incorporate many of the real-world features, randomness being one of them. The key issues associated with stochastic finite elements are identified in this text, and an instructive review of relevant theoretical topics is presented. Special attention is devoted to a spectral approach to stochastic finite elements analysis, which can be construed as an extension of the deterministic FEM to stochastic problems. A number of problems from structural mechanics are treated in the book demonstrating the usefulness of the spectral approach.
目次
- Representation of stochastic processes
- stochastic finite element method - response representation
- stochastic finite element method - response statistics
- numerical examples.
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