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Stochastic Finite Elements: A Spectral Approach, Revised Edition (Dover Civil and Mechanical Engineering)

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Stochastic Finite Elements: A Spectral Approach, Revised Edition (Dover Civil and Mechanical Engineering) Cover

 

Synopses & Reviews

Publisher Comments:

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.

Book News Annotation:

This is a reprint, with a brief new preface, of a 1991 book published by Springer-Verlag. Although the field has changed, the authors agreed to a reprinting of the book because it stands as an uncluttered tutorial on the seminal concepts. Ghanem (Johns Hopkins U.) and Spanos (Rice University) treat the theories and concepts behind analyzing a class of discrete mathematical models of engineering systems whose properties and excitations can be represented as random processes. They address students and researchers in mechanical and other branches of engineering. Annotation (c)2003 Book News, Inc., Portland, OR (booknews.com)

Synopsis:

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. 1991 edition.

Synopsis:

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. 1991 edition.

Synopsis:

Designed for those involved in analysis and design of random systems, this 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. 93 figures. 7 tables.

1991 edition.

Table of Contents

1 INTRODUCTION

  1.1 Motivation

  1.2 Review of Available Techniques

  1.3 The Mathematical Model

  1.4 Outline

2 REPRESENTATION OF STOCHASTIC PROCESSES

  2.1 Preliminary Remarks

  2.2 Review of the Theory

  2.3 Karhunen-Loeve Expansion

    2.3.1 Derivation

    2.3.2 Properties

    2.3.3 Solution of the Integral Equation

  2.4 Homogeneous Chaos

    2.4.1 Preliminary Remarks

    2.4.2 Definitions and Properties

    2.4.3 Construction of the Polynomial Chaos

3 SFEM: Response Representation

  3.1 Preliminary Remarks

  3.2 Deterministic Finite Elements

    3.2.1 Problem Definition

    3.2.2 Variational Approach

    3.2.3 Galerkin Approach

    3.2.4 "p-Adaptive Methods, Spectral Methods and Hierarchical Finite Element Bases"

  3.3 Stochastic Finite Elements

    3.3.1 Preliminary Remarks

    3.3.2 Monte Carlo Simulation (MCS)

    3.3.3 Perturbation Method

    3.3.4 Neumann Expansion Method

    3.3.5 Improved Neumann Expansion

    3.3.6 Projection on the Homogeneous Chaos

    3.3.7 Geometrical and Variational Extensions

4 SFEM: Response Statistics

  4.1 Reliability Theory Background

  4.2 Statistical Moments

    4.2.1 Moments and Cummulants Equations

    4.2.2 Second Order Statistics

  4.3 Approximation to the Probability Distribution

  4.4 Reliability Index and Response Surface Simulation

5 NUMERICAL EXAMPLES

  5.1 Preliminary Remarks

  5.2 One Dimensional Static Problem

    5.2.1 Formulation

    5.2.2 Results

  5.3 Two Dimensional Static Problem

    5.3.1 Formulation

    5.3.2 Results

  5.4 One Dimensional Dynamic Problem

    5.4.1 Description of the Problem

    5.4.2 Implementation

    5.4.3 Results

6 SUMMARY AND CONCLUDING REMARKS

  6.1 SUMMARY AND CONCLUDING REMARKS

  BIBLIOGRAPHY

  ADDITIONAL REFERENCES

  INDEX

Product Details

ISBN:
9780486428185
Author:
Ghanem, Roger G.
Publisher:
Dover Publications
Author:
Spanos, Pol D.
Author:
Engineering
Location:
Minneola, N.Y.
Subject:
Engineering - Civil
Subject:
Engineering - General
Subject:
Applied
Subject:
Stochastic processes
Subject:
Finite element method
Subject:
Civil
Subject:
Engineering - Mechanical
Subject:
Random systems
Subject:
discrete mathematical models
Subject:
second order stochastic processes
Subject:
Civil Engineering-General
Edition Number:
Rev. ed.
Edition Description:
Revised
Series:
Dover Civil and Mechanical Engineering
Series Volume:
no. 7-4936
Publication Date:
20120731
Binding:
TRADE PAPER
Language:
English
Illustrations:
93 Figures 7 Tables
Pages:
240
Dimensions:
8.5 x 5.38 in 0.63 lb

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Stochastic Finite Elements: A Spectral Approach, Revised Edition (Dover Civil and Mechanical Engineering) New Trade Paper
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Product details 240 pages Dover Publications - English 9780486428185 Reviews:
"Synopsis" by ,
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. 1991 edition.
"Synopsis" by ,
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. 1991 edition.
"Synopsis" by ,
Designed for those involved in analysis and design of random systems, this 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. 93 figures. 7 tables.

1991 edition.

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