Stochastic Finite Elements: A Spectral Approach

by Roger G. Ghanem, Pol D. Spanos

Overview

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 ©2003 Book News, Inc., Portland, OR

Product Details

ISBN-13:	9781461277958
Publisher:	Springer New York
Publication date:	09/16/2011
Edition description:	Softcover reprint of the original 1st ed. 1991
Pages:	214
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

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