Stochastic Finite Elements: A Spectral Approach

Roger G. Ghanem and Pol D. Spanos

Publisher:

Dover Publications

Publication Date:

2012

Number of Pages:

222

Format:

Paperback

Price:

16.95

ISBN:

9780486428185

Category:

Monograph

MAA Review
Table of Contents

We do not plan to review this book.

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