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Stochastic Finite Elements

A Spectral Approach

Autor: Roger G. Ghanem, Pol D. Spanos

Jazyk:

Vazba: Brožovaná

Vydavatel: Dover Publications Inc.

Dostupnost: Skladem u dodavatele

Odesíláme za 9-15 dnů

299 Kč

1 INTRODUCTION 1.1 Motivation 1.2 Review of Available Techniques 1.3 The Mathematical Model...

Informace o knize

Autor

Roger G. Ghanem, Pol D. Spanos

Jazyk

Angličtina

Vazba

Kniha - Brožovaná

Vydáno

2003

Stránek

224

EAN

9780486428185

ISBN

0486428184

Enbook ID

02566103

Vydavatel

Dover Publications Inc.

Hmotnost

258

Rozměry

235 x 138 x 22

Kompletní popis

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