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Stochastic Finite Elements

A Spectral Approach

Autor: Roger G. Ghanem, Pol D. Spanos

Limbă:

Legare: Carte broșată

Editura: Dover Publications Inc.

Disponibilitate: În depozitul extern

Expediem în 9-15 zile

73.51 lei

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

Informații despre carte

Autor

Roger G. Ghanem, Pol D. Spanos

Limbă

engleză

Legare

Carte - Carte broșată

Publicat

2003

Pagini

224

EAN

9780486428185

ISBN

0486428184

Enbook ID

02566103

Editura

Dover Publications Inc.

Greutate

258

Dimensiuni

235 x 138 x 22

Descriere completă

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