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Book synopsis

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

Book details

Book category Books in English Technology, engineering, agriculture Technology: general issues Engineering: general

• Full title: Stochastic Finite Elements
• Subtitle: A Spectral Approach
• Author: Roger G. Ghanem, Pol D. Spanos
• Language: English
• Binding: Paperback
• Number of pages: 224
• EAN: 9780486428185
• ISBN: 0486428184
• ID: 02566103
• Publisher: Dover Publications Inc.
• Weight: 258 g
• Dimensions: 138 × 235 × 22 mm
• Date of publishing: 30. June 2003

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