Stochastic Finite Element Methods : an Introduction.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Papadopoulos, Vissarion
Otros Autores: Giovanis, Dimitris G.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing, 2017.
Colección:Mathematical engineering.
Temas:
Finite element method.
Stochastic models.
Méthode des éléments finis.
Modèles stochastiques.
Finite element method
Stochastic models
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Preface
  • Acknowledgements
  • Contents
  • List of Figures
  • List of Tables
  • 1 Stochastic Processes
  • 1.1 Moments of Random Processes
  • 1.1.1 Autocorrelation and Autocovariance Function
  • 1.1.2 Stationary Stochastic Processes
  • 1.1.3 Ergodic Stochastic Processes
  • 1.2 Fourier Integrals and Transforms
  • 1.2.1 Power Spectral Density Function
  • 1.2.2 The Fourier Transform of the Autocorrelation Function
  • 1.3 Common Stochastic Processes
  • 1.3.1 Gaussian Processes
  • 1.3.2 Markov Processes
  • 1.3.3 Brownian Process
  • 1.3.4 Stationary White Noise
  • 1.3.5 Random Variable Case1.3.6 Narrow and Wideband Random Processes
  • 1.3.7 Kanai
  • Tajimi Power Spectrum
  • 1.4 Solved Numerical Examples
  • 1.5 Exercises
  • 2 Representation of a Stochastic Process
  • 2.1 Point Discretization Methods
  • 2.1.1 Midpoint Method
  • 2.1.2 Integration Point Method
  • 2.1.3 Average Discretization Method
  • 2.1.4 Interpolation Method
  • 2.2 Series Expansion Methods
  • 2.2.1 The Karhunen
  • LoÃv̈e Expansion
  • 2.2.2 Spectral Representation Method
  • 2.2.3 Simulation Formula for Stationary Stochastic Fields
  • 2.3 Non-Gaussian Stochastic Processes2.4 Solved Numerical Examples
  • 2.5 Exercises
  • 3 Stochastic Finite Element Method
  • 3.1 Stochastic Principle of Virtual Work
  • 3.2 Nonintrusive Monte Carlo Simulation
  • 3.2.1 Neumann Series Expansion Method
  • 3.2.2 The Weighted Integral Method
  • 3.3 Perturbation-Taylor Series Expansion Method
  • 3.4 Intrusive Spectral Stochastic Finite Element Method (SSFEM)
  • 3.4.1 Homogeneous Chaos
  • 3.4.2 Galerkin Minimization
  • 3.5 Closed Forms and Analytical Solutions with Variability Response Functions (VRFs)
  • 3.5.1 Exact VRF for Statically Determinate Beams3.5.2 VRF Approximation for General Stochastic FEM Systems
  • 3.5.3 Fast Monte Carlo Simulation
  • 3.5.4 Extension to Two-Dimensional FEM Problems
  • 3.6 Solved Numerical Examples
  • 3.7 Exercises
  • 4 Reliability Analysis
  • 4.1 Definition
  • 4.1.1 Linear Limit-State Functions
  • 4.1.2 Nonlinear Limit-State Functions
  • 4.1.3 First- and Second-Order Approximation Methods
  • 4.2 Monte Carlo Simulation (MCS)
  • 4.2.1 The Law of Large Numbers
  • 4.2.2 Random Number Generators
  • 4.2.3 Crude Monte Carlo Simulation
  • 4.3 Variance Reduction Methods4.3.1 Importance Sampling
  • 4.3.2 Latin Hypercube Sampling (LHS)
  • 4.4 Monte Carlo Methods in Reliability Analysis
  • 4.4.1 Crude Monte Carlo Simulation
  • 4.4.2 Importance Sampling
  • 4.4.3 The Subset Simulation (SS)
  • 4.5 Artificial Neural Networks (ANN)
  • 4.5.1 Structure of an Artificial Neuron
  • 4.5.2 Architecture of Neural Networks
  • 4.5.3 Training of Neural Networks
  • 4.5.4 ANN in the Framework of Reliability Analysis
  • 4.6 Numerical Examples
  • 4.7 Exercises
  • Appendix A Probability Theory

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