Stochastic Finite Element Methods and Its Applications to Aircraft Engineering

Chapter 1 Introduction

1. 1 Engineering background
1.2 Engineering uncertainties
1.2. 1 Unpredictable loading conditions
1.2.2 Randomness of material properties
1.2.3 Major developments in stochastic finite element methods
1.3 The aim and layout of book
1.3.1 The aim
1.3.2 Book layout
Chapter2 Mathematical background
2. 1 Probability theory
2. 1. 1 The development of probability theory.
2.1.2 Probability space
2.1.3 Distribution
2.1.4 Characteristic function
2.1.5 Moments
2. 1.6 Cumulants
2.1.7 Covariance matrix
2.1.8 Entropy
2.1.9 Stochastic convergences
2.1.10 Basic limit theorems and inequities
2.2 Stochastic field
2.2.1 Second-order random field
2.2.2 Mercer's theorem
2.2.3 Stationary random fields
2.2.4 Spectral expansion of stationary random fields
2.2.5 Ergodicity
2.2.6 Gaussian random fields
2.3 Stochastic Analysis
2.3.1 Brownian motion
2.3.2 Stochastic differential equations
2.4 Statistics
2.4.1 Estimation
2.4.2 Preliminary nonparametric statistics
Chapter 3 Representation of random fields
3. 1 Constitutive laws
3.2 Stochastic constitutive lairs
3.2.1 The spectral representation method
3.2 2 Karhunen-Loeve expansion method
3.2.3 Other representation methods
3.3 Representation of Non-Gaussian fields
……
Chapter 4 Solvers of stochastic linear equations
Chapter 5 Aircraft engineering applications
Chapter 6 Reliability analysis
Chapter 7 Uncertainties in aircraft big data and de-noising technologies
Chapter 8 Future directions
Index Ⅰ General convention
Index Ⅱ Abbreviation
Index Ⅲ Symbolic notation