This book is designed as a brief guide for engineers, researchers and senior students who deal with the analysis and modeling of structures with stochastic nature, from large engineering projects such as aircraft structures, through to small engineered components like soil and civil structures.
Stochastic Finite Element Methods and Its Applications to Aircraft Engineering provides a formidable resource covering theories and applications of SFEMs, including the fundamentals and research frontiers of SFEMs, its applications to advanced material modeling and stochastic computational engineering analysis and engineering reliability analysis.
目 录
Chapter 1 Introduction 001
1.1 Engineering background 001
1.2 Engineering uncertainties 004
1.2.1 Unpredictable loading conditions 005
1.2.2 Randomness of material properties 007
1.2.3 Major developments in stochastic finite element methods 009
1.3 The aim and layout of book 011
1.3.1 The aim 011
1.3.2 Book layout 012
Chapter 2 Mathematical background 017
2.1 Probability theory 017
2.1.1 The development of probability theory 017
2.1.2 Probability space 018
2.1.3 Distribution 019
2.1.4 Characteristic function 020
2.1.5 Moments 022
2.1.6 Cumulants 024
2.1.7 Covariance matrix 026
2.1.8 Entropy 027
2.1.9 Stochastic convergences 029
2.1.10 Basic limit theorems and inequities 030
2.2 Stochastic field 032
2.2.1 Second-order random field 033
2.2.2 Mercer's theorem 034
2.2.3 Stationary random fields 035
2.2.4 Spectral expansion of stationary random fields 037
2.2.5 Ergodicity 039
2.2.6 Gaussian random fields 040
2.3 Stochastic Analysis 041
2.3.1 Brownian motion 041
2.3.2 Stochastic differential equations 042
2.4 Statistics 043
2.4.1 Estimation 043
2.4.2 Preliminary nonparametric statistics 045
Chapter 3 Representation of random fields 049
3.1 Constitutive laws 049
3.2 Stochastic constitutive laws 051
3.2.1 The spectral representation method 053
3.2 2 Karhunen-Loève expansion method 054
3.2.3 Other representation methods 056
3.3 Representation of Non-Gaussian fields 058
Chapter 4 Solvers of stochastic linear equations 063
4.1 The discretization of the stochastic fields 063
4.2 Monte Carlo method 065
4.3 Perturbation method 066
4.4 The neumann expansion method 067
4.5 The polynomial chaos expansion method 068
4.6 The joint diagonalization strategy 070
Chapter 5 Aircraft engineering applications 075
5.1 Aircraft structural health monitoring with uncertainties 076
5.2 Aircraft composite materials 078
5.3 Analysis of typical aircraft structures 079
5.3.1 Aircraft composite material modeling with random properties 080
5.3.2 Stochastic modeling of commercial aircraft rudder 085
5.3.3 Stochastic modeling of reinforced composite floor under fire
conditions 089
Chapter 6 Reliability analysis 094
6.1 Introduction of engineering reliability analysis 094
6.2 Codes of practice 096
6.3 Airworthiness regulations 097
6.4 Reliability analysis for a single structural element 100
6.4.1 Random properties of loading and resistance only 100
6.4.2 Single structural member with multi random variables 101
6.4.3 Reliability index for linear failure functions 102
6.4.4 Reliability index for nonlinear failure functions 102
6.5 Application to reliability analysis 105
6.5.1 Reliability analysis of simply supported beam 105
6.5.2 Reliability analysis of structural glass 107
Chapter 7 Uncertainties in aircraft big data and de-noising technologies 112
7.1 Uncertainties in aircraft big data 112
7.1.1 The "Cocktail party affect" 113
7.1.2 System model 114
7.1.3 Literature review 118
7.2 Blind source separation algorithm I 119
7.2.1 Cost function 119
7.2.2 Minimizing the cost function via numerical procedures 120
7.2.3 Parameterization of A 121
7.2.4 The explicit form of matrix 121
7.2.5 Numerical methods 122
7.2.6 Numerical simulation 127
7.3 Blind source separation algorithm II 132
7.3.1 Cost function 132
7.3.2 Numerical simulations 136
Chapter 8 Future directions 142
Index I General convention 146
Index II Abbreviation 147
Index III Symbolic notation 149
