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随机有限单元法及其在航空工程中的应用 英文PDF|Epub|txt|kindle电子书版本网盘下载
- 汪峰著 著
- 出版社： 广州：世界图书广东出版公司
- ISBN：9787510083594
- 出版时间：2014
- 标注页数：151页
- 文件大小：13MB
- 文件页数：162页
- 主题词：有限元法－应用－航空工程－英文
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图书目录
Chapter 1 Introduction1
1.1 Engineering background1
1.2 Engineering uncertainties4
1.2.1 Unpredictable loading conditions5
1.2.2 Randomness of material properties7
1.2.3 Major developments in stochastic finite element methods9
1.3 The aim and layout of book11
1.3.1 The aim11
1.3.2 Book layout12
Chapter 2 Mathematical background17
2.1 Probability theory17
2.1.1 The development of probability theory17
2.1.2 Probability space18
2.1.3 Distribution19
2.1.4 Characteristic function20
2.1.5 Moments22
2.1.6 Cumulants24
2.1.7 Covariance matrix26
2.1.8 Entropy27
2.1.9 Stochastic convergences29
2.1.10 Basic limit theorems and inequities30
2.2 Stochastic field32
2.2.1 Second-order random field33
2.2.2 Mercer’s theorem34
2.2.3 Stationary random fields35
2.2.4 Spectral expansion of stationary random fields37
2.2.5 Ergodicity39
2.2.6 Gaussian random fields40
2.3 Stochastic Analysis41
2.3.1 Brownian motion41
2.3.2 Stochastic differential equations42
2.4 Statistics43
2.4.1 Estimation43
2.4.2 Preliminary nonparametric statistics45
Chapter 3 Representation of random fields49
3.1 Constitutive laws49
3.2 Stochastic constitutive laws51
3.2.1 The spectral representation method53
3.2.2 Karhunen-Loève expansion method54
3.2.3 Other representation methods56
3.3 Representation of Non-Gaussian fields58
Chapter 4 Solvers of stochastic linear equations63
4.1 The discretization of the stochastic fields63
4.2 Monte Carlo method65
4.3 Perturbation method66
4.4 The neumann expansion method67
4.5 The polynomial chaos expansion method68
4.6 Thejoint diagonalization strategy70
Chapter 5 Aircraft engineering applications75
5.1 Aircraft structural health monitoring with uncertainties76
5.2 Aircraft composite materials78
5.3 Analysis of typical aircraft structures79
5.3.1 Aircraft composite material modeling with random properties80
5.3.2 Stochastic modeling of commercial aircraft rudder85
5.3.3 Stochastic modeling of reinforced composite floor under fire conditions89
Chapter 6 Reliability analysis94
6.1 Introduction of engineering reliability analysis94
6.2 Codes of practice96
6.3 Airworthiness regulations97
6.4 Reliability analysis for a single structural element100
6.4.1 Random properties of loading and resistance only100
6.4.2 Single structural member with multi random variables101
6.4.3 Reliability index for linear failure functions102
6.4.4 Reliability index for nonlinear failure functions102
6.5 Application to reliability analysis105
6.5.1 Reliability analysis of simply supported beam105
6.5.2 Reliability analysis of structural glass107
Chapter 7 Uncertainties in aircraft big data and de-noising technologies112
7 1 Uncertainties in aircraft big data112
7.1.1 The“Cocktail party affect”113
7.1.2 System model114
7.1.3 Literature review118
7.2 Blind source separation algorithm Ⅰ119
7.2.1 Cost function119
7.2.2 Minimizing the cost function via numerical procedures120
7.2.3 Parameterization of A121
7.2.4 The explicit form of matrix J121
7.2.5 Numerical methods122
7.2.6 Numerical simulation127
7 3 Blind source separation algorithm Ⅱ132
7.3.1 Cost function132
7.3.2 Numerical simulations136
Chapter 8 Future directions142
Index Ⅰ General convention146
Index Ⅱ Abbreviation147
Index Ⅲ Symbolic notation149