书名：《随机有限单元法及其在航空工程中的应用》

作者：汪峰

出版社：世界图书出版公司

出版时间：2014.8

定价：46.00元

ISBN：978-7-5100-8359-4

作者简介：

汪峰，1984年10月出生于湖南；2007年于英国威尔士大学斯旺西分校获土木工程本科一等荣誉学士学位；2011年获英国斯旺西大学计算力学博士学位，师从英国两院院士、美国工程院外籍院士、中国科学院外籍院士、著名有限元专家Roger Owen教授；2011年7月任职于中国商用飞机有限责任公司北京民用飞机技术研究中心。

内容简介：
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 1Introduction   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