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Uncertainty Quantification of Stochastic Defects in Materials [Kõva köide]

(Nantong University, China)
  • Formaat: Hardback, 196 pages, kõrgus x laius: 234x156 mm, kaal: 453 g, 6 Tables, black and white; 29 Line drawings, black and white; 129 Halftones, black and white; 158 Illustrations, black and white
  • Sari: Emerging Materials and Technologies
  • Ilmumisaeg: 21-Dec-2021
  • Kirjastus: CRC Press
  • ISBN-10: 1032128739
  • ISBN-13: 9781032128733
Teised raamatud teemal:
Uncertainty Quantification of Stochastic Defects in MaterialsSuurem pilt
  • Formaat: Hardback, 196 pages, kõrgus x laius: 234x156 mm, kaal: 453 g, 6 Tables, black and white; 29 Line drawings, black and white; 129 Halftones, black and white; 158 Illustrations, black and white
  • Sari: Emerging Materials and Technologies
  • Ilmumisaeg: 21-Dec-2021
  • Kirjastus: CRC Press
  • ISBN-10: 1032128739
  • ISBN-13: 9781032128733
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781032128733.html
Märksõnad:
Uncertainty Quantification of Stochastic Defects in Materials investigates the uncertainty quantification methods for stochastic defects in material microstructures. It provides effective supplementary approaches for conventional experimental observation with the consideration of stochastic factors and uncertainty propagation. Pursuing a comprehensive numerical analytical system, this book establishes a fundamental framework for this topic, while emphasizing the importance of stochastic and uncertainty quantification analysis and the significant influence of microstructure defects on the material macro properties.

Key Features











Consists of two parts: one exploring methods and theories and the other detailing related examples





Defines stochastic defects in materials and presents the uncertainty quantification for defect location, size, geometrical configuration, and instability





Introduces general Monte Carlo methods, polynomial chaos expansion, stochastic finite element methods, and machine learning methods





Provides a variety of examples to support the introduced methods and theories





Applicable to MATLAB® and ANSYS software

This book is intended for advanced students interested in material defect quantification methods and material reliability assessment, researchers investigating artificial material microstructure optimization, and engineers working on defect influence analysis and nondestructive defect testing.
Preface xi
Author xiii
Chapter 1 Overview
1(4)
References
3(2)
Chapter 2 Uncertainty Quantification
5(16)
2.1 Stochastic Defects
5(1)
2.2 Uncertainty Quantification
6(4)
2.2.1 Probability Theory
6(1)
2.2.2 Evidence Theory
7(2)
2.2.3 Possibility Theory
9(1)
2.2.4 Interval Analysis
9(1)
2.2.5 Convex Modeling
9(1)
2.3 Correlation Analysis
10(3)
2.3.1 Pearson Correlation Coefficient
10(1)
2.3.2 Spearman Correlation Coefficient
11(1)
2.3.3 Kendall Correlation Coefficient
12(1)
2.4 Sensitivity Analysis
13(2)
References
15(6)
Section I Methods and Theories
Chapter 3 Monte Carlo Methods
21(16)
3.1 Introduction
21(3)
3.1.1 Mathematical Formulation of MC Integration
21(1)
3.1.2 Plain (Crude) MC Algorithm
22(1)
3.1.3 Geometric MC Algorithm
23(1)
3.2 Advanced MC Methods
24(3)
3.2.1 Importance Sampling Algorithm
24(2)
3.2.2 Weight Function Approach
26(1)
3.2.3 Latin Hypercube Sampling Approach
26(1)
3.3 Random Interpolation Quadrature
27(1)
3.4 Iterative MC Methods for Linear Equations
28(4)
3.4.1 Iterative MC Algorithms
29(2)
3.4.2 Convergence and Mapping
31(1)
3.5 Markov Chain MC Methods for the Eigenvalue Problem
32(4)
3.5.1 Formulation of the Eigenvalue Problem
32(2)
3.5.2 Method for Choosing the Number of Iterations k
34(1)
3.5.3 Method for Choosing the Number of Chains
35(1)
References
36(1)
Chapter 4 Polynomial Chaos Expansion
37(14)
4.1 Fundamental Description of PCE
37(1)
4.2 Stochastic Approximation
38(1)
4.3 Hermite Polynomials and Gram-Charlier Series
39(3)
4.4 Karhunen-Loeve Transform
42(2)
4.5 Karhunen-Loeve Expansion
44(1)
4.6 Comparison and Discussion
45(4)
References
49(2)
Chapter 5 Stochastic Finite Element Method
51(20)
5.1 Methods for Discretization of Random Fields
51(5)
5.1.1 Point Discretization Methods
51(1)
5.1.1.1 The Midpoint Method
51(1)
5.1.1.2 The Shape Function Method
52(1)
5.1.2 Average Discretization Methods
52(2)
5.1.2.1 Spatial Average
52(1)
5.1.2.2 The Weighted Integral Method
53(1)
5.1.3 Series Expansion Methods
54(2)
5.2 Perturbation Method
56(3)
5.3 Spectral SFEM
59(5)
5.4 Neumann SFEM
64(2)
5.5 Finite Element Reliability Analysis
66(3)
References
69(2)
Chapter 6 Machine Learning Methods
71(16)
6.1 Artificial Neural Networks
71(5)
6.1.1 Components of ANN
71(3)
6.1.2 Learning Paradigms
74(1)
6.1.3 Theoretical Properties
74(20)
6.1.3.1 Computational Power
74(1)
6.1.3.2 Capacity
75(1)
6.1.3.3 Convergence
75(1)
6.1.3.4 Generalization and Statistics
75(1)
6.2 Radial Basis Network
76(1)
6.3 Backpropagation Neural Network
76(1)
6.4 Restricted Boltzmann Machine
77(3)
6.5 Hopfield Neural Network
80(1)
6.6 Convolutional Neural Network
81(2)
References
83(4)
Section II Examples
Chapter 7 Numerical Examples
87(20)
7.1 Importance Sampling
87(3)
7.2 Orthogonal Polynomial
90(2)
7.3 Gram-Charlier Series
92(2)
7.4 Kriging Surrogate Model
94(12)
7.4.1 Numerical Issues of the Kriging Model
96(2)
7.4.1.1 Issue 1: Requirement of Sufficient Effective Samples
96(2)
7.4.1.2 Issue 2: Effects of the Correlation Matrix
98(1)
7.4.2 Subset Simulation
98(2)
7.4.3 Kriging Surrogate Model with Subset Simulation
100(12)
7.4.3.1 The Six-Hump Camel-Back Function
100(2)
7.4.3.2 Vibration Analysis of a Wing Structure
102(4)
References
106(1)
Chapter 8 Monte Carlo-Based Finite Element Method
107(16)
8.1 Introduction
107(1)
8.2 Graphene Material Description
108(1)
8.3 Monte Carlo-Based Finite Element Method
109(3)
8.4 Graphene with Stochastic Defects
112(1)
8.5 Buckling Results and Discussion
112(8)
8.5.1 Probability Analysis
112(2)
8.5.2 Comparison and Discussion
114(4)
8.5.3 Displacement Results of Graphene Sheets
118(2)
8.6 Conclusion
120(1)
References
120(3)
Chapter 9 Impacts of Vacancy Defects in Resonant Vibration
123(22)
9.1 Introduction
123(1)
9.2 Materials and Methods
124(4)
9.3 Validation of the Model
128(2)
9.4 Results and Discussion
130(12)
9.4.1 Amount of Vacancy Defects
130(3)
9.4.2 Geometrical Parameters
133(4)
9.4.3 Material Parameters
137(1)
9.4.4 Graphene Sheets with Vacancy Defects
137(5)
9.5 Conclusions
142(1)
References
142(3)
Chapter 10 Uncertainty Quantification in Nanomaterials
145(18)
10.1 Introduction
145(1)
10.2 Model Formation
146(3)
10.2.1 Graphene Sheets
146(2)
10.2.2 LHS Method
148(1)
10.3 Program Implementation
149(1)
10.4 Discussion and Results
150(9)
10.4.1 Statistical Results
150(3)
10.4.2 Comparison and Discussion
153(2)
10.4.3 Uncertainty Analysis
155(4)
10.5 Conclusion
159(1)
References
159(4)
Chapter 11 Equivalent Young's Modulus Prediction
163(20)
11.1 Introduction
163(1)
11.2 Materials and Methods
164(2)
11.3 Results and Discussion
166(14)
11.3.1 Regular Deterministic Vacancy Defects
166(5)
11.3.2 Randomly Distributed Vacancy Defects
171(9)
11.4 Conclusion
180(1)
References
180(3)
Chapter 12 Strengthening Possibility by Random Vacancy Defects
183(12)
12.1 Introduction
183(1)
12.2 Materials and Methods
183(2)
12.3 Results and Discussion
185(8)
12.4 Conclusion
193(1)
References
193(2)
Index 195
Dr. Liu Chu received her B.E. degree in Materials Science and Engineering, and M.E. degree in Mechanics from Dalian Maritime University, China, and the Ph.D. in Mechanics from the Institut national des sciences appliquées de Rouen (INSA Rouen), France. Dr. Chu focuses on research in computational material mechanics and structural reliability. Her recent research interests include low-dimensional nanomaterial vacancy defects quantification, artificial material microstructure optimization, and mechanical structure reliability analysis. Since 2018, Dr. Chu has published 18 peer-reviewed science and technical papers in international journals and conferences. She is a member of IEEE and has served as a reviewer of several international journals.