Uncertainty and Optimization in Structural Mechanics

Uncertainty and Optimization in Structural Mechanics......Page 1
Uncertainty and Optimization in Structural Mechanics......Page 2
Copyright......Page 3
Table of Contents......Page 4
Preface......Page 7
1.1. Introduction......Page 10
1.2. The optimization problem......Page 12
1.3. Sources of uncertainty......Page 13
1.4. Dealing with uncertainty......Page 15
1.4.1. Reliability optimization......Page 20
1.4.2. Robust optimization......Page 21
1.4.3. Multi-object optimization......Page 22
1.4.5. Worst-case scenario based optimization......Page 23
1.4.8. Fuzzy sets......Page 24
1.5.2. Global sensitivity analysis......Page 25
2.1. Introduction......Page 26
2.3.2. Risks and probabilistic modeling......Page 27
2.3.4. Probability of failure in a structure......Page 28
2.4.1. Calculating the probability of failure using the Monte Carlo method......Page 29
2.5.1. The Rjanitzyne?Cornell index......Page 30
2.5.2. The Hasofer?Lind index......Page 31
2.5.3. The FORM method......Page 32
2.5.4. The SORM method......Page 34
2.6. Overview of the resistance?sollicitation problem......Page 35
2.6.1. Probability of failure......Page 36
2.6.2. Reliability indices......Page 37
2.7. System reliability in mechanics......Page 42
2.7.1. Combinations of types of failure......Page 43
2.7.2. Assessment of the failure probability of a system......Page 44
2.8.2. Discretization and modeling random fields......Page 45
2.8.3. Mechano-reliability coupling......Page 46
2.8.4. Surface response coupling......Page 50
3.1. Introduction......Page 51
3.3. Classifying structural optimization problems......Page 52
3.3.2. Topological optimization......Page 53
3.3.3. Shape optimization......Page 55
4.1. Introduction......Page 58
4.1.2. Classifying optimization methods......Page 59
4.2. User classification......Page 60
4.4. Multi-objective genetic algorithms......Page 61
4.5.1. Robustness criteria in multi-objective optimization......Page 63
4.6. Normal boundary intersection method......Page 64
4.6.1. Description of the NBI method......Page 65
Ensure good distribution on the Pareto front......Page 70
4.7. Multi-objective structural optimization problem......Page 73
5.2. Modeling uncertainty......Page 76
5.2.1. Parametric methods......Page 77
5.2.2. Non-parametric methods......Page 78
5.3. Accounting for robustness in optimum research......Page 80
5.4.1. Defining uncertainty in design parameters......Page 81
5.4.2. Robustness criteria in multi-objective optimization......Page 82
5.5. Resolution method......Page 83
5.6. Examples of mono-objective optimization......Page 84
6.1. Introduction......Page 86
6.2. Overview of reliability optimization......Page 87
6.4. The reliability indicator approach......Page 88
6.5. The single-loop approach......Page 89
6.6. The sequential optimization and reliability assessment approach......Page 94
7.2. Standard method......Page 100
7.3. The optimal security factors OSFs method......Page 102
7.4. Extension of the OSF method to multiple failure scenarios......Page 106
8.1. Introduction......Page 120
8.2. Definitions in topology optimization......Page 121
8.3. Topology optimization methods......Page 122
8.4. Reliability coupling and topology optimization......Page 125
8.5. Illustration and validation of the RBTO model......Page 127
8.6.1. Static analysis......Page 129
8.6.2. Modal analysis......Page 130
Bibliography......Page 132
Index......Page 138