Abdelkhalak El Hami is Professor at the Institut National des Sciences Appliquées, Rouen, France. He is the author of many articles and books on optimization and uncertainty.Bouchaib Radi is Professor in the Faculty of Sciences and Technology at the University of Hassan Premier, Settat, Morocco. His research interests are in such areas as structural optimization, parallel computation, contact problem and metal forming. He is the author of many scientific articles and books.

• Preface ixChapter 1 Uncertainty 11.1. Introduction 11.2. The optimization problem 31.3. Sources of uncertainty 41.4. Dealing with uncertainty 61.4.1. Reliability optimization 111.4.2. Robust optimization 121.4.3. Multi-object optimization 131.4.4. Stochastic optimization 141.4.5. Worst-case scenario based optimization 141.4.6. Non-probabilistic optimization 151.4.7. Interval modeling 151.4.8. Fuzzy sets 151.5. Analyzing sensitivity 161.5.1. Local sensitivity analysis 161.5.2. Global sensitivity analysis 16Chapter 2 Reliability in Mechanical Systems 172.1. Introduction 172.2. A structure reliability problem 182.3. Modeling a structure reliability problem 182.3.1. A deterministic mechanical model 182.3.2. Risks and probabilistic modeling 182.3.3. Types of failure in a structure 192.3.4. Probability of failure in a structure 192.4. Calculating the probability of failure in a structure 202.4.1. Calculating the probability of failure using the Monte Carlo method 202.4.2. Calculating the probability of failure using a reliability index 212.5. Reliability indices 212.5.1. The Rjanitzyne–Cornell index 212.5.2. The Hasofer–Lind index 222.5.3. The FORM method 232.5.4. The SORM method 252.6. Overview of the resistance–sollicitation problem 262.6.1. Probability of failure 272.6.2. Reliability indices 282.7. System reliability in mechanics 332.7.1. Combinations of types of failure 342.7.2. Assessment of the failure probability of a system 352.8. The finite element method and structural reliability 362.8.1. Context and objectives of the problem 362.8.2. Discretization and modeling random fields 362.8.3. Mechano-reliability coupling 372.8.4. Surface response coupling 41Chapter 3 Optimal Structural Design 433.1. Introduction 433.2. Historical development of structural optimization 443.3. Classifying structural optimization problems 443.3.1. Dimensional optimization 453.3.2. Topological optimization 453.3.3. Shape optimization 47Chapter 4. Multi-object Optimization with Uncertainty .. 514.1. Introduction 514.1.1. Choice of an optimization method 524.1.2. Classifying optimization methods 524.2. User classification 534.3. Design classification 544.4. Multi-objective genetic algorithms 544.5. Robust multi-objective optimization 564.5.1. Robustness criteria in multi-objective optimization 564.6. Normal boundary intersection method 574.6.1. Description of the NBI method 584.7. Multi-objective structural optimization problem 66Chapter 5 Robust Optimization 695.1. Introduction 69Table of Contents vii5.2. Modeling uncertainty 695.2.1. Parametric methods 705.2.2. Non-parametric methods 715.3. Accounting for robustness in optimum research 735.4. Robustness criteria 745.4.1. Defining uncertainty in design parameters 745.4.2. Robustness criteria in multi-objective optimization 755.5. Resolution method 765.6. Examples of mono-objective optimization 77Chapter 6 Reliability Optimization 796.1. Introduction 796.2. Overview of reliability optimization 806.3. Reliability optimization methods 816.4. The reliability indicator approach 816.5. The single-loop approach 826.6. The sequential optimization and reliability assessment approach 87Chapter 7 Optimal Security Factors Approach 937.1. Introduction 937.2. Standard method 937.3. The optimal security factors (OSFs) method 957.4. Extension of the OSF method to multiple failure scenarios 99Chapter 8 Reliability-based Topology Optimization 1138.1. Introduction 1138.2. Definitions in topology optimization 1148.3. Topology optimization methods 1158.4. Reliability coupling and topology optimization 1188.5. Illustration and validation of the RBTO model 1208.6. Application of the RBTO model to mechanics 1228.6.1. Static analysis 1228.6.2. Modal analysis 123Bibliography 125Index 131