Abdelkhalak El Hami is University Professor at INSA Rouen Normandie, France, and is the author (or co-author) of over sixty books. He is responsible for several European educational and/or research projects as a specialist in the fields of optimization, reliability and AI of multiphysics systems.Mohamed Eid is University Professor at the Settat Faculty of Science and Technology, Hassan Premier University, Morocco. He is the author of several books, specializing in numerical optimization methods and system reliability.

• Preface ixChapter 1 Introduction to Optimization in Mechanics 11.1 Introduction 11.2 Problems of general dynamics 21.2.1 Finite element methods 41.2.2 Modal assumption method 51.2.3 Direct integration 71.3 Structural optimization 91.3.1 Design optimization 91.3.2 Shape optimization 101.3.3 Topological optimization 101.3.4 Definitions and formulation of an optimization problem 131.4 Structures with uncertain parameters 151.4.1 Monte Carlo simulation 161.4.2 Analytical method 161.4.3 Stochastic finite element method 161.4.4 Fuzzy logic method 171.4.5 Bibliography study of reliability methods 181.4.6 Bibliography study of reliability optimization methods 241.5 Conclusion 26Chapter 2 Modal Synthesis and Reliability Optimization Methods 272.1 Introduction 272.2 State of the art of modal synthesis methods 272.2.1 Introduction 272.2.2 Model reduction method for elastodynamic systems 282.2.3 Fixed-interface method (Craig Bampton) 292.2.4 Reduction of junction degrees of freedom 312.3 Coupling of modal synthesis and RBDO methods 332.4 Numerical application 342.4.1 L-Plate embedded at the ends 342.4.2 Analysis of results 372.4.3 A vibrating connecting rod 382.4.4 Application: transient model reduction 422.5 Conclusion 44Chapter 3 Modal Synthesis Methods and Stochastic Finite Element Methods 453.1 Introduction 453.2 Linear dynamical problems 463.2.1 Equations of motion 463.2.2 Solution in transient state 473.2.3 Solution in the harmonic domain 483.2.4 Direct integration 493.3 Modal synthesis methods 523.3.1 Introduction 523.3.2 Substructure assembly technique 543.3.3 Fixed-interface method 553.3.4 MacNeal’s open-interface method 593.3.5 Open interface method 613.3.6 Hybrid method 643.3.7 Reduction of junction d.o.f 643.4 Stochastic finite element methods 673.4.1 Introduction 673.4.2 Discretization of random fields 673.4.3 Methods for calculating moments 693.5 Conclusion 78Chapter 4 Fatigue and Reliability Optimization for Structures Subjected to Random Vibrations 794.1 Introduction 794.2 Fatigue damage analysis 804.2.1 Formulations and developments 804.2.2 Strategy for the fatigue damage analysis 834.3 Reliability optimization of structures subjected to random vibrations 844.3.1 Deterministic optimization 844.3.2 Reliability-based design optimization (RBDO) 854.3.3 Reliability optimization of structures subjected to random vibrations 924.4 Applications 944.4.1 Problem description 944.4.2 Results and discussion 974.5. Conclusion 101Chapter 5 Optimization and Shaping 1035.1 Introduction 1035.2 Different approaches to process optimization 1035.3 Characterization of forming processes by objective functions 1075.4 Deterministic and probabilistic optimization of a T-shaped tube 1075.4.1 Selection of objective function and definition of constraints 1095.4.2 Deterministic formulation of the optimization problem 1135.4.3 Probabilistic formulation of the optimization problem 1165.4.4 Sensitivity of optimums to uncertainties 1235.5 Deterministic and reliable optimization of a tube with two expansion areas 1255.5.1 Deterministic formulation of the optimization problem 1295.5.2 Reliability formulation of the optimization problem 1305.5.3 Numerical results 130Chapter 6 Reliability and FSI Optimization 1336.1 Introduction 1336.2 Reliability optimization in mechanics 1346.2.1 Deterministic optimization 1346.2.2 Different approaches to RBDO 1356.2.3 Traditional approach 1376.2.4 Hybrid approach 1386.2.5 Hybrid frequency approach 1406.3 Safest point (SP) method 1426.4 Numerical simulation 1466.4.1 Reliability calculation for an aircraft wing 1466.4.2 RBDO application to the aircraft wing 148Chapter 7 Reliability-based Optimization for Dental Implants 1637.1 Introduction 1637.2 Stochastic approach 1647.2.1 Monte Carlo (MC) method 1647.2.2 Generalized polynomial chaos (GPC) method 1657.3 Deterministic design optimization 1667.4 Reliability-based design optimization (RBDO) 1667.4.1 Traditional method 1677.4.2 Optimal safety factor (OSF) using GPC 1687.5 Numerical result 1707.5.1 2D dental implant 1717.6 Conclusion 176Appendices 177Appendix 1 Binomial Distribution 179Appendix 2 Geometric Distribution 181Appendix 3 Poisson Distribution 183Appendix 4 Exponential Distribution 185Appendix 5 Normal Distribution 187Appendix 6 Log-Normal Distribution 191Appendix 7 Weibull Distribution 195Appendix 8 Pareto Distribution 199Appendix 9 Extreme Value Distribution 201Appendix 10 Asymptotic Distributions 203Appendix 11 Introduction to Optimization 209Appendix 12 Notion of Statistics 221References 235Index 249