Optimization is generally a reduction operation of a definite quantity. This process naturally takes place in our environment and through our activities. For example, many natural systems evolve, in order to minimize their potential energy. Modeling these phenomena then largely relies on our capacity to artificially reproduce these processes. In parallel, optimization problems have quickly emerged from human activities, notably from economic concerns. This book includes the most recent ideas coming from research and industry in the field of optimization, reliability and the recognition of accompanying uncertainties. It is made up of eight chapters which look at the reviewing of uncertainty tools, system reliability, optimal design of structures and their optimization (of sizing, form, topology and multi-objectives) – along with their robustness and issues on optimal safety factors. Optimization reliability coupling will also be tackled in order to take into account the uncertainties in the modeling and resolution of the problems encountered. The book is aimed at students, lecturers, engineers, PhD students and researchers. Contents 1. Uncertainty. 2. Reliability in Mechanical Systems. 3. Optimal Structural Design. 4. Multi-object Optimization with Uncertainty. 5. Robust Optimization. 6. Reliability Optimization. 7. Optimal Security Factors Approach. 8. Reliability-based Topology Optimization. About the Authors 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.

This open access book reports on innovative methods, technologies and strategies for mastering uncertainty in technical systems. Despite the fact that current research on uncertainty is mainly focusing on uncertainty quantification and analysis, this book gives emphasis to innovative ways to master uncertainty in engineering design, production and product usage alike. It gathers authoritative contributions by more than 30 scientists reporting on years of research in the areas of engineering, applied mathematics and law, thus offering a timely, comprehensive and multidisciplinary account of theories and methods for quantifying data, model and structural uncertainty, and of fundamental strategies for mastering uncertainty. It covers key concepts such as robustness, flexibility and resilience in detail. All the described methods, technologies and strategies have been validated with the help of three technical systems, i.e. the Modular Active Spring-Damper System, the Active Air Spring and the 3D Servo Press, which have been in turn developed and tested during more than ten years of cooperative research. Overall, this book offers a timely, practice-oriented reference guide to graduate students, researchers and professionals dealing with uncertainty in the broad field of mechanical engineering.

The volume presents a collaboration between internationally recognized experts on anti-optimization and structural optimization, and summarizes various novel ideas, methodologies and results studied over 20 years. The book vividly demonstrates how the concept of uncertainty should be incorporated in a rigorous manner during the process of designing real-world structures. The necessity of anti-optimization approach is first demonstrated, then the anti-optimization techniques are applied to static, dynamic and buckling problems, thus covering the broadest possible set of applications. Finally, anti-optimization is fully utilized by a combination of structural optimization to produce the optimal design considering the worst-case scenario. This is currently the only book that covers the combination of optimization and anti-optimization. It shows how various optimization techniques are used in the novel anti-optimization technique, and how the structural optimization can be exponentially enhanced by incorporating the concept of worst-case scenario, thereby increasing the safety of the structures designed in various fields of engineering./a

The book covers new developments in structural topology optimization. Basic features and limitations of Michell’s truss theory, its extension to a broader class of support conditions, generalizations of truss topology optimization, and Michell continua are reviewed. For elastic bodies, the layout problems in linear elasticity are discussed and the method of relaxation by homogenization is outlined. The classical problem of free material design is shown to be reducible to a locking material problem, even in the multiload case. For structures subjected to dynamic loads, it is explained how they can be designed so that the structural eigenfrequencies of vibration are as far away as possible from a prescribed external excitation frequency (or a band of excitation frequencies) in order to avoid resonance phenomena with high vibration and noise levels. For diffusive and convective transport processes and multiphysics problems, applications of the density method are discussed. In order to take uncertainty in material parameters, geometry, and operating conditions into account, techniques of reliability-based design optimization are introduced and reviewed for their applicability to topology optimization.

Computational optimization methods have matured over the last few years due to extensive research by applied mathematicians and engineers. These methods have been applied to many practical applications. Several general-purpose optimization programs and programs for specific engineering applications have become available to solve particular optimization problems.Written by leading researchers in the field of optimization, this highly readable book covers state-of-the-art computational algorithms as well as applications of optimization to structural and mechanical systems. Formulations of the problems and numerical solutions are presented, and topics requiring further research are also suggested.

This book – comprised of three separate volumes – presents the recent developments and research discoveries in structural and solid mechanics; it is dedicated to Professor Isaac Elishakoff. This third volume is devoted to non-deterministic mechanics. Modern Trends in Structural and Solid Mechanics 3 has broad scope, covering topics such: design optimization under uncertainty, interval field approaches, convex analysis, quantum inspired topology optimization and stochastic dynamics. The book is illustrated by many applications in the field of aerospace engineering, mechanical engineering, civil engineering, biomedical engineering and automotive engineering. This book is intended for graduate students and researchers in the field of theoretical and applied mechanics.

Uncertainties play a dominant role in the design and optimization of structures and infrastructures. In optimum design of structural systems due to variations of the material, manufacturing variations, variations of the external loads and modelling uncertainty, the parameters of a structure, a structural system and its environment are not given, fi