Abdelkhalak El Hami

Most physical problems can be written in the form of mathematical equations (differential, integral, etc.). Mathematicians have always sought to find analytical solutions to the equations encountered in the different sciences of the engineer (mechanics, physics, biology, etc.). These equations are sometimes complicated and much effort is required to simplify them. In the middle of the 20th century, the arrival of the first computers gave birth to new methods of resolution that will be described by numerical methods. They allow solving numerically as precisely as possible the equations encountered (resulting from the modeling of course) and to approach the solution of the problems posed. The approximate solution is usually computed on a computer by means of a suitable algorithm. The objective of this book is to introduce and study the basic numerical methods and those advanced to be able to do scientific computation. The latter refers to the implementation of approaches adapted to the treatment of a scientific problem arising from physics (meteorology, pollution, etc.) or engineering (structural mechanics, fluid mechanics, signal processing, etc.) .

This book deals with the various aspects of stochastic dynamics, the resolution of large mechanical systems, and inverse problems. It integrates the most recent ideas from research and industry in the field of stochastic dynamics and optimization in structural mechanics over 11 chapters. These chapters provide an update on the various tools for dealing with uncertainties, stochastic dynamics, reliability and optimization of systems. The optimization–reliability coupling in structures dynamics is approached in order to take into account the uncertainties in the modeling and the resolution of the problems encountered. Accompanied by detailed examples of uncertainties, optimization, reliability, and model reduction, this book presents the newest design tools. It is intended for students and engineers and is a valuable support for practicing engineers and teacher-researchers.

This book is dedicated to the general study of fluid structure interaction with consideration of uncertainties. The fluid-structure interaction is the study of the behavior of a solid in contact with a fluid, the response can be strongly affected by the action of the fluid. These phenomena are common and are sometimes the cause of the operation of certain systems, or otherwise manifest malfunction. The vibrations affect the integrity of structures and must be predicted to prevent accelerated wear of the system by material fatigue or even its destruction when the vibrations exceed a certain threshold.

This book aims to provide an efficient methodology of solving a fluid mechanics problem, based on an awareness of the physical. It meets different objectives of the student, the future engineer or scientist: Simple sizing calculations are required to master today's numerical approach for solving complex practical problems.

The book aims to provide an efficient methodology of solving a fluid mechanics problem. It aims to meet different objectives of the student, the future engineer or scientist. Using simple sizing calculations, and more advanced analytical calculations, the book covers all the essential numerical approaches for solving complex practical problems.

In this book, the authors present in detail several recent methodologies and algorithms that they developed during the last fifteen years. The deterministic methods account for uncertainties through empirical safety factors, which implies that the actual uncertainties in materials, geometry and loading are not truly considered. This problem becomes much more complicated when considering biomechanical applications where a number of uncertainties are encountered in the design of prosthesis systems. This book implements improved numerical strategies and algorithms that can be applied to biomechanical studies.

This book is dedicated to the general study of the dynamics of mechanical structures with consideration of uncertainties. The goal is to get the appropriate forms of a part in minimizing a given criterion. In all fields of structural mechanics, the impact of good design of a room is very important to its strength, its life and its use in service. The development of the engineer's art requires considerable effort to constantly improve structural design techniques.

In this book, the authors present in detail several recent methodologies and algorithms that we have developed during the last fifteen years. The deterministic methods account for uncertainties through empirical safety factors, which implies that the actual uncertainties in materials, geometry and loading are not truly considered. This problem becomes much more complicated when considering biomechanical applications where a number of uncertainties are encountered in the design of prosthesis systems. This book implements improved numerical strategies and algorithms that can be applied only in biomechanical studies.

Manufacturing industries strive to improve the quality and reliability of their products, while simultaneously reducing production costs. To do this, modernized work tools must be produced; this will enable a reduction in the duration of the product development cycle, optimization of product development procedures, and ultimately improvement in the productivity of design and manufacturing phases. Numerical simulations of forming processes are used to this end, and in this book various methods and models for forming processes (including stamping, hydroforming and additive manufacturing) are presented. The theoretical and numerical advances of these processes involving large deformation mechanics on the basis of large transformations are explored, in addition to the various techniques for optimization and calculation of reliability. The advances and techniques within this book will be of interest to professional engineers in the automotive, aerospace, defence and other industries, as well as graduates and undergraduates in these fields.

This book describes the methods used to detect material defects at the nanoscale. The authors present different theories, polarization states and interactions of light with matter, in particular optical techniques using polarized light. Combining experimental techniques of polarized light analysis with techniques based on theoretical or statistical models to study faults or buried interfaces of mechatronic systems, the authors define the range of validity of measurements of carbon nanotube properties. The combination of theory and pratical methods presented throughout this book provide the reader with an insight into the current understanding of physicochemical processes affecting the properties of materials at the nanoscale.

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.