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Book Description
Cet ouvrage s'adresse aux élèves des écoles d'ingénieurs, aux étudiants de Masters scientifiques et en première année de Doctorat, et intéressera également les ingénieurs de bureaux d'études. Les progrès réalisés en informatique ont contribué à une utilisation sans cesse croissante des programmes de calcul par éléments finis. Le non linéaire a envahi les bureaux d'études et lors du dimensionnement, on peut être confronté à de grands déplacements, du flambage, de la plasticité, du contact... La raison en est relativement simple : à vouloir toujours tout optimiser, on met moins de matière qu'avant. En conséquence, les structures sont plus souples et les hypothèses de mécanique linéaire en arrivent à ne plus être valables. Cet ouvrage constitue une aide pour l'utilisateur de code éléments finis qui y trouvera dans une première partie un rappel de la mécanique linéaire, ses hypothèses et ses limites. La seconde partie constitue le coeur de l'ouvrage. On aborde divers points de la mécanique non linéaire dont le flambage, la plasticité et les outils d'analyse numérique spécifiques pour les simulations en statique ou dynamique non linéaire. On explicite, pour un élément fini triangulaire, où résident les différences entre la construction de la matrice de raideur initiale et la matrice de raideur tangente. Dans la dernière partie sont développés des exercices d'application de difficulté progressive, couvrant les différents chapitres de la seconde partie, avec une explication des modèles développés et une analyse critique des résultats obtenus.
Book Description
Cet ouvrage s'adresse aux élèves des écoles d'ingénieurs, aux étudiants de Masters scientifiques et en première année de Doctorat, et intéressera également les ingénieurs de bureaux d'études. Les progrès réalisés en informatique ont contribué à une utilisation sans cesse croissante des programmes de calcul par éléments finis. Le non linéaire a envahi les bureaux d'études et lors du dimensionnement, on peut être confronté à de grands déplacements, du flambage, de la plasticité, du contact... La raison en est relativement simple : à vouloir toujours tout optimiser, on met moins de matière qu'avant. En conséquence, les structures sont plus souples et les hypothèses de mécanique linéaire en arrivent à ne plus être valables. Cet ouvrage constitue une aide pour l'utilisateur de code éléments finis qui y trouvera dans une première partie un rappel de la mécanique linéaire, ses hypothèses et ses limites. La seconde partie constitue le coeur de l'ouvrage. On aborde divers points de la mécanique non linéaire dont le flambage, la plasticité et les outils d'analyse numérique spécifiques pour les simulations en statique ou dynamique non linéaire. On explicite, pour un élément fini triangulaire, où résident les différences entre la construction de la matrice de raideur initiale et la matrice de raideur tangente. Dans la dernière partie sont développés des exercices d'application de difficulté progressive, couvrant les différents chapitres de la seconde partie, avec une explication des modèles développés et une analyse critique des résultats obtenus.
Author: P. G. Drazin Publisher: Cambridge University Press ISBN: 9780521406680 Category : Mathematics Languages : en Pages : 354
Book Description
The theories of bifurcation, chaos and fractals as well as equilibrium, stability and nonlinear oscillations, are part of the theory of the evolution of solutions of nonlinear equations. A wide range of mathematical tools and ideas are drawn together in the study of these solutions, and the results applied to diverse and countless problems in the natural and social sciences, even philosophy. The text evolves from courses given by the author in the UK and the United States. It introduces the mathematical properties of nonlinear systems, mostly difference and differential equations, as an integrated theory, rather than presenting isolated fashionable topics. Topics are discussed in as concrete a way as possible and worked examples and problems are used to explain, motivate and illustrate the general principles. The essence of these principles, rather than proof or rigour, is emphasized. More advanced parts of the text are denoted by asterisks, and the mathematical prerequisites are limited to knowledge of linear algebra and advanced calculus, thus making it ideally suited to both senior undergraduates and postgraduates from physics, engineering, chemistry, meteorology etc. as well as mathematics.
Author: Jean-Marc Ginoux Publisher: Springer ISBN: 3319552392 Category : Technology & Engineering Languages : en Pages : 402
Book Description
This book reveals the French scientific contribution to the mathematical theory of nonlinear oscillations and its development. The work offers a critical examination of sources with a focus on the twentieth century, especially the period between the wars. Readers will see that, contrary to what is often written, France's role has been significant. Important contributions were made through both the work of French scholars from within diverse disciplines (mathematicians, physicists, engineers), and through the geographical crossroads that France provided to scientific communication at the time. This study includes an examination of the period before the First World War which is vital to understanding the work of the later period. By examining literature sources such as periodicals on the topic of electricity from that era, the author has unearthed a very important text by Henri Poincaré, dating from 1908. In this work Poincaré applied the concept of limit cycle (which he had introduced in 1882 through his own works) to study the stability of the oscillations of a device for radio engineering. The “discovery” of this text means that the classical perspective of the historiography of this mathematical theory must be modified. Credit was hitherto attributed to the Russian mathematician Andronov, from correspondence dating to 1929. In the newly discovered Poincaré text there appears to be a strong interaction between science and technology or, more precisely, between mathematical analysis and radio engineering. This feature is one of the main components of the process of developing the theory of nonlinear oscillations. Indeed it is a feature of many of the texts referred to in these chapters, as they trace the significant developments to which France contributed. Scholars in the fields of the history of mathematics and the history of science, and anyone with an interest in the philosophical underpinnings of science will find this a particularly engaging account of scientific discovery and scholarly communication from an era full of exciting developments.
Author: Khemais Saanouni Publisher: John Wiley & Sons ISBN: 1118600878 Category : Technology & Engineering Languages : en Pages : 397
Book Description
The aim of this book is to summarize the current most effective methods for modeling, simulating, and optimizing metal forming processes, and to present the main features of new, innovative methods currently being developed which will no doubt be the industrial tools of tomorrow. It discusses damage (or defect) prediction in virtual metal forming, using advanced multiphysical and multiscale fully coupled constitutive equations. Theoretical formulation, numerical aspects as well as application to various sheet and bulk metal forming are presented in detail. Virtual metal forming is nowadays inescapable when looking to optimize numerically various metal forming processes in order to design advanced mechanical components. To do this, highly predictive constitutive equations accounting for the full coupling between various physical phenomena at various scales under large deformation including the ductile damage occurrence are required. In addition, fully 3D adaptive numerical methods related to time and space discretization are required in order to solve accurately the associated initial and boundary value problems. This book focuses on these two main and complementary aspects with application to a wide range of metal forming and machining processes. Contents 1. Elements of Continuum Mechanics and Thermodynamics. 2. Thermomechanically-Consistent Modeling of the Metals Behavior with Ductile Damage. 3. Numerical Methods for Solving Metal Forming Problems. 4. Application to Virtual Metal Forming.
Author: Miriam Schuster Publisher: Springer Nature ISBN: 3658398213 Category : Technology & Engineering Languages : en Pages : 356
Book Description
Laminated safety glass enables the safe construction of transparent structures. The mechanical behaviour depends on the polymeric interlayer both in the intact and in the post fracture state. In the present work, the mechanical behaviour of ethylene vinyl acetate-based (EVA) and ionoplastic interlayers is investigated for the intact laminated safety glass condition. In particular, the influence of the semi-crystalline structure on the stiffness behaviour is studied with X-Ray Diffraction, Differential Scanning Calorimetry and Dynamic-Mechanical-Thermal-Analysis. The studies on the mechanical behaviour of the interlayer in the fractured laminated safety glass were carried out with polyvinyl butyral-based (PVB) interlayers. First, the temperature and frequency (time) dependent linearity limits are determined in Dynamic-Mechanical-Thermal-Analyses, second, the nonlinear viscoelastic material behaviour is investigated with tensile relaxation tests at different temperatures and strain levels.
Author: Giovanni Astarita Publisher: Springer Science & Business Media ISBN: 1468437461 Category : Science Languages : en Pages : 749
Book Description
At the VIIth International Congress on Rheology, which was held in Goteborg in 1976, Proceedings were for the first time printed in advance and distributed to all participants at the time of the Congress. Although of course we Italians would be foolish to even try to emulate our Swedish friends as far as efficiency of organization is concerned, we decided at the very beginning that, as far as the Proceedings were concerned, the VIIIth International Congress on Rheology in Naples would follow the standards of time liness set by the Swedish Society of Rheology. This book is the result we have obtained. We wish to acknowledge the cooperation of Plenum Press in producing it within the very tight time schedule available. Every four years, the International Congress on Rheology represents the focal point where all rheologists meet, and the state of the art is brought up to date for everybody interested; the Proceedings represent the written record of these milestones of scientific progress in rheology. We have tried to make use of the traditions of having invited lectures, and of leaving to the organizing committee the freedom to choose the lecturers as they see fit, in order to collect a group of invited lectures which gives as broad as possible a landscape of the state of the art in every relevant area of rheology. The seventeen invited lectures are collected in the first volume of the proceedings.
Author: Jean-Charles Craveur
Author: Jean-Charles Craveur
Author: Nikolai Mitrofanovich Krylov
Author: Claude Stolz
Author: Nikolaĭ Mitrofanovich Krylov
Author: P. G. Drazin
Author: Jean-Marc Ginoux
Author: 
Author: Khemais Saanouni
Author: Miriam Schuster
Author: Giovanni Astarita