Tenseurs Variations Et Milieux Continus
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Tenseurs Variations Et Milieux Continus
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Author : Jean-François Ganghoffer
language : fr
Publisher: Ellipses Marketing
Release Date : 2003
Tenseurs Variations Et Milieux Continus written by Jean-François Ganghoffer and has been published by Ellipses Marketing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with categories.
La 4e de couverture indique : L'ouvrage propose une base mathématique solide pour l'étude des milieux continus, visant à supprimer le hiatus qui existe parfois entre les enseignements de mathématiques et ceux des sciences de l'ingénieur. La première partie donne l'essentiel de l'analyse tensorielle et de la géométrie différentielle nécessaires pour formuler les équations de l'élasticité dans un cadre de grandes déformations. La formulation des lois de comportement élastique non linéaire est abordée et les méthodes de résolution des équations linéarisées sont traitées en déplacements et en contraintes. Cette partie s'achève avec le problème des contacts plan et tridimensionnel. La seconde partie aborde la formulation variationnelle des équations des milieux continus en s'appuyant d'une part sur les méthodes d'homogénéisation et d'autre part sur le calcul des variations développé dans un contexte mathématique, puis mis en situation en mécanique.Ce livre développe une synthèse très riche de notions mathématiques en calcul différentiel, calcul tensoriel et calcul des variations. Coeur de l'ouvrage, la partie consacrée aux milieux continus solides peut être abordée indépendamment.
Mod Lisation Et Calcul Des Milieux Continus
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Author : Patrick Le Tallec
language : fr
Publisher: Editions Ecole Polytechnique
Release Date : 2009
Mod Lisation Et Calcul Des Milieux Continus written by Patrick Le Tallec and has been published by Editions Ecole Polytechnique this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Continuum mechanics categories.
L’ouvrage est une introduction à la mécanique des milieux continus tridimensionnels. Quatre aspects sont plus particulièrement considérés : la modélisation macroscopique des milieux continus et de leur mouvement, en y décrivant les déformations et en rappelant les lois de conservation que doit respecter tout mouvement ; la description des efforts qui génèrent le mouvement des milieux continus, avec l’introduction de la notion de tenseur de contraintes et l’écriture des équations globales qui les régissent ; l’introduction à l’échelle microscopique des comportements élémentaires qui permet de compléter la modélisation en introduisant les relations de comportement traduisant le lien local entre déformations et efforts ; la résolution de problèmes d’équilibre élastique. Cette étape de résolution de problèmes globaux utilise le principe des puissances virtuelles pour écrire, analyser et résoudre les problèmes posés, et pour en valider les solutions. Elle permet d’aborder de nombreuses situations pratiques et de sensibiliser les étudiants aux problèmes de distribution d’efforts, de discontinuités de solutions, d’incompatibilité de déformations, et d’instabilités géométriques. [Source : 4e de couv.]
Analyse Des Structures Et Milieux Continus
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Author : François Frey
language : fr
Publisher: EPFL Press
Release Date : 1998-01-01
Analyse Des Structures Et Milieux Continus written by François Frey and has been published by EPFL Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Continuum mechanics categories.
Tensor Analysis And Continuum Mechanics
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Author : Wilhelm Flügge
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Tensor Analysis And Continuum Mechanics written by Wilhelm Flügge and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Science categories.
Through several centuries there has been a lively interaction between mathematics and mechanics. On the one side, mechanics has used mathemat ics to formulate the basic laws and to apply them to a host of problems that call for the quantitative prediction of the consequences of some action. On the other side, the needs of mechanics have stimulated the development of mathematical concepts. Differential calculus grew out of the needs of Newtonian dynamics; vector algebra was developed as a means . to describe force systems; vector analysis, to study velocity fields and force fields; and the calcul~s of variations has evolved from the energy principles of mechan ics. In recent times the theory of tensors has attracted the attention of the mechanics people. Its very name indicates its origin in the theory of elasticity. For a long time little use has been made of it in this area, but in the last decade its usefulness in the mechanics of continuous media has been widely recognized. While the undergraduate textbook literature in this country was becoming "vectorized" (lagging almost half a century behind the development in Europe), books dealing with various aspects of continuum mechanics took to tensors like fish to water. Since many authors were not sure whether their readers were sufficiently familiar with tensors~ they either added' a chapter on tensors or wrote a separate book on the subject.
Continuum Mechanics Through The Twentieth Century
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Author : Gerard A Maugin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-08
Continuum Mechanics Through The Twentieth Century written by Gerard A Maugin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-08 with Science categories.
This overview of the development of continuum mechanics throughout the twentieth century is unique and ambitious. Utilizing a historical perspective, it combines an exposition on the technical progress made in the field and a marked interest in the role played by remarkable individuals and scientific schools and institutions on a rapidly evolving social background. It underlines the newly raised technical questions and their answers, and the ongoing reflections on the bases of continuum mechanics associated, or in competition, with other branches of the physical sciences, including thermodynamics. The emphasis is placed on the development of a more realistic modeling of deformable solids and the exploitation of new mathematical tools. The book presents a balanced appraisal of advances made in various parts of the world. The author contributes his technical expertise, personal recollections, and international experience to this general overview, which is very informative albeit concise.
Milieux Continus En Transformations Finies
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Author : Claude Stolz
language : fr
Publisher: Editions Ecole Polytechnique
Release Date : 2009
Milieux Continus En Transformations Finies written by Claude Stolz and has been published by Editions Ecole Polytechnique this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Continuum mechanics categories.
Cet ouvrage propose une introduction à la mécanique des milieux continus en transformations finies. La mécanique est abordée selon deux points de vue : l'analyse des singularités potentielles en front de fissure avec comme illustration la rupture en mode altiplan et la modélisation d'un endommagement local de la matière défini par une élongation limite critique.--[Memento].
M Canique Des Milieux Continus
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Author : Luc Dormieux
language : fr
Publisher:
Release Date : 2017-08-16
M Canique Des Milieux Continus written by Luc Dormieux and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-16 with categories.
Cet ouvrage propose une présentation de la mécanique des milieux continus destinée aux élèves des écoles d'ingénieurs et des formations universitaires (L3 et M1). Chaque chapitre comporte un exposé synthétique des concepts qui est ensuite illustré et complété sous forme d'exercices corrigés. L'initiation au calcul tensoriel qui occupe les premières pages de cet ouvrage est rapidement mise à profit dans le cadre de la description mathématique de la transformation géométrique et de la représentation des efforts intérieurs. On traite les deux points de vue lagrangien et eulérien. Les concepts de contrainte et de déformation sont d'abord mis en oeuvre à l'occasion d'une brève introduction au calcul à la rupture. La théorie de l'élasticité est essentiellement présentée et illustrée dans le cas de la linéarité, mais une initiation à l'élasticité en transformation finie est proposée en exercices. On détaille d'abord les méthodes de résolution directe basées sur des potentiels en déplacement ou en contrainte. Ensuite, une place importante est réservée aux méthodes variationnelles. En particulier, la méthode des éléments finis est illustrée dans le cadre de plusieurs exercices. L'ouvrage propose également une introduction à la mécanique des fluides. L'attention est dirigée principalement vers l'étude des écoulements potentiels. Celle-ci est complétée par une prise de contact avec la notion de couche limite en raison de l'interconnexion de ces deux modélisations. L'étude des milieux curvilignes élastiques clôture cet ouvrage.
Tensor Analysis And Continuum Mechanics
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Author : Y.R. Talpaert
language : en
Publisher: Springer
Release Date : 2003-01-31
Tensor Analysis And Continuum Mechanics written by Y.R. Talpaert and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-31 with Mathematics categories.
This book is designed for students in engineering, physics and mathematics. The material can be taught from the beginning of the third academic year. It could also be used for self study, given its pedagogical structure and the numerous solved problems which prepare for modem physics and technology. One of the original aspects of this work is the development together of the basic theory of tensors and the foundations of continuum mechanics. Why two books in one? Firstly, Tensor Analysis provides a thorough introduction of intrinsic mathematical entities, called tensors, which is essential for continuum mechanics. This way of proceeding greatly unifies the various subjects. Only some basic knowledge of linear algebra is necessary to start out on the topic of tensors. The essence of the mathematical foundations is introduced in a practical way. Tensor developments are often too abstract, since they are either aimed at algebraists only, or too quickly applied to physicists and engineers. Here a good balance has been found which allows these extremes to be brought closer together. Though the exposition of tensor theory forms a subject in itself, it is viewed not only as an autonomous mathematical discipline, but as a preparation for theories of physics and engineering. More specifically, because this part of the work deals with tensors in general coordinates and not solely in Cartesian coordinates, it will greatly help with many different disciplines such as differential geometry, analytical mechanics, continuum mechanics, special relativity, general relativity, cosmology, electromagnetism, quantum mechanics, etc ..
Theory Of Elasticity
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Author : Horst H. E. Leipholz
language : en
Publisher: Springer
Release Date : 1974-03-31
Theory Of Elasticity written by Horst H. E. Leipholz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974-03-31 with Science categories.
This book is designed for use by students and teachers in the field of applied mechanics and mathematics, and for practitioners in civil and mechanical engineering. Since tensor calculus is an indispensable prerequisite when dealing with the theory of elasticity in a modern way, the first part of the book consists in an introduction into this subject. In the second part, the physical foundations of the theory of elasticity are given, including nonlinearities. The excursion into the field of geometric and physical nonlinearities is done in order to prepare the reader for further advances into the most recent developments of the theory. The book itself, in the remainder, is restricted to linear problems only. The third part of the book deals with the mathematical theory of linear elasticity in full extent. Curvilinear problems, two- and three-dimensional problems are included. Stress has been put on working out a systematic approach to the solutions of all kinds of stress states, not neglecting triaxial problems. Also, energy methods have been dealt with, taking into account the generalization and extension of these methods by Rüdiger and Reiss ner. The fourth and last part of the book consists in an application of the general methods, as outlined in part 3, to special structures like plates and shells, thus giving hopefully something of interest to the practising engineer.
M Canique Pour L Ing Nieur
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Author : Guillaume Puel
language : fr
Publisher: Dunod
Release Date : 2021-01-06
M Canique Pour L Ing Nieur written by Guillaume Puel and has been published by Dunod this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-06 with Technology & Engineering categories.
Cet ouvrage, fruit de l’enseignement de première année à l’École Centrale de Paris, présente en un seul volume les éléments de mécanique des milieux continus étendus aux fluides, soldes rigides et structures minces. Chaque chapitre débute avec une motivation précise et une hiérarchie des compétences à acquérir, et s’achève par un résumé des formules les plus significatives. Les concepts physiques et mathématiques sont tous définis lors de leur apparition et de nombreux exercices d’application permettent de maîtriser la résolution des problèmes, mais aussi d'illustrer les grandeurs physiques pertinentes.