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Author: CHASKALOVIC Joël Publisher: Lavoisier ISBN: 2743064803 Category : Languages : en Pages : 382
Book Description
Qu’il s’agisse d’applications en physique ou en mécanique, en médecine ou en biologie, mais aussi en économie, dans les médias et en marketing, ou encore dans le domaine des finances, la traduction phénoménologique du système étudié conduit très souvent à la résolution d’équations différentielles ou aux dérivées partielles. Incontestablement, ce sont les éléments finis qui ont bouleversé le monde de l’approximation numérique des équations aux dérivées partielles. Cet ouvrage est composé de deux parties : la première est un abrégé de cours portant sur les outils de base de l’analyse mathématique des équations aux dérivées partielles et la seconde contient des problèmes corrigés qui abordent l’approximation par éléments finis des formulations variationnelles des problèmes aux limites elliptiques. Des applications en mécanique des solides déformables, à la résistance des matériaux, en mécanique des fluides et en thermique ainsi que quelques problèmes non linéaires y sont présentés.Cet ouvrage s'adresse aux étudiants en sciences et techniques de l'ingénieur des universités et des grandes écoles.
Author: CHASKALOVIC Joël Publisher: Lavoisier ISBN: 2743064803 Category : Languages : en Pages : 382
Book Description
Qu’il s’agisse d’applications en physique ou en mécanique, en médecine ou en biologie, mais aussi en économie, dans les médias et en marketing, ou encore dans le domaine des finances, la traduction phénoménologique du système étudié conduit très souvent à la résolution d’équations différentielles ou aux dérivées partielles. Incontestablement, ce sont les éléments finis qui ont bouleversé le monde de l’approximation numérique des équations aux dérivées partielles. Cet ouvrage est composé de deux parties : la première est un abrégé de cours portant sur les outils de base de l’analyse mathématique des équations aux dérivées partielles et la seconde contient des problèmes corrigés qui abordent l’approximation par éléments finis des formulations variationnelles des problèmes aux limites elliptiques. Des applications en mécanique des solides déformables, à la résistance des matériaux, en mécanique des fluides et en thermique ainsi que quelques problèmes non linéaires y sont présentés.Cet ouvrage s'adresse aux étudiants en sciences et techniques de l'ingénieur des universités et des grandes écoles.
Author: Jean Claude Sabonnadiere Publisher: Springer Science & Business Media ISBN: 1468487396 Category : Computers Languages : en Pages : 194
Book Description
The finite element method (FEM) has been understood, at least in principle, for more than 50 years. The integral formulation on which it is based has been known for a longer time (thanks to the work of Galerkin, Ritz, Courant and Hilbert,1.4 to mention the most important). However, the method could not be applied in a practical way since it involved the solution of a large number of linear or non-linear algebraic equations. Today it is quite common, with the aid of computers, to solve non-linear algebraic problems of several thousand equations. The necessary numerical methods and programming techniques are now an integral part of the teaching curriculum in most engineering schools. Mechanical engineers, confronted with very complicated structural problems, were the first to take advantage of advanced computational methods and high level languages (FORTRAN) to transform the mechanical models into algebraic equations (1956). In recent times (1960), the FEM has been studied by applied mathematicians and, having received rigorous treatment, has become a part of the more general study of partial differential equations, gradually replacing the finite difference method which had been considered the universal tool to solve these types of problems.
Author: I Antonescu Publisher: CRC Press ISBN: 1000100375 Category : Education Languages : en Pages : 537
Book Description
This volume contains papers and reports from the Conference held in Romania, June 2000. The book covers many topics, for example, place, role and content of geotechnical engineering in civil, environmental and earthquake engineering.
Author: P.G. Ciarlet Publisher: Elsevier ISBN: 0080875254 Category : Mathematics Languages : en Pages : 551
Book Description
The objective of this book is to analyze within reasonable limits (it is not a treatise) the basic mathematical aspects of the finite element method. The book should also serve as an introduction to current research on this subject. On the one hand, it is also intended to be a working textbook for advanced courses in Numerical Analysis, as typically taught in graduate courses in American and French universities. For example, it is the author’s experience that a one-semester course (on a three-hour per week basis) can be taught from Chapters 1, 2 and 3 (with the exception of Section 3.3), while another one-semester course can be taught from Chapters 4 and 6. On the other hand, it is hoped that this book will prove to be useful for researchers interested in advanced aspects of the numerical analysis of the finite element method. In this respect, Section 3.3, Chapters 5, 7 and 8, and the sections on “Additional Bibliography and Comments should provide many suggestions for conducting seminars.
Author: Philippe G. Ciarlet Publisher: SIAM ISBN: 9780898719208 Category : Mathematics Languages : en Pages : 553
Book Description
The Finite Element Method for Elliptic Problems is the only book available that analyzes in depth the mathematical foundations of the finite element method. It is a valuable reference and introduction to current research on the numerical analysis of the finite element method, as well as a working textbook for graduate courses in numerical analysis. It includes many useful figures, and there are many exercises of varying difficulty. Although nearly 25 years have passed since this book was first published, the majority of its content remains up-to-date. Chapters 1 through 6, which cover the basic error estimates for elliptic problems, are still the best available sources for material on this topic. The material covered in Chapters 7 and 8, however, has undergone considerable progress in terms of new applications of the finite element method; therefore, the author provides, in the Preface to the Classics Edition, a bibliography of recent texts that complement the classic material in these chapters. Audience: this book is particularly useful to graduate students, researchers, and engineers using finite element methods. The reader should have knowledge of analysis and functional analysis, particularly Hilbert spaces, Sobolev spaces, and differential calculus in normed vector spaces. Other than these basics, the book is mathematically self-contained.
Author: Gérard Meunier Publisher: John Wiley & Sons ISBN: 0470393807 Category : Science Languages : en Pages : 618
Book Description
Written by specialists of modeling in electromagnetism, this book provides a comprehensive review of the finite element method for low frequency applications. Fundamentals of the method as well as new advances in the field are described in detail. Chapters 1 to 4 present general 2D and 3D static and dynamic formulations by the use of scalar and vector unknowns and adapted interpolations for the fields (nodal, edge, face or volume). Chapter 5 is dedicated to the presentation of different macroscopic behavior laws of materials and their implementation in a finite element context: anisotropy and hysteretic properties for magnetic sheets, iron losses, non-linear permanent magnets and superconductors. More specific formulations are then proposed: the modeling of thin regions when finite elements become misfit (Chapter 6), infinite domains by using geometrical transformations (Chapter 7), the coupling of 2D and 3D formulations with circuit equations (Chapter 8), taking into account the movement, particularly in the presence of Eddy currents (Chapter 9) and an original approach for the treatment of geometrical symmetries when the sources are not symmetric (Chapter 10). Chapters 11 to 13 are devoted to coupled problems: magneto-thermal coupling for induction heating, magneto-mechanical coupling by introducing the notion of strong and weak coupling and magneto-hydrodynamical coupling focusing on electromagnetic instabilities in fluid conductors. Chapter 14 presents different meshing methods in the context of electromagnetism (presence of air) and introduces self-adaptive mesh refinement procedures. Optimization techniques are then covered in Chapter 15, with the adaptation of deterministic and probabilistic methods to the numerical finite element environment. Chapter 16 presents a variational approach of electromagnetism, showing how Maxwell equations are derived from thermodynamic principles.
Author: SAANOUNI Khemais Publisher: Lavoisier ISBN: 2746282259 Category : Languages : en Pages : 578
Book Description
Cet ouvrage fait le point sur les méthodes actuelles les plus performantes pour modéliser, simuler et optimiser les procédés de mise en forme des structures minces et massives et d'en donner les tendances des nouvelles méthodes innovantes actuellement en cours de développement et qui feront à n'en pas douter les "outils" industriels de demain dans le domaine du formage virtuel. Par rapport aux ouvrages récents dédiés aux méthodes numériques en mise en forme, le principal apport de ce livre se trouve rassemblé au deuxième chapitre qui concerne le développement des modèles de comportement multiphysiques à fortes capacités prédictives, utilisables dans les codes de calcul des structures pour simuler et optimiser tous types de procédés de mise en forme par grandes déformations irréversibles de structures métalliques minces et/ou massives et leur "optimisation" vis-à-vis de l'avènement de l'endommagement ductile.
Author: CHASKALOVIC Joël
Author: CHASKALOVIC Joël
Author: Jean Claude Sabonnadiere
Author: I Antonescu
Author: P.G. Ciarlet
Author: Philippe G. Ciarlet
Author: Gérard Meunier
Author: I. Galligani
Author: SAANOUNI Khemais
Author: Ammar Dhouib
Author: