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Triangulations, and more precisely meshes, are at the heart of many problems relating to a wide variety of scientific disciplines, and in particular numerical simulations of all kinds of physical phenomena. In Volume 1, the theoretical foundations relating to triangulations, finite element shape functions and their interpretations as geometric patches were explored. This has made it possible to build tools that make the geometric modeling of any object possible. These elements are used in Volume 2 to treat meshing problems in their different implementations. Meshing, Geometric Modeling and Numerical Simulation 3 offers technical additions to the methods seen in the first two volumes and a significant portion of this book is dedicated to mesh visualization problems and solutions, especially those with a high degree of complexity.
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.
The 16th ICSMGE responds to the needs of the engineering and construction community, promoting dialog and exchange between academia and practice in various aspects of soil mechanics and geotechnical engineering. This is reflected in the central theme of the conference 'Geotechnology in Harmony with the Global Environment'. The proceedings of the conference are of great interest for geo-engineers and researchers in soil mechanics and geotechnical engineering. Volume 1 contains 5 plenary session lectures, the Terzaghi Oration, Heritage Lecture, and 3 papers presented in the major project session. Volumes 2, 3, and 4 contain papers with the following topics: Soil mechanics in general; Infrastructure and mobility; Environmental issues of geotechnical engineering; Enhancing natural disaster reduction systems; Professional practice and education. Volume 5 contains the report of practitioner/academic forum, 20 general reports, a summary of the sessions and workshops held during the conference.
This book focuses on iterative solvers and preconditioners for mixed finite element methods. It provides an overview of some of the state-of-the-art solvers for discrete systems with constraints such as those which arise from mixed formulations. Starting by recalling the basic theory of mixed finite element methods, the book goes on to discuss the augmented Lagrangian method and gives a summary of the standard iterative methods, describing their usage for mixed methods. Here, preconditioners are built from an approximate factorisation of the mixed system. A first set of applications is considered for incompressible elasticity problems and flow problems, including non-linear models. An account of the mixed formulation for Dirichlet’s boundary conditions is then given before turning to contact problems, where contact between incompressible bodies leads to problems with two constraints. This book is aimed at graduate students and researchers in the field of numerical methods and scientific computing.
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.
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.
Le chauffage par induction est actuellement absent dans beaucoup d'applications industrielles, et pourtant, il a une capacité importante d'innovations technologiques dès lors qu'un apport de chaleur est nécessaire. Cette absence vient du fait que les acteurs du chauffage par induction se sont intéressés essentiellement aux applications traditionnelles d'induction pour la fusion, l'élaboration et le traitement thermique des matériaux de bonnes conductivités électrique et thermique. L'objectif de cet ouvrage Électrothermie est donc de développer des méthodologies d'analyse et de la conception des systèmes du chauffage par induction pour les matériaux peu conducteurs. Dans ce cadre, les modèles analytiques et numériques couplés des phénomènes électromagnétiques et thermiques sont utilisés pour étudier et concevoir des installations du plasma inductif, de démontrer la faisabilité d'une technique du contrôle non destructif thermo inductive, et enfin illustrer les performance du chauffage par induction pour l'élaboration des matériaux composites à base de fibres de carbone.