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Author: Patrick De Buhan Publisher: Elsevier ISBN: 0081021135 Category : Technology & Engineering Languages : en Pages : 344
Book Description
Elastic, Plastic and Yield Design of Reinforced Structures presents a whole set of new results which have been published by the authors over the last 30 years in the field of continuum solid mechanics applied to the analysis and design of reinforced civil engineering structures. The focus is on the development and application of up-scaling/homogenization methods in the design of such composite structures, with a special emphasis on the plastic behavior and ultimate strength of materials. The specificity of the book is highlighted by at least two completely innovative concepts which lie at the very heart of the book’s originality: the elaboration of a fully comprehensive homogenization-based method for the design of reinforced structures (and not only materials), through the study of macroscopic behavior, and the development of a multiphase model for materials reinforced by linear inclusions, which considerably extends the range of applicability of the classical homogenization procedure. Sums up almost thirty years of original research in the field of mechanics applied to the analysis and design of reinforced civil engineering structures Focuses on the application of upscaling/homogenization methods to the design of civil engineering structures Highlights the elaboration of a fully comprehensive homogenization-based method for the design of reinforced structures (and not only materials), through the concept of macroscopic behavior Features development of a multiphase model for materials reinforced by linear inclusions, which considerably extends the range of applicability of the classical homogenization procedure.
Author: Patrick De Buhan Publisher: Elsevier ISBN: 0081021135 Category : Technology & Engineering Languages : en Pages : 344
Book Description
Elastic, Plastic and Yield Design of Reinforced Structures presents a whole set of new results which have been published by the authors over the last 30 years in the field of continuum solid mechanics applied to the analysis and design of reinforced civil engineering structures. The focus is on the development and application of up-scaling/homogenization methods in the design of such composite structures, with a special emphasis on the plastic behavior and ultimate strength of materials. The specificity of the book is highlighted by at least two completely innovative concepts which lie at the very heart of the book’s originality: the elaboration of a fully comprehensive homogenization-based method for the design of reinforced structures (and not only materials), through the study of macroscopic behavior, and the development of a multiphase model for materials reinforced by linear inclusions, which considerably extends the range of applicability of the classical homogenization procedure. Sums up almost thirty years of original research in the field of mechanics applied to the analysis and design of reinforced civil engineering structures Focuses on the application of upscaling/homogenization methods to the design of civil engineering structures Highlights the elaboration of a fully comprehensive homogenization-based method for the design of reinforced structures (and not only materials), through the concept of macroscopic behavior Features development of a multiphase model for materials reinforced by linear inclusions, which considerably extends the range of applicability of the classical homogenization procedure.
Author: J.P. Boehler Publisher: Springer Science & Business Media ISBN: 9401136440 Category : Technology & Engineering Languages : en Pages : 709
Book Description
Present developments in materials science, mechanics and engineering, as well as the demands of modern technology, result in a new and growing interest in plasticity and in bordering domains of the mechanical behavior of materials. This growing interest is attested to by the success of both The International Journal of Plasticity, which after its inception rapidly became the leading journal for plasticity research, and the series ofInternational Symposia on Plasticity and Its Current Applications, which is now the premier international forum for plasticity research dissemination. The First International Symposium on Plasticity and Its Current Applications was conceived and organized by Professor Akhtar S. Khan, and was held at the University of Oklahoma (Norman, Oklahoma, USA) from July 30 to August 3, 1984. It was attended by over one hundred scientists from fifteen countries. "Plasticity '89: the Second International Symposium on Plasticity and Its Current Applications" was held at Mie University (Tsu, Japan) from July 31 to August 4, 1989; this symposium was co-chaired by Professors Khan and Tokuda. The main emphasis of this meeting was on dynamic plasticity and micromechanics, although it included other aspects of plasticity as well. It was attended by over two hundred researchers from twenty-three nations.
Author: Markus Kirkilionis Publisher: Springer Science & Business Media ISBN: 3662052814 Category : Mathematics Languages : en Pages : 427
Book Description
Applied mathematics is a central connecting link between scientific observations and their theoretical interpretation. Nonlinear analysis has surely contributed major developments which nowadays shape the face of applied mathematics. At the beginning of the millennium, all sciences are expanding at increased speed. Technological, ecological, economical and medical problem solving is a central issue of every modern society. Mathematical models help to expose fundamental structures hidden in these problems and serve as unifying tools to deepen our understanding. What are the new challenges applied mathematics has to face with the increased diversity of scientific problems? In which direction should the classical tools of nonlinear analysis be developed further? How do new available technologies influence the development of the field? How can problems be solved which have been beyond reach in former times? It is the aim of this book to explore new developments in the field by way of discussion of selected topics from nonlinear analysis.
Author: Pablo Pedregal Publisher: Springer Science & Business Media ISBN: 9783764356972 Category : Mathematics Languages : en Pages : 238
Book Description
Weak convergence is a basic tool of modern nonlinear analysis because it enjoys the same compactness properties that finite dimensional spaces do: basically, bounded sequences are weak relatively compact sets. Nonetheless, weak conver gence does not behave as one would desire with respect to nonlinear functionals and operations. This difficulty is what makes nonlinear analysis much harder than would normally be expected. Parametrized measures is a device to under stand weak convergence and its behavior with respect to nonlinear functionals. Under suitable hypotheses, it yields a way of representing through integrals weak limits of compositions with nonlinear functions. It is particularly helpful in comprehending oscillatory phenomena and in keeping track of how oscilla tions change when a nonlinear functional is applied. Weak convergence also plays a fundamental role in the modern treatment of the calculus of variations, again because uniform bounds in norm for se quences allow to have weak convergent subsequences. In order to achieve the existence of minimizers for a particular functional, the property of weak lower semicontinuity should be established first. This is the crucial and most delicate step in the so-called direct method of the calculus of variations. A fairly large amount of work has been devoted to determine under what assumptions we can have this lower semicontinuity with respect to weak topologies for nonlin ear functionals in the form of integrals. The conclusion of all this work is that some type of convexity, understood in a broader sense, is usually involved.
Author: ROYET Paul Publisher: Lavoisier ISBN: 2746295369 Category : Languages : en Pages : 730
Book Description
Au regard du Code de l’environnement, les digues, considérées comme ouvrages hydrauliques, ne doivent pas rompre de façon dangereuse pour les populations. En tant que moyen de prévention du risque d’inondation ou de submersion, les performances et les limites de ces digues doivent être connues avec précision. Les digues de protection constituent donc une question politique mise en évidence par plusieurs événements récents (Xynthia 2010, la NouvelleOrléans 2005, Rhône aval 2003, Gard 2002, Aude 1999). Cet ouvrage rassemble les contributions présentées lors du 2e colloque national Digues maritimes et fluviales de protection contre les submersions (Digues2013), organisé par l’Irstea et Promosciences, les 12, 13 et 14 juin 2013 au Centre des Congrès d’AixenProvence, avec le soutien du MEDDE, du CFBR, et de la Région ProvenceAlpesCôte d’Azur. Il s’adresse aux maîtres d’ouvrages, gestionnaires, concepteurs, constructeurs, enseignants et chercheurs, services de contrôle, organismes financeurs, agissant dans les domaines d’activités liés, directement ou indirectement, à la sûreté des digues maritimes et fluviales.
Author: Juan Casado-Díaz Publisher: Springer Nature ISBN: 3030981916 Category : Mathematics Languages : en Pages : 119
Book Description
This book aims the optimal design of a material (thermic or electrical) obtained as the mixture of a finite number of original materials, not necessarily isotropic. The problem is to place these materials in such a way that the solution of the corresponding state equation minimizes a certain functional that can depend nonlinearly on the gradient of the state function. This is the main novelty in the book. It is well known that this type of problems has no solution in general and therefore that it is needed to work with a relaxed formulation. The main results in the book refer to how to obtain such formulation, the optimality conditions, and the numerical computation of the solutions. In the case of functionals that do not depend on the gradient of the state equation, it is known that a relaxed formulation consists of replacing the original materials with more general materials obtained via homogenization. This includes materials with different properties of the originals but whose behavior can be approximated by microscopic mixtures of them. In the case of a cost functional depending nonlinearly on the gradient, it is also necessary to extend the cost functional to the set of these more general materials. In general, we do not dispose of an explicit representation, and then, to numerically solve the problem, it is necessary to design strategies that allow the functional to be replaced by upper or lower approximations. The book is divided in four chapters. The first is devoted to recalling some classical results related to the homogenization of a sequence of linear elliptic partial differential problems. In the second one, we define the control problem that we are mainly interested in solving in the book. We obtain a relaxed formulation and their main properties, including an explicit representation of the new cost functional, at least in the boundary of its domain. In the third chapter, we study the optimality conditions of the relaxed problem, and we describe some algorithms to numerically solve the problem. We also provide some numerical experiments carried out using such algorithms. Finally, the fourth chapter is devoted to briefly describe some extensions of the results obtained in Chapters 2 and 3 to the case of dealing with several state equations and the case of evolutive problems. The problems covered in the book are interesting for mathematicians and engineers whose work is related to mathematical modeling and the numerical resolution of optimal design problems in material sciences. The contents extend some previous results obtained by the author in collaboration with other colleagues.
Author: Doïna Cioranescu Publisher: Oxford University Press on Demand ISBN: 9780198565543 Category : Mathematics Languages : en Pages : 262
Book Description
Composite materials are widely used in industry: well-known examples of this are the superconducting multi-filamentary composites which are used in the composition of optical fibres. Such materials are complicated to model, as different points in the material will have different properties. The mathematical theory of homogenization is designed to deal with this problem, and hence is used to model the behaviour of these important materials. This book provides a self-contained and authoritative introduction to the subject for graduates and researchers in the field.
Author: Graeme W. Milton Publisher: SIAM ISBN: 1611977487 Category : Mathematics Languages : en Pages : 761
Book Description
Composites have been studied for more than 150 years, and interest in their properties has been growing. This classic volume provides the foundations for understanding a broad range of composite properties, including electrical, magnetic, electromagnetic, elastic and viscoelastic, piezoelectric, thermal, fluid flow through porous materials, thermoelectric, pyroelectric, magnetoelectric, and conduction in the presence of a magnetic field (Hall effect). Exact solutions of the PDEs in model geometries provide one avenue of understanding composites; other avenues include microstructure-independent exact relations satisfied by effective moduli, for which the general theory is reviewed; approximation formulae for effective moduli; and series expansions for the fields and effective moduli that are the basis of numerical methods for computing these fields and moduli. The range of properties that composites can exhibit can be explored either through the model geometries or through microstructure-independent bounds on the properties. These bounds are obtained through variational principles, analytic methods, and Hilbert space approaches. Most interesting is when the properties of the composite are unlike those of the constituent materials, and there has been an explosion of interest in such composites, now known as metamaterials. The Theory of Composites surveys these aspects, among others, and complements the new body of literature that has emerged since the book was written. It remains relevant today by providing historical background, a compendium of numerous results, and through elucidating many of the tools still used today in the analysis of composite properties. This book is intended for applied mathematicians, physicists, and electrical and mechanical engineers. It will also be of interest to graduate students.
Author: Patrick De Buhan
Author: Patrick De Buhan
Author: J.P. Boehler
Author: Markus Kirkilionis
Author: 
Author: Pablo Pedregal
Author: ROYET Paul
Author: Juan Casado-Díaz
Author: Doïna Cioranescu
Author: 
Author: Graeme W. Milton