Homogenization Of Reticulated Structures
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Homogenization Of Reticulated Structures
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Author : Doina Cioranescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Homogenization Of Reticulated Structures written by Doina Cioranescu 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 2012-12-06 with Mathematics categories.
This book presents recent works on lattice type structure. Some of the results discussed here have already been published in mathematical journals, but we give here a comprehensive and unified presentation. We have also added some new topics such as those contained in Chapter 4 treating elastic problems for gridworks. The aim of this book is to give continuous simple models for thin reticulated structures (which may have a very complex pattern). This means that we have to treat partial differential equations depending on several small parameters and give the asymptotic behavior with respect to these parameters (which can be the period, the thickness of the material, or the thickness of a plate or of a beam). This book is written from the point of view of the applied mathematician, atten tion being paid to the mathematical rigor, convergence results, and error estimates. It consists of six chapters and more than a hundred figures. The basic ideas are presented in the first two chapters, while the four last ones study some particular models, using the ideas of Chapters 1 and 2. Chapter 1 is an introduction to homogenization methods in perforated domains. Here the parameter to be taken into consideration is the period. After describing the multiple-scale method (which consists in asymptotic expansions), we focus our attention on the variational method introduced by Tartar, whose main idea is the construction of rapidly oscillating test functions.
Mechanics Of Periodically Heterogeneous Structures
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Author : L.I. Manevitch
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Mechanics Of Periodically Heterogeneous Structures written by L.I. Manevitch 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 Technology & Engineering categories.
Rigorous presentation of Mathematical Homogenization Theory is the subject of numerous publications. This book, however, is intended to fill the gap in the analytical and numerical performance of the corresponding asymptotic analysis of the static and dynamic behaviors of heterogenous systems. Numerous concrete applications to composite media, heterogeneous plates and shells are considered. A lot of details, numerical results for cell problem solutions, calculations of high-order terms of asymptotic expansions, boundary layer analysis etc., are included.
Mechanics Of Generalized Continua
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Author : Gérard A. Maugin
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-03-24
Mechanics Of Generalized Continua written by Gérard 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 2010-03-24 with Mathematics categories.
In their 1909 publication Théorie des corps déformables, Eugène and François Cosserat made a historic contribution to materials science by establishing the fundamental principles of the mechanics of generalized continua. The chapters collected in this volume showcase the many areas of continuum mechanics that grew out of the foundational work of the Cosserat brothers. The included contributions provide a detailed survey of the most recent theoretical developments in the field of generalized continuum mechanics and can serve as a useful reference for graduate students and researchers in mechanical engineering, materials science, applied physics and applied mathematics.
Asymptotical Mechanics Of Thin Walled Structures
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Author : Igor V. Andrianov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Asymptotical Mechanics Of Thin Walled Structures written by Igor V. Andrianov 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 2013-06-29 with Science categories.
In this book a detailed and systematic treatment of asymptotic methods in the theory of plates and shells is presented. The main features of the book are the basic principles of asymptotics and their applications, traditional approaches such as regular and singular perturbations, as well as new approaches such as the composite equations approach. The book introduces the reader to the field of asymptotic simplification of the problems of the theory of plates and shells and will be useful as a handbook of methods of asymptotic integration. Providing a state-of-the-art review of asymptotic applications, this book will be useful as an introduction to the field for novices as well as a reference book for specialists.
Research Directions In Distributed Parameter Systems
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Author : Ralph C. Smith
language : en
Publisher: SIAM
Release Date : 2003-01-01
Research Directions In Distributed Parameter Systems written by Ralph C. Smith and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.
Written by the plenary speakers for the Conference on Future Directions in Distributed Parameter Systems (October 2000), the volume addresses the state of the art, open questions, and important research directions in applications modeled by partial differential equations and delay systems. Topics include electromagnetic theory for dielectric and conductive materials, flow control, cardiovascular and respiratory models, homogenization and systems theory, optimal and geometric control, reduced-order models for large-scale systems, smart materials, and nondestructive evaluation and structural health monitoring for systems, including nuclear power plants.
Multi Scale Modelling For Structures And Composites
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Author : G. Panasenko
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-06-15
Multi Scale Modelling For Structures And Composites written by G. Panasenko 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 2005-06-15 with Mathematics categories.
Numerous applications of rod structures in civil engineering, aircraft and spacecraft confirm the importance of the topic. On the other hand the majority of books on structural mechanics use some simplifying hypotheses; these hypotheses do not allow to consider some important effects, for instance the boundary layer effects near the points of junction of rods. So the question concerning the limits of applicability of structural mechanics hypotheses and the possibilities of their refinement arise. In this connection the asymptotic analysis of equations of mathematical physics, the equations of elasticity in rod structures (without these hypotheses and simplifying assumptions being imposed) is undertaken in the present book. Moreover, a lot of modern structures are made of composite materials and therefore the material of the rods is not homogeneous. This inhomogeneity of the material can generate some unexpected effects. These effects are analysed in this book. The methods of multi-scale modelling are presented by the homogenization, multi-level asymptotic analysis and the domain decomposition. These methods give an access to a new class of hybrid models combining macroscopic description with "microscopic zooms".
Imperfect Bifurcation In Structures And Materials
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Author : Kiyohiro Ikeda
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Imperfect Bifurcation In Structures And Materials written by Kiyohiro Ikeda 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 2013-03-09 with Science categories.
Many physical systems lose or gain stability and pattern through bifurca tion behavior. Extensive research of this behavior is carried out in many fields of science and engineering. The study of dynamic bifurcation be havior, for example, has made clear the mechanism of dynamic instability and chaos. The group-theoretic bifurcation theory is an established means to deal with the formation and selection of patterns in association with symmetry-breaking bifurcation. Since all physical systems are "imperfect," in that they inevitably involve some initial imperfections, the study of im perfect bifurcation (bifurcation of imperfect systems) has drawn a keen mathematical interest to yield a series of important results, such as the universal unfolding. In structural mechanics, bifurcation behavior has been studied to model the buckling and failure of structural systems. The sharp reduction of the strength of structural systems by initial imperfections is formulated as im perfection sensitivity laws. A series of statistical studies has been conducted to make clear the dependence of the strength of structures on the statis tical variation of initial imperfections. A difficulty in these studies arises from the presence of a large number of initial imperfections. At this state, most of these studies are carried out based on the Monte Carlo simulation for a number of initial imperfections, or, on an imperfection sensitivity law against a single initial imperfection.
Random Perturbation Methods With Applications In Science And Engineering
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Author : Anatoli V. Skorokhod
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-21
Random Perturbation Methods With Applications In Science And Engineering written by Anatoli V. Skorokhod 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 2007-06-21 with Mathematics categories.
This book develops methods for describing random dynamical systems, and it illustrats how the methods can be used in a variety of applications. Appeals to researchers and graduate students who require tools to investigate stochastic systems.
Stability And Wave Motion In Porous Media
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Author : Brian Straughan
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-10
Stability And Wave Motion In Porous Media written by Brian Straughan 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 2008-12-10 with Technology & Engineering categories.
This book describes several tractable theories for fluid flow in porous media. The important mathematical quations about structural stability and spatial decay are address. Thermal convection and stability of other flows in porous media are covered. A chapter is devoted to the problem of stability of flow in a fluid overlying a porous layer. Nonlinear wave motion in porous media is analysed. In particular, waves in an elastic body with voids are investigated while acoustic waves in porous media are also analysed in some detail. A chapter is enclosed on efficient numerical methods for solving eigenvalue problems which occur in stability problems for flows in porous media. Brian Straughan is a professor at the Department of Mathemactical Sciences at Durham University, United Kingdom.
The Energy Method Stability And Nonlinear Convection
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Author : brian straughan
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-10-01
The Energy Method Stability And Nonlinear Convection written by brian straughan 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 2003-10-01 with Mathematics categories.
Six new chapters (14-19) deal with topics of current interest: multi-component convection diffusion, convection in a compressible fluid, convenction with temperature dependent viscosity and thermal conductivity, penetrative convection, nonlinear stability in ocean circulation models, and numerical solution of eigenvalue problems.