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© 1999

Homogenization of Reticulated Structures

Benefits

  • Presents recent developments in reticulated/lattice-type structures Analyzing reticulated structures, which are easily visualized, makes it easy to learn about homogenization techniques The topic is timely - there is a great deal of need for mathematical tools and methods for structural modeling from the engineering community Includes many interesting applications Well written and provides a nice background for both non-specialists and mathematicians

Book

Part of the Applied Mathematical Sciences book series (AMS, volume 136)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Doina Cioranescu, Jeannine Saint Jean Paulin
    Pages 1-70
  3. Doina Cioranescu, Jeannine Saint Jean Paulin
    Pages 71-142
  4. Doina Cioranescu, Jeannine Saint Jean Paulin
    Pages 143-180
  5. Doina Cioranescu, Jeannine Saint Jean Paulin
    Pages 181-218
  6. Doina Cioranescu, Jeannine Saint Jean Paulin
    Pages 219-300
  7. Doina Cioranescu, Jeannine Saint Jean Paulin
    Pages 301-334
  8. Back Matter
    Pages 335-348

About this book

Introduction

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.

Keywords

Eigenvalue Extension Lattice-Type Structures Reticulated Structures behavior convergence differential equation homogenization partial differential equation

Authors and affiliations

  1. 1.Laboratoire d’Analyse NumériqueUniversité Paris VI et CNRSParis, Cedex 05France
  2. 2.Département de MathèmatiqueUniversité de MetzMetz, Cedex 01France

Bibliographic information

  • Book Title Homogenization of Reticulated Structures
  • Authors Doina Cioranescu
    Jeannine Saint Jean Paulin
  • Series Title Applied Mathematical Sciences
  • DOI https://doi.org/10.1007/978-1-4612-2158-6
  • Copyright Information Springer-Verlag New York 1999
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-98634-0
  • Softcover ISBN 978-1-4612-7437-7
  • eBook ISBN 978-1-4612-2158-6
  • Series ISSN 0066-5452
  • Edition Number 1
  • Number of Pages XX, 346
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Analysis
    Computational Intelligence
    Math. Applications in Chemistry
  • Buy this book on publisher's site
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