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Homogenization of Reticulated Structures

  • Book
  • © 1999

Overview

Authors:
  1. Doina Cioranescu

    1. Laboratoire d’Analyse Numérique, Université Paris VI et CNRS, Paris, Cedex 05, France

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  2. Jeannine Saint Jean Paulin

    1. Département de Mathèmatique, Université de Metz, Metz, Cedex 01, France

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  • 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

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

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xx
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  2. Homogenization in Perforated Media

    • Doina Cioranescu, Jeannine Saint Jean Paulin
    Pages 1-70

  3. Lattice-Type Structures

    • Doina Cioranescu, Jeannine Saint Jean Paulin
    Pages 71-142

  4. Thermal Problem For Gridworks

    • Doina Cioranescu, Jeannine Saint Jean Paulin
    Pages 143-180

  5. Elasticity Problem for Gridworks

    • Doina Cioranescu, Jeannine Saint Jean Paulin
    Pages 181-218

  6. Thermal Problems For Thin Tall Structures

    • Doina Cioranescu, Jeannine Saint Jean Paulin
    Pages 219-300

  7. Elasticity Problems For Thin Tall Structures

    • Doina Cioranescu, Jeannine Saint Jean Paulin
    Pages 301-334

  8. Back Matter

    Pages 335-348
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Keywords

About this book

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.

Authors and Affiliations

  • Laboratoire d’Analyse Numérique, Université Paris VI et CNRS, Paris, Cedex 05, France

    Doina Cioranescu

  • Département de Mathèmatique, Université de Metz, Metz, Cedex 01, France

    Jeannine Saint Jean Paulin

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

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York 1999

  • Softcover ISBN: 978-1-4612-7437-7Published: 19 September 2011

  • eBook ISBN: 978-1-4612-2158-6Published: 06 December 2012

  • Series ISSN: 0066-5452

  • Series E-ISSN: 2196-968X

  • Edition Number: 1

  • Number of Pages: XX, 346

  • Topics: Analysis, Computational Intelligence, Math. Applications in Chemistry

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