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Mechanics of Periodically Heterogeneous Structures

  • Book
  • © 2002

Overview

Authors:
  1. Leonid I. Manevitch

    1. Institute of Chemical Physics, Moscow, Russia

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  2. Victor G. Oshmyan

    1. Institute of Chemical Physics, Russia

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  3. Igor V. Andrianov

    1. Institute of Chemical Physics, Moscow, Russia

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  • Non-homogeneous media are a classical but still urgent problem in solid mechanics
  • This monograph reports the current state of homogenization methods
  • A lot of the presented results have still not been published in English

Part of the book series: Foundations of Engineering Mechanics (FOUNDATIONS)

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Table of contents (11 chapters)

  1. Front Matter

    Pages I-IX
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  2. Introduction

    • Leonid I. Manevitch, Victor G. Oshmyan, Igor V. Andrianov
    Pages 1-6

  3. Definitions, assumptions and theorems in homogenization problems

    • Leonid I. Manevitch, Victor G. Oshmyan, Igor V. Andrianov
    Pages 7-19

  4. Application of cell functions for the calculation of binary composite elastic moduli

    • Leonid I. Manevitch, Victor G. Oshmyan, Igor V. Andrianov
    Pages 20-57

  5. Asymptotic study of linear vibrations of a stretched beam with concentrated masses and discrete elastic supports

    • Leonid I. Manevitch, Victor G. Oshmyan, Igor V. Andrianov
    Pages 58-75

  6. Reinforced plates

    • Leonid I. Manevitch, Victor G. Oshmyan, Igor V. Andrianov
    Pages 76-127

  7. Problems of elasticity theory for reinforced orthotropic plates

    • Leonid I. Manevitch, Victor G. Oshmyan, Igor V. Andrianov
    Pages 128-155

  8. Reinforced shells

    • Leonid I. Manevitch, Victor G. Oshmyan, Igor V. Andrianov
    Pages 156-187

  9. Corrugated plates

    • Leonid I. Manevitch, Victor G. Oshmyan, Igor V. Andrianov
    Pages 188-211

  10. Other periodic structures

    • Leonid I. Manevitch, Victor G. Oshmyan, Igor V. Andrianov
    Pages 212-232

  11. Perforated plates and shells

    • Leonid I. Manevitch, Victor G. Oshmyan, Igor V. Andrianov
    Pages 233-253

  12. Concluding remarks. Perspectives and open problems

    • Leonid I. Manevitch, Victor G. Oshmyan, Igor V. Andrianov
    Pages 254-254

  13. Back Matter

    Pages 255-266
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Keywords

About this book

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.

Authors and Affiliations

  • Institute of Chemical Physics, Moscow, Russia

    Leonid I. Manevitch, Igor V. Andrianov

  • Institute of Chemical Physics, Russia

    Victor G. Oshmyan

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