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Asymptotic methods in mechanics of solids

  • Svetlana M. Bauer
  • Sergei B. Filippov
  • Andrei L. Smirnov
  • Petr E. Tovstik
  • Rémi Vaillancourt

Part of the International Series of Numerical Mathematics book series (ISNM, volume 167)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. S. M. Bauer, S. B. Filippov, A. L. Smirnov, P. E. Tovstik, R. Vaillancourt
    Pages 1-49
  3. S. M. Bauer, S. B. Filippov, A. L. Smirnov, P. E. Tovstik, R. Vaillancourt
    Pages 51-88
  4. S. M. Bauer, S. B. Filippov, A. L. Smirnov, P. E. Tovstik, R. Vaillancourt
    Pages 89-153
  5. S. M. Bauer, S. B. Filippov, A. L. Smirnov, P. E. Tovstik, R. Vaillancourt
    Pages 155-237
  6. S. M. Bauer, S. B. Filippov, A. L. Smirnov, P. E. Tovstik, R. Vaillancourt
    Pages 239-290
  7. S. M. Bauer, S. B. Filippov, A. L. Smirnov, P. E. Tovstik, R. Vaillancourt
    Pages 291-318
  8. Back Matter
    Pages 319-325

About this book

Introduction

The construction of solutions of singularly perturbed systems of equations and boundary value problems that are characteristic for the mechanics of thin-walled structures are the main focus of the book. The theoretical results are supplemented by the analysis of problems and exercises. Some of the topics are rarely discussed in the textbooks, for example, the Newton polyhedron, which is a generalization of the Newton polygon for equations with two or more parameters. After introducing the important concept of the index of variation for functions special attention is devoted to eigenvalue problems containing a small parameter. The main part of the book deals with methods of asymptotic solutions of linear singularly perturbed boundary and boundary value problems without or with turning points, respectively. As examples, one-dimensional equilibrium, dynamics and stability problems for rigid bodies and solids are presented in detail. Numerous exercises and examples as well as vast references to the relevant Russian literature not well known for an English speaking reader makes this a indispensable textbook on the topic.

Keywords

boundary value problems eigenvalue problems regular perturbations singular perturbations thin-walled structures

Authors and affiliations

  • Svetlana M. Bauer
    • 1
  • Sergei B. Filippov
    • 2
  • Andrei L. Smirnov
    • 3
  • Petr E. Tovstik
    • 4
  • Rémi Vaillancourt
    • 5
  1. 1.Faculty of Mathematics and MechanicsSt. Petersburg State UniversitySt. PetersburgRussia
  2. 2.Faculty of Mathematics and MechanicsSt. Petersburg State UniversitySt. PetersburgRussia
  3. 3.Faculty of Mathematics and MechanicsSt. Petersburg State UniversitySt. PetersburgRussia
  4. 4.Faculty of Mathematics and MechanicsSt. Petersburg State UniversitySt. PetersburgRussia
  5. 5.Department of Mathematics and StatisticsUniversity of OttawaOttawaCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-18311-4
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-18310-7
  • Online ISBN 978-3-319-18311-4
  • Series Print ISSN 0373-3149
  • Series Online ISSN 2296-6072
  • Buy this book on publisher's site
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