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Asymptotic methods in mechanics of solids

  • Book
  • © 2015

Overview

Authors:
  1. Svetlana M. Bauer

    1. Faculty of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia

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  2. Sergei B. Filippov

    1. Faculty of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia

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  3. Andrei L. Smirnov

    1. Faculty of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia

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  4. Petr E. Tovstik

    1. Faculty of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia

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  5. Rémi Vaillancourt

    1. Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada

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  • For students: Numerous exercises with answers and solutions, plots and tables
  • For researchers: Vast references to the relevant Russian literature not well known or unavailable for an English speaking reader
  • For engineers: Numerous problems on deformation, buckling and vibrations of thin-walled structural elements with a comparison of results obtained by asymptotic, analytical and numerical approaches
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xxi
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  2. Asymptotic Estimates

    • S. M. Bauer, S. B. Filippov, A. L. Smirnov, P. E. Tovstik, R. Vaillancourt
    Pages 1-49

  3. Asymptotic Estimates for Integrals

    • S. M. Bauer, S. B. Filippov, A. L. Smirnov, P. E. Tovstik, R. Vaillancourt
    Pages 51-88

  4. Regular Perturbation of Ordinary Differential Equations

    • S. M. Bauer, S. B. Filippov, A. L. Smirnov, P. E. Tovstik, R. Vaillancourt
    Pages 89-153

  5. Singularly Perturbed Linear Ordinary Differential Equations

    • S. M. Bauer, S. B. Filippov, A. L. Smirnov, P. E. Tovstik, R. Vaillancourt
    Pages 155-237

  6. Singularly Perturbed Linear Ordinary Differential Equations with Turning Points

    • S. M. Bauer, S. B. Filippov, A. L. Smirnov, P. E. Tovstik, R. Vaillancourt
    Pages 239-290

  7. Asymptotic Integration of Nonlinear Differential Equations

    • S. M. Bauer, S. B. Filippov, A. L. Smirnov, P. E. Tovstik, R. Vaillancourt
    Pages 291-318

  8. Back Matter

    Pages 319-325
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Keywords

About this book

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.

Reviews

“The book might be considered as an advanced course with emphasize on applications. … this book is a valuable contribution and a valuable complement of the existing literature in the field of asymptotic methods. The integration of the applications from Mechanics of solids should enlarge the circle of the potential readers.” (Vladimir Răsvan, zbMATH 1330.34001, 2016)

Authors and Affiliations

  • Faculty of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia

    Svetlana M. Bauer, Sergei B. Filippov, Andrei L. Smirnov, Petr E. Tovstik

  • Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada

    Rémi Vaillancourt

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