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Nonlinear Problems of Elasticity

  • Stuart S. Antman

Part of the Applied Mathematical Sciences book series (AMS, volume 107)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Stuart S. Antman
    Pages 1-10
  3. Stuart S. Antman
    Pages 11-48
  4. Stuart S. Antman
    Pages 49-84
  5. Stuart S. Antman
    Pages 85-123
  6. Stuart S. Antman
    Pages 173-226
  7. Stuart S. Antman
    Pages 227-257
  8. Stuart S. Antman
    Pages 259-324
  9. Stuart S. Antman
    Pages 325-342
  10. Stuart S. Antman
    Pages 343-370
  11. Stuart S. Antman
    Pages 371-383
  12. Stuart S. Antman
    Pages 385-455
  13. Stuart S. Antman
    Pages 457-530
  14. Stuart S. Antman
    Pages 531-601
  15. Stuart S. Antman
    Pages 603-628
  16. Stuart S. Antman
    Pages 629-664
  17. Stuart S. Antman
    Pages 665-673
  18. Stuart S. Antman
    Pages 675-681
  19. Stuart S. Antman
    Pages 683-698
  20. Back Matter
    Pages 699-752

About this book

Introduction

This second edition is an enlarged, completely updated, and extensively revised version of the authoritative first edition. It is devoted to the detailed study of illuminating specific problems of nonlinear elasticity, directed toward the scientist, engineer, and mathematician who wish to see careful treatments of precisely formulated problems. Special emphasis is placed on the role of nonlinear material response. The mathematical tools from nonlinear analysis are given self-contained presentations where they are needed. This book begins with chapters on (geometrically exact theories of) strings, rods, and shells, and on the applications of bifurcation theory and the calculus of variations to problems for these bodies. The book continues with chapters on tensors, three-dimensional continuum mechanics, three-dimensional elasticity, large-strain plasticity, general theories of rods and shells, and dynamical problems. Each chapter contains a wealth of interesting, challenging, and tractable exercises.

 Reviews of the first edition:

``A scholarly work, it is uncompromising in its approach to model formulation, while achieving striking generality in the analysis of particular problems. It will undoubtedly become a standard research reference in elasticity but will be appreciated also by teachers of both solid mechanics and applied analysis for its clear derivation of equations and wealth of examples.'' --- J. M. Ball, (Bulletin of the American Mathematical Society), 1996.

``It is destined to become a standard reference in the field which belongs on the bookshelf of anyone working on the application of mathematics to continuum mechanics. For graduate students, it provides a fascinating introduction to an active field of mathematical research.'' --- M. Renardy, (SIAM Review), 1995.

``The monograph is a masterpiece for writing a modern theoretical treatise on a field of natural sciences. It is highly recommended to all scientists, engineers and mathematicians interested in a careful treatment of uncompromised nonlinear problems of elasticity, and it is a `must' for applied mathematicians working on such problems.'' --- L. v Wolfersdorf, (Zeitschrift fur Angewandte Mathematik und Mechanik), 1995.

Keywords

Extension angular momentum bifurcation elasticity mechanics momentum tensor

Authors and affiliations

  • Stuart S. Antman
    • 1
  1. 1.Department of Mathematics and Institute for Physical Science and TechnologyUniversity of MarylandCollege ParkUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-4147-6
  • Copyright Information Springer-Verlag New York 1995
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-4149-0
  • Online ISBN 978-1-4757-4147-6
  • Series Print ISSN 0066-5452
  • Buy this book on publisher's site