© 2015

Geometric Continuum Mechanics and Induced Beam Theories


  • Devoted to fundamental questions on the foundations of continuum mechanics

  • Presents application of the fundamental concepts of continuum mechanics to beam theories

  • All classical beam theories, where the cross sections remain rigid and plain, are presented

  • Augmented beam theories, where cross section deformation is allowed, are derived as well


Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM, volume 75)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Simon R. Eugster
    Pages 1-13
  3. Geometric Continuum Mechanics

    1. Front Matter
      Pages 15-15
    2. Simon R. Eugster
      Pages 17-32
    3. Simon R. Eugster
      Pages 33-42
  4. Induced Beam Theories

    1. Front Matter
      Pages 43-43
    2. Simon R. Eugster
      Pages 45-53
    3. Simon R. Eugster
      Pages 55-73
    4. Simon R. Eugster
      Pages 75-81
    5. Simon R. Eugster
      Pages 83-99
    6. Simon R. Eugster
      Pages 101-115
    7. Simon R. Eugster
      Pages 117-121
  5. Back Matter
    Pages 123-146

About this book


This research monograph discusses novel approaches to geometric continuum mechanics and introduces beams as constraint continuous bodies. In the coordinate free and metric independent geometric formulation of continuum mechanics as well as for beam theories, the principle of virtual work serves as the fundamental principle of mechanics. Based on the perception of analytical mechanics that forces of a mechanical system are defined as dual quantities to the kinematical description, the virtual work approach is a systematic way to treat arbitrary mechanical systems. Whereas this methodology is very convenient to formulate induced beam theories, it is essential in geometric continuum mechanics when the assumptions on the physical space are relaxed and the space is modeled as a smooth manifold. The book addresses researcher and graduate students in engineering and mathematics interested in recent developments of a geometric formulation of continuum mechanics and a hierarchical development of induced beam theories.


Applications of Beam Theories Beam Theories Continuum Mechanics Foundations of Continuum Mechanics Nonlinear Beam Theories

Authors and affiliations

  1. 1.Institute for Nonlinear MechanicsUniversity of StuttgartStuttgartGermany

Bibliographic information

  • Book Title Geometric Continuum Mechanics and Induced Beam Theories
  • Authors Simon R. Eugster
  • Series Title Lecture Notes in Applied and Computational Mechanics
  • Series Abbreviated Title Lect.Notes in Applied (formerly:Lect.Notes Appl.Mechan.)
  • DOI
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Hardcover ISBN 978-3-319-16494-6
  • Softcover ISBN 978-3-319-36851-1
  • eBook ISBN 978-3-319-16495-3
  • Series ISSN 1613-7736
  • Series E-ISSN 1860-0816
  • Edition Number 1
  • Number of Pages IX, 146
  • Number of Illustrations 12 b/w illustrations, 0 illustrations in colour
  • Topics Solid Mechanics
    Classical and Continuum Physics
    Solid Mechanics
  • Buy this book on publisher's site
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“This book presents elements of Geometric continuum Mechanics with application to rod theories. … the book may be used in courses to the advanced undergraduate students that already have knowledge about the classical beam theories. Also it will be useful to the graduate students of Mechanics and the researchers in Mechanics.” (Teodor Atanacković, zbMATH 1330.74002, 2016)