© 2010

Finite Rotation Shells

Basic Equations and Finite Elements for Reissner Kinematics

  • Editors
  • K. Wiśniewski


  • Develops shell equations with drilling rotation from various sets of 3D equations with rotations,

  • Expounds the role of the Rotation Constraint equation as a means to introduce the drilling rotation,

  • Describes and evaluates several enhanced, mixed, and mixed/enhanced 4-node elements with drilling rotations,

  • Presents a fairly complete set of numerical test for shells,


Table of contents

  1. Front Matter
    Pages i-xiii
  2. Preliminaries

    1. Front Matter
      Pages 1-1
    2. K. Wiśniewski
      Pages 2-5
  3. Shell Equations

    1. Front Matter
      Pages 21-21
    2. K. Wiśniewski
      Pages 22-29
    3. K. Wiśniewski
      Pages 30-48
    4. K. Wiśniewski
      Pages 49-59
    5. K. Wiśniewski
      Pages 97-124
  4. Finite Rotations for Shells

    1. Front Matter
      Pages 125-125
    2. K. Wiśniewski
      Pages 126-177
    3. K. Wiśniewski
      Pages 178-227
  5. Four-Node Shell Elements

    1. Front Matter
      Pages 229-229
    2. K. Wiśniewski
      Pages 230-267
    3. K. Wiśniewski
      Pages 396-417
  6. Numerical Examples

    1. Front Matter
      Pages 419-419

About this book


This book covers theoretical and computational aspects of non-linear shells. Several advanced topics of shell equations and finite elements, not included in standard textbooks on finite elements, are addressed.

Key features include: several sets of 3D equations with the rotations introduced by either the polar decomposition equation or the rotation constraint equation; shell equations based on Reissner kinematics for finite rotations and strains, formulated in terms of different strains and stresses; a comprehensive account of finite rotations, including their properties and parameterization, as well as the algorithmic issues pertaining to rotation parameters; a comprehensive description and evaluation of several enhanced, mixed, and mixed/enhanced 4-node elements; a selection of useful remedies for such problems as: poor accuracy of in-plane shear strain, transverse shear locking, over-stiffening of warped elements, locking in sinusoidal bending, and deterioration of accuracy for extremely thin elements; a large set of numerical benchmarks for finite rotation shells; an extensive bibliography and comprehensive index.

Shells have been a subject of the author’s research for years, and all the methods described in the book have been implemented and tested in the field.

The book can be useful for graduate students, professional engineers, and researchers specializing in shells, Finite Elements and applied numerical methods.


computational mechanics deformation finite elements finite rotation shells four-node shell elements kinematics mechanics reissner kinematics rotation shells stress

Bibliographic information

  • Book Title Finite Rotation Shells
  • Book Subtitle Basic Equations and Finite Elements for Reissner Kinematics
  • Authors K. Wisniewski
  • Series Title Lecture Notes on Numerical Methods in Engineering and Sciences
  • DOI
  • Copyright Information Springer Science+Business Media B.V. 2010
  • Publisher Name Springer, Dordrecht
  • eBook Packages Engineering Engineering (R0)
  • Hardcover ISBN 978-90-481-8760-7
  • Softcover ISBN 978-94-007-3198-1
  • eBook ISBN 978-90-481-8761-4
  • Series ISSN 1877-7341
  • Edition Number 1
  • Number of Pages XIV, 483
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Computational Intelligence
    Solid Mechanics
  • Buy this book on publisher's site
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From the reviews:

“This outstanding, very important and useful book presets a modern continuum mechanics and mathematical framework to study the physical behaviours of shells, and to formulate and evaluate finite element procedures. … The monograph is written in an accessible and self-contained manner. It will be of interest to mathematicians and engineers working in solid mechanics. Moreover, it would be good as a textbook for graduate courses in mechanics of elastic shells (specializing in shells, finite elements and applied numerical methods).” (Ján Lovíšek, Mathematical Reviews, Issue 2012 g)

“The objective is to provide a comprehensive introduction to finite rotation shells and to nonlinear shell finite elements. The book is intended for both teaching and self-study, and emphasizes fundamental aspects and techniques of the subject. This book also contains several topics related to nonlinear shells such as the parametrization of finite rotations, the methods of inclusion of the drilling rotation, various methods of treating the normal strain, and the mixed finite elements.” (V. Leontiev, Zentralblatt MATH, Vol. 1201, 2011)