Finite Rotation Shells

Basic Equations and Finite Elements for Reissner Kinematics

  • Editors
  • K. Wiśniewski

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
    2. K. Wiśniewski
      Pages 420-456
  7. Back Matter
    Pages 457-483

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

  • DOI
  • Copyright Information Springer Science+Business Media B.V. 2010
  • Publisher Name Springer, Dordrecht
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-90-481-8760-7
  • Online ISBN 978-90-481-8761-4
  • Series Print ISSN 1877-7341
  • Buy this book on publisher's site