Computational Tensor Analysis of Shell Structures

  • Steve Naomis
  • Paul C. M. Lau

Part of the Lecture Notes in Engineering book series (LNENG, volume 58)

Table of contents

  1. Front Matter
    Pages N1-XII
  2. Steve Naomis, Paul C. M. Lau
    Pages 1-8
  3. Steve Naomis, Paul C. M. Lau
    Pages 9-59
  4. Steve Naomis, Paul C. M. Lau
    Pages 60-100
  5. Steve Naomis, Paul C. M. Lau
    Pages 101-156
  6. Steve Naomis, Paul C. M. Lau
    Pages 157-181
  7. Steve Naomis, Paul C. M. Lau
    Pages 182-183
  8. Back Matter
    Pages 184-304

About this book


This book presents a method which is capable of evaluating the deformation characteristics of thin shell structures A free vibration analysis is chosen as a convenient means of studying the displacement behaviour of the shell, enabling it to deform naturally without imposing any particular loading conditions. The strain-displacement equations for thin shells of arbitrary geometry are developed. These relationships are expressed in general curvilinear coordinates and are formulated entirely in the framework of tensor calculus. The resulting theory is not restricted to shell structures characterized by any particular geometric form, loading or boundary conditions. The complete displacement and strain equations developed by Flugge are approximated by the curvilinear finite difference method and are applied to computing the natural frequencies and mode shapes of general thin shells. This approach enables both the displacement components and geometric properties of the shell to be approximated numerically and accurately. The selection of an appropriate displacement field to approximate the deformation of the shell within each finite difference mesh is discussed in detail. In addition, comparisons are made between the use of second and third-order finite difference interpolation meshes.


Computational analysis Fundament Schalentragwerke Shell structures Tensor analysis Tensorenberechnung beam structure

Authors and affiliations

  • Steve Naomis
  • Paul C. M. Lau
    • 1
  1. 1.Civil Engineering DepartmentUniversity of Western AustraliaNedlandsAustralia

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1990
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-52852-4
  • Online ISBN 978-3-642-84243-6
  • Series Print ISSN 0176-5035
  • Buy this book on publisher's site