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© 2010

Singular Problems in Shell Theory

Computing and Asymptotics

Book

Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM, volume 54)

Table of contents

  1. Front Matter
  2. Evariste Sanchez-Palencia, Olivier Millet, Fabien Béchet
    Pages 1-11
  3. Evariste Sanchez-Palencia, Olivier Millet, Fabien Béchet
    Pages 13-32
  4. Evariste Sanchez-Palencia, Olivier Millet, Fabien Béchet
    Pages 33-68
  5. Evariste Sanchez-Palencia, Olivier Millet, Fabien Béchet
    Pages 69-86
  6. Evariste Sanchez-Palencia, Olivier Millet, Fabien Béchet
    Pages 87-105
  7. Evariste Sanchez-Palencia, Olivier Millet, Fabien Béchet
    Pages 107-145
  8. Evariste Sanchez-Palencia, Olivier Millet, Fabien Béchet
    Pages 147-170
  9. Evariste Sanchez-Palencia, Olivier Millet, Fabien Béchet
    Pages 171-194
  10. Evariste Sanchez-Palencia, Olivier Millet, Fabien Béchet
    Pages 195-217
  11. Evariste Sanchez-Palencia, Olivier Millet, Fabien Béchet
    Pages 219-233
  12. Evariste Sanchez-Palencia, Olivier Millet, Fabien Béchet
    Pages 235-245
  13. Back Matter

About this book

Introduction

It is known that deformations of thin shells exhibit peculiarities such as propagation of singularities, edge and internal layers, piecewise quasi inextensional deformations, sensitive problems and others, leading in most cases to numerical locking phenomena under several forms, and very poor quality of computations for small relative thickness. Most of these phenomena have a local and often anisotropic character (elongated in some directions), so that efficient numerical schemes should take them in consideration. This book deals with various topics in this context: general geometric formalism, analysis of singularities, numerical computing of thin shell problems, estimates for finite element approximation (including non-uniform and anisotropic meshes), mathematical considerations on boundary value problems in connection with sensitive problems encountered for very thin shells; and others. Most of numerical computations presented here use an adaptive anisotropic mesh procedure which allows a good computation of the physical peculiarities on one hand, and the possibility to perform automatic computations (without a previous mathematical description of the singularities) on the other. The book is recommended for PhD students, postgraduates and researchers who want to improve their knowledge in shell theory and in particular in the areas addressed (analysis of singularities, numerical computing of thin and very thin shell problems, sensitive problems). The lecture of the book may not be continuous and the reader may refer directly to the chapters concerned.

Keywords

Adaptive mesh Anisotropic mesh Finite Element estimation Internal layers Koiter model Sensitive problems Shell theory shells simulation singular perturbation

Authors and affiliations

  1. 1.Institut Jean Le Rond d’AlembertParisFrance
  2. 2.La Rochelle UniversityLa RochelleFrance
  3. 3.Metz UniversityMetzFrance

Bibliographic information

  • Book Title Singular Problems in Shell Theory
  • Book Subtitle Computing and Asymptotics
  • Authors Evariste Sanchez-Palencia
    Olivier Millet
    Fabien Bechet
  • Series Title Lecture Notes in Applied and Computational Mechanics
  • DOI https://doi.org/10.1007/978-3-642-13815-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering Engineering (R0)
  • Hardcover ISBN 978-3-642-13814-0
  • Softcover ISBN 978-3-642-26433-7
  • eBook ISBN 978-3-642-13815-7
  • Series ISSN 1613-7736
  • Series E-ISSN 1860-0816
  • Edition Number 1
  • Number of Pages XIV, 266
  • Number of Illustrations 238 b/w illustrations, 0 illustrations in colour
  • Topics Solid Mechanics
    Classical Mechanics
    Solid Mechanics
    Civil Engineering
    Automotive Engineering
  • Buy this book on publisher's site
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Reviews

From the reviews:

“The book under review is devoted to a mathematically rigorous study of singularities in linear elastic shell theory which appear for very small thickness. … This well-written book is a reader-friendly and good organized research work in the field of mathematical theory of shells. It can be recommended to highly-qualified experts in this field.” (Igor Andrianov, Zentralblatt MATH, Vol. 1208, 2011)