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Singular Problems in Shell Theory

Computing and Asymptotics

  • Book
  • © 2010

Overview

Authors:
  1. Evariste Sanchez-Palencia

    1. Institut Jean Le Rond d’Alembert, Paris, France

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  2. Olivier Millet

    1. La Rochelle University, La Rochelle, France

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    You can also search for this author in PubMed   Google Scholar

  3. Fabien Béchet

    1. Metz University, Metz, France

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  • State of the art of singular problems in shell theory
  • Written by experts in the field
  • Introduces new concepts

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

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Table of contents (11 chapters)

  1. Front Matter

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  2. Introduction

    • Evariste Sanchez-Palencia, Olivier Millet, Fabien Béchet
    Pages 1-11

  3. Geometric Formalism of Shell Theory

    • Evariste Sanchez-Palencia, Olivier Millet, Fabien Béchet
    Pages 13-32

  4. Singularities and Boundary Layers in Thin Elastic Shell Theory

    • Evariste Sanchez-Palencia, Olivier Millet, Fabien Béchet
    Pages 33-68

  5. Anisotropic Error Estimates in the Layers

    • Evariste Sanchez-Palencia, Olivier Millet, Fabien Béchet
    Pages 69-86

  6. Numerical Simulation with Anisotropic Adaptive Mesh

    • Evariste Sanchez-Palencia, Olivier Millet, Fabien Béchet
    Pages 87-105

  7. Singularities of Parabolic Inhibited Shells

    • Evariste Sanchez-Palencia, Olivier Millet, Fabien Béchet
    Pages 107-145

  8. Singularities of Hyperbolic Inhibited Shells

    • Evariste Sanchez-Palencia, Olivier Millet, Fabien Béchet
    Pages 147-170

  9. Singularities of Elliptic Well-Inhibited Shells

    • Evariste Sanchez-Palencia, Olivier Millet, Fabien Béchet
    Pages 171-194

  10. Generalities on Boundary Conditions for Equations and Systems: Introduction to Sensitive Problems

    • Evariste Sanchez-Palencia, Olivier Millet, Fabien Béchet
    Pages 195-217

  11. Numerical Simulations for Sensitive Shells

    • Evariste Sanchez-Palencia, Olivier Millet, Fabien Béchet
    Pages 219-233

  12. Examples of Non-inhibited Shell Problems (Non-geometrically Rigid Problems)

    • Evariste Sanchez-Palencia, Olivier Millet, Fabien Béchet
    Pages 235-245

  13. Back Matter

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Keywords

About this book

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.

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)

Authors and Affiliations

  • Institut Jean Le Rond d’Alembert, Paris, France

    Evariste Sanchez-Palencia

  • La Rochelle University, La Rochelle, France

    Olivier Millet

  • Metz University, Metz, France

    Fabien Béchet

Bibliographic Information

  • Book Title: Singular Problems in Shell Theory

  • Book Subtitle: Computing and Asymptotics

  • Authors: Evariste Sanchez-Palencia, Olivier Millet, Fabien Béchet

  • Series Title: Lecture Notes in Applied and Computational Mechanics

  • DOI: https://doi.org/10.1007/978-3-642-13815-7

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2010

  • Hardcover ISBN: 978-3-642-13814-0Published: 11 August 2010

  • Softcover ISBN: 978-3-642-26433-7Published: 13 October 2012

  • eBook ISBN: 978-3-642-13815-7Published: 07 September 2010

  • Series ISSN: 1613-7736

  • Series E-ISSN: 1860-0816

  • Edition Number: 1

  • Number of Pages: XIV, 266

  • Number of Illustrations: 238 b/w illustrations

  • Topics: Solid Mechanics, Classical Mechanics, Solid Mechanics, Civil Engineering, Automotive Engineering

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