Singular Problems in Shell Theory

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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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.

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

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)

• 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

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