Geometric Formalism of Shell Theory -- Singularities and Boundary Layers in Thin Elastic Shell Theory -- Anisotropic Error Estimates in the Layers -- Numerical Simulation with Anisotropic Adaptive Mesh -- Singularities of Parabolic Inhibited Shells -- Singularities of Hyperbolic Inhibited Shells -- Singularities of Elliptic Well-Inhibited Shells -- Generalities on Boundary Conditions for Equations and Systems: Introduction to Sensitive Problems -- Numerical Simulations for Sensitive Shells -- Examples of Non-inhibited Shell Problems (Non-geometrically Rigid Problems).

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.