Singular Problems in Shell Theory Computing and Asymptotics [Hardcover]

This book deals with various aspects in relation with thin shell theory: general geometric formalism of shell theory, analysis of singularities, numerical computing of thin shell problems, mathematical considerations on boundary values problems.

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).

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)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-unifl³n