Asymptotical Mechanics of Thin-Walled Structures

In this book a detailed and systematic treatment of asymptotic methods in the theory of plates and shells is presented. The main features of the book are the basic principles of asymptotics and their applications, traditional approaches such as regular and singular perturbations, as well as new approaches such as the composite equations approach. The book introduces the reader to the field of asymptotic simplification of the problems of the theory of plates and shells and will be useful as a handbook of methods of asymptotic integration. Providing a state-of-the-art review of asymptotic applications, this book will be useful as an introduction to the field for novices as well as a reference book for specialists.

1 Asymptotic Approximations.- 2 Regular Perturbations of Parameters.- 3 Singular Perturbation Problems.- 4 Boundary Value Problems of Isotropic Cylindrical Shells.- 5 Boundary Value Problems — Orthotropic Shells.- 6 Composite Boundary Value Problems — Isotropic Shells.- 7 Composite Boundary Value Problems — Orthotropic Shells.- 8 Averaging.- 9 Continualization.- 10 Homogenization.- 11 Intermediate Asymptotics — Dynamical Edge Effect Method.- 12 Localization.- 13 Improvement of Perturbation Series.- 14 Matching of Limiting Asymptotic Expansions.- 15 Complex Variables in Nonlinear Dynamics.- 16 Other Asymptotical Approaches.- Afterword.- References.