Bendings of Surfaces and Stability of Shells
About this Title
A V Pogorelov
Publication: Translations of Mathematical Monographs
Publication Year: 1988; Volume 72
ISBNs: 978-0-8218-4525-7 (print); 978-1-4704-4486-0 (online)
MathSciNet review: MR972263
MSC: Primary 73L05; Secondary 53C45, 58G40, 73-02, 73H05
This book contains an accessible exposition of the geometric theory of stability of elastic shells, starting from the basic facts of the theory of finite and infinitesimal bendings of surfaces. The author has included a number of new results obtained in recent years. In particular, the complete solution of the problem of stability of spherical shells under an external pressure is contained here without any assumptions regarding the character of buckling.
Within the framework of the mathematical model of the phenomenon, the author gives a complete investigation of the loss of stability of a general, strictly convex shell fastened along an edge under external pressure. The author considers the question of the loss of stability of cylindrical shells under axial compression and the effect of various factors on the critical load, among other questions. In contrast to the author's 1967 book on the subject, this work is limited to a relatively small number of classical problems on the loss of stability of shells, but these problems are investigated more thoroughly.
Table of Contents
- Bendings of surfaces and elastic deformations of shells
- Elastic states of general convex shells
- Supercritical elastic states of a cylindrical shell under axial compression
- Infinitesimal bendings of surfaces and the stability of shells
- Loss of stability of a cylindrical shell under axial compression