This title deals with the new developments and application of the geometric method to the nonlinear stability problem for thin non-elastic shells. A.V. Pogorelov (Harkov, Ukraine) was the first to provide in his monographs the geometric construction of the deformed shell surface in a post-critical stage and deriving explicitly the asymptotic formulas for the upper and lower critical loads. The geometric method by Pogorelov is one of the most important analytical methods developed during the 20th century. Its power consists in its ability to provide a clear geometric picture of the post critical form of a deformed shell surface, successfully applied to a direct variational approach to the nonlinear shell stability problems. Until now, most of Pogorelov's monographs were written in Russian, which limited the diffusion of his ideas among the international scientific community. This book is intended to assist and encourage the researchers in this field to apply the geometric method and the related results to everyday engineering practice.
Further developments of the geometric method are carried out in this book and are directed to stability of thin shells in the case of elastic anisotropy, elastic anisotropy with linear memory and elasto-plastic properties of the shell material. This book is intended to serve both as a textbook for postgraduate students in structural engineering and applied mathematics, and as a reference monograph for academic and industrial researchers.