Asymptotic Methods in the Buckling Theory of Elastic Shells - Hardcover

Andrei L. Smirnov; Petr E. Tovstik

Hardcover

ISBN 10: 9810247265 ISBN 13: 9789810247263

Publisher: World Scientific Publishing Company, 2001

Synopsis

This book contains solutions to the most typical problems of thin elastic shells buckling under conservative loads. The linear problems of bifurcation of shell equilibrium are considered using a two-dimensional theory of the Kirchhoff-Love type. The explicit approximate formulas obtained by means of the asymptotic method permit one to estimate the critical loads and find the buckling modes.The solutions to some of the buckling problems are obtained for the first time in the form of explicit formulas. Special attention is devoted to the study of the shells of negative Gaussian curvature, the buckling of which has some specific features. The buckling modes localized near the weakest lines or points on the neutral surface are constructed, including the buckling modes localized near the weakly supported shell edge. The relations between the buckling modes and bending of the neutral surface are analyzed. Some of the applied asymptotic methods are standard; the others are new and are used for the first time in this book to study thin shell buckling. The solutions obtained in the form of simple approximate formulas complement the numerical results, and permit one to clarify the physics of buckling.

About this title

Review

"The book will be of interest not only to researchers but also to mathematicians specializing in asymptotic methods for PDEs." -- Mathematical Reviews, 2003

Recommended as a valuable reference to all those working in this field of great theoretical significance. -- ZAMM

The book is a valuable collection of asymptotic techniques...a valuable addition to the literature on shells. -- Applied Mechanics Reviews, Sept 2002

Edition details

• Publisher: World Scientific Publishing Company
• Publication date: 2001
• ISBN 10: 9810247265
• ISBN 13: 9789810247263
• Binding: Hardcover
• Language: English
• Number of pages: 360