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ABSTRACT: 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.
TABLE OF CONTENTS:
Equations of Thin Elastic Shell Theory
Basic Equations of Shell Buckling
Simple Buckling Problems
Buckling Modes Localized near Parallels
Non-homogeneous Axial Compression of Cylindrical Shells
Buckling Modes Localized at a Point
Semi-momentless Buckling Modes
Effect of Boundary Conditions on Semi-momentless Modes
Torsion and Bending of Cylindrical and Conic Shells
Nearly Cylindrical and Conic Shells
Shells of Revolution of Negative Gaussian Curvature
Surface Bending and Shell Buckling
Buckling Modes Localized at an Edge
Shells of Revolution under General Stress State
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