Asymptotic Methods in the Buckling Theory of Elastic Shells.
Title:
Asymptotic Methods in the Buckling Theory of Elastic Shells.
Author:
Tovstik, Petr E.
ISBN:
9789812794567
Personal Author:
Physical Description:
1 online resource (359 pages)
Series:
Series on Stability, Vibration and Control of Systems, Series A ; v.4
Series on Stability, Vibration and Control of Systems, Series A
Contents:
Contents -- Preface -- Introduction -- Basic notation -- 1 Equations of Thin Elastic Shell Theory -- 1.1 Elements of Surface Theory -- 1.2 Equilibrium Equations and Boundary Conditions -- 1.3 Errors of 2D Shell Theory of Kirchhoff-Love Type -- 1.4 Membrane Stress State -- 1.5 Technical Shell Theory Equations -- 1.6 Technical Theory Equations in the Other Cases -- 1.7 Shallow Shells -- 1.8 Initial Imperfections -- 1.9 Cylindrical Shells -- 1.10 The Potential Energy of Shell Deformation -- 1.11 Problems and Exercises -- 2 Basic Equations of Shell Buckling -- 2.1 Types of Elastic Shell Buckling -- 2.2 The Buckling Equations -- 2.3 The Buckling Equations for a Membrane State -- 2.4 Buckling Equations of the General Stress State -- 2.5 Problems and Exercises -- 3 Simple Buckling Problems -- 3.1 Buckling of a Shallow Convex Shell -- 3.2 Shallow Shell Buckling Modes -- 3.3 The Non-Uniqueness of Buckling Modes -- 3.4 A Circular Cylindrical Shell Under Axial Compression -- 3.5 A Circular Cylindrical Shell Under External Pressure -- 3.6 Estimates of Critical Load -- 3.7 Problems and Examples -- 4 Buckling Modes Localized near Parallels -- 4.1 Local Shell Buckling Modes -- 4.2 Construction Algorithm of Buckling Modes -- 4.3 Buckling Modes of Convex Shells of Revolution -- 4.4 Buckling of Shells of Revolution Without Torsion -- 4.5 Buckling of Shells of Revolution Under Torsion -- 4.6 Problems and Exercises -- 5 Non-homogeneous Axial Compression of Cylindrical Shells -- 5.1 Buckling Modes Localized near Generatrix -- 5.2 Reconstruction of the Asymptotic Expansions -- 5.3 Axial Compression and Bending of Cylindrical Shell -- 5.4 The Influence of Internal Pressure -- 5.5 Buckling of a Non-Circular Cylindrical Shell -- 5.6 Cylindrical Shell with Curvature of Variable Sign -- 5.7 Problems and Exercises.
6 Buckling Modes Localized at a Point -- 6.1 Local Buckling of Convex Shells -- 6.2 Construction of the Buckling Mode -- 6.3 Ellipsoid of Revolution Under Combined Load -- 6.4 Cylindrical Shell Under Axial Compression -- 6.5 Construction of the Buckling Modes -- 6.6 Problems and Exercises -- 7 Semi-momentless Buckling Modes -- 7.1 Basic Equations and Boundary Conditions -- 7.2 Buckling Modes for a Conic Shell -- 7.3 Effect of Initial Membrane Stress Resultants -- 7.4 Semi-Momentless Buckling Modes of Cylindrical Shells -- 7.5 Problems and Exercises -- 8 Effect of Boundary Conditions on Semi-momentless Modes -- 8.1 Construction Algorithm for Semi-Momentless Solutions -- 8.2 Semi-Momentless Solutions -- 8.3 Edge Effect Solutions -- 8.4 Separation of Boundary Conditions -- 8.5 The Effect of Boundary Conditions on the Critical Load -- 8.6 Boundary Conditions and Buckling of a Cylindrical Shell -- 8.7 Conic Shells Under External Pressure -- 8.8 Problems and Exercises -- 9 Torsion and Bending of Cylindrical and Conic Shells -- 9.1 Torsion of Cylindrical Shells -- 9.2 Cylindrical Shell under Combined Loading -- 9.3 A Shell with Non-Constant Parameters Under Torsion -- 9.4 Bending of a Cylindrical Shell -- 9.5 The Torsion and Bending of a Conic Shell -- 9.6 Problems and Exercises -- 10 Nearly Cylindrical and Conic Shells -- 10.1 Basic Relations -- 10.2 Boundary Problem in the Zeroth Approximation -- 10.3 Buckling of a Nearly Cylindrical Shell -- 10.4 Torsion of a Nearly Cylindrical Shell -- 10.5 Problems and Exercises -- 11 Shells of Revolution of Negative Gaussian Curvature -- 11.1 Initial Equations and Their Solutions -- 11.2 Separation of the Boundary Conditions -- 11.3 Boundary Problem in the Zeroth Approximation -- 11.4 Buckling Modes Without Torsion -- 11.5 The Case of the Neutral Surface Bending.
11.6 The Buckling of a Torus Sector -- 11.7 Shell with Gaussian Curvature of Variable Sign -- 11.8 Problems and Exercises -- 12 Surface Bending and Shell Buckling -- 12.1 The Transformation of Potential Energy -- 12.2 Pure Bending Buckling Mode of Shells of Revolution -- 12.3 The Buckling of a Weakly Supported Shell of Revolution -- 12.4 Weakly Supported Cylindrical and Conical Shells -- 12.5 Weakly Supported Shells of Negative Gaussian Curvature -- 12.6 Problems and Exercises -- 13 Buckling Modes Localized at an Edge -- 13.1 Rectangular Plates Under Compression -- 13.2 Cylindrical Shells and Panels Under Axial Compression -- 13.3 Cylindrical Panel with a Weakly Supported Edge -- 13.4 Shallow Shell with a Weak Edge Support -- 13.5 Modes of Shells of Revolution Localized near an Edge -- 13.6 Buckling Modes with Turning Points -- 13.7 Modes Localized near the Weakest Point on an Edge -- 13.8 Problems and Exercises -- 14 Shells of Revolution under General Stress State -- 14.1 The Basic Equations and Edge Effect Solutions -- 14.2 Buckling with Pseudo-bending Modes -- 14.3 The Cases of Significant Effect of Pre-buckling strains -- 14.4 The Weakest Parallel Coinciding With an Edge -- 14.5 Problems and Exercises -- Bibliography -- List of Figures -- List of Tables -- Index -- About the Authors and Editors.
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. 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 Points; 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. Readership: Engineers designing real thin-walled structures;
graduate students in civil engineering, mechanical engineering and applied mathematics; researchers in thin shell theory and its applications; mathematicians interested in asymptotic methods.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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