Stability of Elastic Structures

By: N.A. Alfutov, V. Balmont (Translator), E. Evseev (Translator)

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Hardcover | 28 February 2000

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356 Pages

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23.5 x 15.88 x 1.91

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The subject discussed in this book is the stability of thin-walled elastic systems under static loads. The presentation of these problems is based on modern approaches to elastic-stability theory. Special attention is paid to the formulation of elastic-stability criteria, to the statement of column, plate and shell stability problems, to the derivation of basic relationships, and to a discussion of the boundaries of the application of analytic relationships. The author has tried to avoid arcane, nonstandard problems and elaborate and unexpected solutions, which bring real pleasure to connoisseurs, but confuse students and cause bewilderment to some practical engineers. The author has an apprehension that problems which, though interesting, are limited in application can divert the reader's attention from the more prosaic but no less sophisticated general problems of stability theory.

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Basic Theory of Elastic Stability	p. 1
Equilibrium Paths for Deformed Systems	p. 2
Stable and Unstable Equilibrium States	p. 6
Bifurcation Points, Limit Points, and Critical Loads	p. 12
Energy Criterion for Bifurcational Stability Loss	p. 15
Homogeneous Linearized Equations	p. 23
Supercritical Behavior of Elastic Structures	p. 27
Stability of Elastic Structures Under Combined Loading: Boundary of Stability Region	p. 31
On the Statement of Stability Problems for Thin-Walled Structures	p. 37
Energy Method for the Solution of Stability Problems	p. 45
Principle of Virtual Displacements	p. 45
Variational Approaches in the Linear Theory of Elasticity	p. 52
Two Basic Forms of the Energy Criterion for Bifurcational Stability Loss	p. 56
Energy Criterion in Bryan Form	p. 60
Energy Criterion in Timoshenko Form	p. 67
Rayleigh-Ritz Method in Stability Analysis	p. 72
The Galerkin Method and its Relationship to the Rayleigh-Ritz Method	p. 77
Stability of Straight Columns	p. 85
Statement of the Problem: Basic Linearized Equation	p. 85
Examples of the Analytic Solution of the Basic Equation	p. 94
Columns on Elastic Foundations and Elastic Supports	p. 103
Stability of Self-Gravitating Column	p. 110
Lateral Torsional Beam Buckling	p. 121
The Inluence of Transverse Shear Strains: Stability of Sandwich Struts	p. 129
Method of Initial Parameters in Stability Analysis	p. 135
Stability of Plates	p. 143
Statement of the Problem: Basic Initial Relations	p. 143
Basic Linearized Equation	p. 152
Solution of Basic Equation for a Rectangular Plate	p. 161
Solution of Basic Equation for a Circular Plate	p. 173
Approximate Solutions of the Basic Linearized Equation	p. 178
Energy Method for the Study of the Stability of Plates	p. 189
Energy Method for the Problem of Plate Bending: Accounting for Shears	p. 189
Application of the Energy Criterion in Bryan Form	p. 194
The Energy Criterion in Timoshenko Form: Thermoelasticity Problem of Plate Stability	p. 198
Stability Criterion Statement via Statically Admissible Initial Internal Forces	p. 203
Examples of Applications of the Energy Method: Inluence of Transverse Shear	p. 206
Stability of Plates under Local Loads	p. 216
Stability of Shells	p. 221
Stability of Circular Ring	p. 221
Basic Initial Relations for a Cylindrical Shell	p. 239
Stability of Cylindrical Shell Subjected to Axial Compression	p. 252
Determination of Critical Value of External Pressure	p. 258
Stability of Cylindrical Shell Under Torsion and Transverse Bending	p. 266
Stability of a Shell Stiffened by Elastic Frames	p. 271
Determination of Critical Loads Using the Stability Criterion in Timoshenko Form	p. 278
Nonlinear Problems: Stability of Real Bars, Plates, and Shells	p. 287
Deformation of Compressed Bar After Stability Loss	p. 287
Supercritical Behavior of Elastic Plates	p. 294
Nonlinear Approaches in Stability Problems for Shells	p. 301
Initial Imperfections in Stability Problems for Bars and Plates	p. 308
Initial Imperfections in Stability Problems for Shells	p. 315
Appendix	p. 321
Eigenvalue Problems	p. 321
Stationary Values and Extrema of Functions and Functionals	p. 324
References	p. 331
Index	p. 335
Table of Contents provided by Publisher. All Rights Reserved.

Stability of Elastic Structures

At a Glance

Hardcover

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