ISBN: 3540657002
TITLE: Stability of Elastic Structures
AUTHOR: Alfutov, N.A.
TOC:
1. Basic Theory of Elastic Stability 1
1.1 Equilibrium Paths for Deformed Systems 2
1.2 Stable and Unstable Equilibrium States 6
1.3 Bifurcation Points, Limit Points, and Critical Loads 12
1.4 Energy Criterion for Bifurcational Stability Loss 15
1.5 Homogeneous Linearized Equations 23
1.6 Supercritical Behavior of Elastic Structures 27
1.7 Stability of Elastic Structures Under Combined Loading: Boundary of Stability Region 31
1.8 On the Statement of Stability Problems for Thin-Walled Structures 37
2. Energy Method for the Solution of Stability Problems 45
2.1 Principle of Virtual Displacements 45
2.2 Variational Approaches in the Linear Theory of Elasticity 52
2.3 Two Basic Forms of the Energy Criterion for Bifurcational Stability Loss 56
2.4 Energy Criterion in Bryan Form 60
2.5 Energy Criterion in Timoshenko Form 67
2.6 Rayleigh-Ritz Method in Stability Analysis 72
2.7 The Galerkin Method and its Relationship to the Rayleigh-Ritz Method 77
3. Stability of Straight Columns 85
3.1 Statement of the Problem: Basic Linearized Equation 85
3.2 Examples of the Analytic Solution of the Basic Equation 94
3.3 Columns on Elastic Foundations and Elastic Supports 103
3.4 Stability of Self-Gravitating Column 110
3.5 Lateral Torsional Beam Buckling 121
3.6 The Influence of Transverse Shear Strains: Stability of Sandwich Struts 129
3.7 Method of Initial Parameters in Stability Analysis 135
4. Stability of Plates 143
4.1 Statement of the Problem: Basic Initial Relations 143
4.2 Basic Linearized Equation 152
4.3 Solution of Basic Equation for a Rectangular Plate 161
4.4 Solution of Basic Equation for a Circular Plate 173
4.5 Approximate Solutions of the Basic Linearized Equation 178
5. Energy Method for the Study of the Stability of Plates 189
5.1 Energy Method for the Problem of Plate Bending: Accounting for Shears 189
5.2 Application of the Energy Criterion in Bryan Form 194
5.3 The Energy Criterion in Timoshenko Form: Thermoelasticity Problem of Plate Stability 198
5.4 Stability Criterion Statement via Statically Admissible Initial Internal Forces 203
5.5 Examples of Applications of the Energy Method: Influence of Transverse Shear 206
5.6 Stability of Plates under Local Loads 216
6. Stability of Shells 221
6.1 Stability of Circular Ring 221
6.2 Basic Initial Relations for a Cylindrical Shell 239
6.3 Stability of Cylindrical Shell Subjected to Axial Compression 252
6.4 Determination of Critical Value of External Pressure 258
6.5 Stability of Cylindrical Shell Under Torsion and Transverse Bending 266
6.6 Stability of a Shell Stiffened by Elastic Frames 271
6.7 Determination of Critical Loads Using the Stability Criterion in Timoshenko Form 278
7. Nonlinear Problems: Stability of Real Bars, Plates, and Shells 287
7.1 Deformation of Compressed Bar After Stability Loss 287
7.2 Supercritical Behavior of Elastic Plates 294
7.3 Nonlinear Approaches in Stability Problems for Shells 301
7.4 Initial Imperfections in Stability Problems for Bars and Plates 308
7.5 Initial Imperfections in Stability Problems for Shells 315
A. Appendix 321
A.1 Eigenvalue Problems 321
A.2 Stationary Values and Extrema of Functions and Functionals 324
References 331
Index 335
END