دانلود کتاب Buckling of bars, plates, and shells

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Contents
List of Symbols
1. Introduction
1.1 Geometric Nonlinearity in Mechanics of Deformable Bodies
1.2 Column Analysis
1.3 Adjacent Equilibrium
1.4 The Slightly Crooked Column
1.5 Stability Theory
1.6 Metric System Units
1.7 General References
References
Problems
2. Straight Bars
2.1 Introduction
2.2 Flexural Instability of Columns
2.2a Influence of Boundary Conditions
2.2b Instability of Frames
2.2c Elastic Lateral Support
2.2d Column on an Elastic Foundation
2.3 Torsional Instability of Columns
2.4 Lateral Instability of Beams
2.5 Beam Columns
2.6 Failure of Slender Bars
References
Problems
3. Rectangular Flat Plates
3.1 Introduction
3.2 Elements of Plate Bending Theory
3.3 Nonlinear Equilibrium Equations
3.3a Summation of Forces and Moments
3.3b Stationary Potential Energy
3.3c Nonlinear Equilibrium Paths
3.4 Linear Stability Equations
3.4a Adjacent-Equilibrium Criterion
3.4b Minimum Potential Energy Criterion
3.5 Applications of the Stability Equation
3.5a Plate Simply Supported on Four Edges
3.5b Other Boundry Conditions
3.5c Shear Loading
3.6 Orthotropic Plates
3.7 Sandwich Plates
3.8 Failure of Plates
References
Problems
4. Circular Rings
4.1 Introduction
4.2 Thin-Ring Deformation Geometry
4.3 Nonlinear Equilibrium Equations for Fluid-Pressure Loading
4.4 Linear Stability Equations
4.4a Adjacent-Equilibrium Criterion
4.4b Minimum Potential Energy Criterion
4.5 Solution for Fluid-Pressure Loading
4.6 Ring on an Elastic Foundation
4.7 Centrally Directed Pressure Loading
4..8 The Donnell Approximations
References
Problems
5. Circular Cylindrical Shells
5.1 Introduction
5.2 Donnell Form of the Nonlinear Equilibrium Equations
5.2a Summation of Forces and Moments
5.2b Stationary Potential Energy
5.2c Nonlinear Equilibrium Paths
5.3 Donnell Form of the Linear Stability Equations
5.3a Adjacent-Equilibrium Criterion
5.3b Minimum Potential Energy Criterion
5.4 Stability Equations for Nonshallow Cylinders
5.4a Dead-Loading
5.4b Fluid-Pressure Loading
5.5 Applications of the Stability Equations
5.5a Uniform Lateral Pressure
5.5b Axial Compression
5.5c Torsion
5.5d Combined Loading
5.6 Orthotropic Cylindrical Shells
5.7 Failure of Cylindrical Shells
References
Problems
6. General Shells
6.1 Introduction
6.2 Nonlinear Equilibrium Equations
6.3 Linear Stability Equations
6.3a Minimum Potential Energy Criterion
6.3b Adjacent-Equilibrium Criterion
6.4 Shells of Revolution
6.4a Stability Equations with Prebuckling Rotations Retained
6.4b Stability Equations with Prebuckling Rotations Omitted
6.5 Applications of the Stability Equations
6.5a Circular Flat Plates
6.5b Shallow Spherical Caps
6.5c Conical Shells
6.5d Segments of Toroidal Shells
References
Problems
7. Influence of Initial Imperfections
7.1 Introduction
7.2 Cylinder with Axisymmetric Imperfections
7.3 Initial-Postbuckling Analysis
7.3a The Koiter Theory
7.3b Two-Bar Frame
7.3c Other Examples
7.4 Conclusions
References
Problems
8. Numerical Solution Methods
8.1 Introduction
8.2 Matrix Notation
8.3 Series Expansions
8.3a The Rayleigh-Ritz Method
8.3b The Galerkin Method
8.3c Buckling of a Cylinder under Bending
8.4 Finite Difference Analysis
8.4a Application to Column Buckling
8.4b Two-dimensional Finite Difference Expressions
8.5 Numerical Integration
8.6 Finite Element Analysis
8.6a Introduction
8.6b Bending of a Beam
8.6c Column Buckling
8.6d Shells of Revolution
References
Problems
9. Nonlinear Analysis
9.1 Introduction
9.2 Two-Column Structure
9.3 Solution Methods for Nonlinear Algebraic Equation Systems
9.4 Postbuckling Behavior of Plates
9.5 Nonlinear Analysis of Cylndrical Shells
9.5a Axisymmetric Behavior
9.5b Bifurcation from a Nonlinear Prebuckling State
9.5c Postbuckling Behavior of Cylindrical Shells
9.5d Bending of Cylinders
9.6 Spherical Caps
9.7 Shells with Elliptic Cross Section
9.8 Shells with Cutouts
9.9 Conclusions
References
Appendix
A.1 Single Degree of Freedom Systems
A.2 Multiple Degree of Freedom Systems
A.3 Continuous Systems
A.4 The Euler Equations
A.5 The Trefftz Criterion
Index