The Stability of Elastic Systems

Preface

Introduction

Chapter 1 Principal Forms of Equilibrium Paths and their Stability


1-1 Conservative Elastic Systems—Generalized Coordinates


1-2 The Total Potential Energy Function—Principal Orthogonal Coordinates of Deformation


1-3 Equilibrium States and Stability—Critical States—Critical and Non-Critical Coordinates


1-4 Branching of Equilibrium Paths at a Critical Point—The Buckling Behavior


1-5 Stability of Equilibrium Near a Simple Branching Point


1-6 Symmetry in the Critical Coordinate at a Simple Branching Point


1-7 Perfect Elastic Systems Depending on Several Load Parameters—Equilibrium Hyper-Surfaces


1-8 Elastic Structural Systems with Non-Orthogonal Generalized Coordinates—Solution of the Non-Linear Equilibrium Equations at a Branching Point


1-9 Several Critical Coordinates—Branching Points of Systems with Several Degrees of Freedom


1-10 Symmetrical Elastic Structural Systems—Complete Symmetry


1-11 Buckling of Geometrically Imperfect Elastic Systems—Equilibrium Paths of Imperfect Systems


1-12 Equilibrium Paths of Imperfect Symmetrical Systems


1-13 Adjacent Branching Points—Coupled Modes of Elastic Buckling

Chapter 2 Analysis of Prismatic Members as Constitutive Elements of a System

Exact Theory


2-1 Buckling of Compressive Members in a Plane—Flexural Elastica


2-2 Transverse Deformations


2-3 Geometrical Compatibility


2-4 Coordinates of Deformation of Compressive Members


2-5 Internal Forces


2-6 Internal Energy


2-7 Summary of Basic Equations for Compressive Members—Generalized Equilibrium Equations


2-8 Inflectional Elastica of Tensile Members


2-9 Summary of Basic Equations for Inflectional Tensile Members


2-10 Non-Inflectional Elastica of Tensile Members—Non-Symmetrical Cases


2-11 Summary of Basic Equations for Non-Symmetrical, Noninflectional—Tensile Members


2-12 Summary of Basic Equations for Symmetrical Tensile Members

Approximate Theory


2-13 Categories of Practical Deformations


2-14 Generalized Equilibrium Equations for Single Members—Buckling of Prismatic Bars


2-15 The First-Order Theory


2-16 Pin-Ended Members or Columns

The Post-Buckling Behavior of Plane Frameworks

Chapter 3 Elastic Buckling and Stability of Statically Determinate Plane Frameworks


3-1 General Forms of the Force-Displacement Relationships for Perfect Members


3-2 Elastic Buckling of Isostatic Frames in Equilibrium—General Theory


3-3 Elastic Stability in Statical Equilibrium


3-4 Applications of the Theory—Tests on Model Frames


3-5 Experimental Determination of Critical States. The Southwell Plot


3-6 The Energy Method—The Total Potential Energy Surfaces of Statically Determinate Frameworks


3-7 Graphical Solution

Chapter 4 Elastic Buckling of Continuous Rigidly-Jointed Plane Frameworks


4-1 Critical States—Distinctions Between Braced and Unbraced Frames


4-2 Critical Loading Systems of Unbraced Frames


4-3 Geometrical Compatibility Conditions of Unbraced Frames


4-4 Continuity Conditions of Unbraced Frames


4-5 Statical Equilibrium of the Unbuckled Frame


4-6 Statical Equilibrium of the Buckled Frame


4-7 The Non-Linear Equations of Post-Critical Equilibrium States


4-8 Solution of the Non-Linear Equations of Post-Critical Equilibrium States

Chapter 5 Elastic Buckling of Rigidly-Jointed Plane Trusses


5-1 The First-Order Theory—Statical Equilibrium of the Unbuckled Truss


5-2 Statical Equilibrium of the Buckled Truss


5-3 The Initial Buckling Condition and the Post-Critical Equilibrium States


5-4 Tests on Model Frames


5-5 An Alternative Solution of the Non-Linear Equilibrium Equations


5-6 Axially-Hyperstatic Rigidly-Jointed Braced Frameworks—Compatibility Conditions of Flexural Contractions of the Members

The Post-Buckling Behavior of Space Frameworks

Chapter 6 Elastic Buckling and Stability of Statically Determinate Space Frameworks


6-1 General Force-Displacement Equilibrium Paths for Perfect Members


6-2 Geometrical Compatibility Conditions in Space


6-3 Critical Equilibrium States


6-4 Statical Equilibrium of the Buckled Framework


6-5 The Post-Critical Equilibrium Paths


6-6 Stability of Critical Equilibrium States


6-7 Model Isostatic Space Frames


6-8 Two Examples of Statical Equilibrium in the Elastic Post-Buckling of Isostatic Space Frames


6-9 The Energy Method—The Total Potential Energy Surfaces of Statically Determinate Space Frameworks

Axially-Hyperstatic Elastic Systems

Chapter 7 Elastic Buckling of Statically Indeterminate Pin-Jointed Systems and Space Frameworks


7-1 Flexural Buckling of Hyperstatic Pin-Jointed Frameworks


7-2 Ultimate Critical States


7-3 Statical Determination of Ultimate Critical Loads


7-4 Determination of Ultimate Critical Loads by the Principle of Virtual Work


7-5 Ultimate Critical States in the Case of Several Load Parameters


7-6 Elements of Elastic Limit-Design


7-7 Geometry and Kinematics of Spherical Reticulated Shells and Some Space Elements


7-8 Some Three-Dimensional Symmetrical Elements and Their Combinations


7-9 The Snap-Through Problem


7-10 Dimensional Model Analysis of the Elastic Stability of Structures

The Post-Buckling Behavior


7-11 Geometrical Compatibility Conditions in Hyperstatic Systems


7-12 Equilibrium of Hyperstatic Pin-Jointed Systems in Post-Buckling


7-13 Test of a Hyperstatic Model Frame


7-14 The Total Potential Energy Surfaces of Hyperstatic Frameworks

Chapter 8 Non-Conservative Aspects of Structural Systems


8-1 Plastic Flexural Buckling of Columns at Finite Deformations—Column Model


8-2 Statical Equilibrium of the Buckled Column


8-3 Initial Plastic Buckling Stress


8-4 Plastic Post-Buckling of Columns or Pin-Jointed Members—Post-Critical Equilibrium Surfaces


8-5 Plastic Buckling of Pin-Jointed Structural Systems


8-6 Buckling of Imperfection-Sensitive Structures Under Dynamic Loading—Existing Models and Estimates


8-7 Dynamic Buckling of Rigidly-Jointed Frameworks and Similar Systems Under Step-Loading


8-8 Quasi-Static Criteria

Appendix I

Appendix II

Appendix III

Appendix IV

Appendix V

Appendix VI

Appendix VII

References and Related Bibliography

Index