Dynamic Pulse Buckling : Theory and Experiment

1. Introduction.- 1.1 Forms of Dynamic Buckling.- 1.2 Examples of Dynamic Pulse Buckling.- 2. Impact Buckling of Bars.- 2.1 Introduction.- 2.2 Elastic Buckling of Long Bars.- 2.2.1 Equations of Motion.- 2.2.2 Static Elastic Buckling of a Simply Supported Bar.- 2.2.3 Theory of Dynamic Elastic Buckling of a Simply Supported Bar.- 2.2.4 Amplification Functions.- 2.2.5 Dynamic Elastic Buckling under Eccentric Load.- 2.2.6 Dynamic Elastic Buckling with Random Imperfections.- 2.2.7 Framing Camera Observations of Dynamic Elastic Buckling.- 2.2.8 Streak Camera Observations--Effects of the Moving Stress Wave.- 2.2.9 Experiments on Rubber Strips--Statistical Observations.- 2.2.10 Buckling Thresholds in Aluminum Strips.- 2.3 Dynamic Plastic Flow Buckling of Bars.- 2.3.1 Introduction.- 2.3.2 Differential Equation of Motion.- 2.3.3 The Initially Straight Bar.- 2.3.4 The Nearly Straight Bar.- 2.3.5 Comparisons of Theoretical Model and Experimental Results.- 3. Dynamic Pulse Buckling of Rings and Cylindrical Shells From Radial Loads.- 3.1 Introduction.- 3.2 Dynamic Plastic Flow Buckling of Rings and Long Cylindrical Shells From Uniform Radial Impulse.- 3.2.1 Introduction.- 3.2.2 Postulated Character of the Motion-Dynamic Flow Buckling.- 3.2.3 Equation of Motion.- 3.2.4 Perfectly Circular Ring, Almost Uniform Initial Radial Velocity.- 3.2.5 Strain Rate Reversal.- 3.2.6 The Buckling Terms-Representative Numerical Cases.- 3.2.7 Experimental Technique and Characteristic Results.- 3.2.8 Comparison of Experiment with Theory.- 3.2.9 Buckling Threshold.- 3.3 Dynamic Elastic Buckling of Rings and Cylindrical Shells From Uniform Radial Impulse.- 3.3.1 Introduction.- 3.3.2 Theory of Elastic Shell Motion.- 3.3.3 Initial Growth of the Flexural Modes--The Stability Parameter.- 3.3.4 Small Initial Velocity--Autoparametric Vibrations.- 3.3.5 Intermediate Initial Velocity--Onset of Pulse Buckling.- 3.3.6 High Initial Velocity--Pulse Buckling.- 3.4 Critical Radial Impulses for Elastic and Plastic Flow Buckling of Rings and Long Cylindrical Shells.- 3.4.1 Approach.- 3.4.2 Strain Hardening in Engineering Metals.- 3.4.3 Equations of Motion.- 3.4.4 Plastic Flow Buckling.- 3.4.5 Summary of Formulas for Critical Impulse.- 3.4.6 Buckling with a Cosine Impulse Distribution.- 3.4.7 Effects of Strain Rate Reversal.- 3.5 Dynamic Pulse Buckling of Cylindrical Shells From Transient Radial Pressure.- 3.5.1 Approach and Equations of Motion.- 3.5.2 Donnell Equations for Elastic Buckling.- 3.5.3 Fourier Series Solution--Static Buckling.- 3.5.4 Critical Pressure-Impulse Curves for Dynamic Buckling.- 3.5.5 Simple Formulas for Critical Curves.- 3.5.6 Experimental Results and Comparison with Theory.- 4. Flow Buckling Of Cylindrical Shells From Uniform Radial Impulse.- 4.1 Plastic Flow Buckling With Hardening and Directional Moments.- 4.1.1 Theory of Plastic Cylindrical Shells.- 4.1.2 Effect of Shell Length on Strain Rates.- 4.1.3 The Unperturbed Motion.- 4.1.4 Axial Strain Distribution.- 4.1.5 Perturbed Motion.- 4.1.6 Directional Moments.- 4.1.7 Governing Equation.- 4.1.8 Modal Solution.- 4.1.9 Amplification Functions.- 4.1.10 Asymptotic Solutions for Terminal Motion.- 4.1.11 Strain Hardening Moments Only.- 4.1.12 Directional Moments Only.- 4.1.13 Directional and Hardening Moments.- 4.1.14 Displacement and Velocity Imperfections.- 4.1.15 Threshold Impulse.- 4.1.16 Comparison of Theory and Experiment.- 4.2 Viscoplastic Flow Buckling with Directional Moments.- 4.2.1 Viscoplastic Moments.- 4.2.2 Theory of Viscoplastic Cylindrical Shells.- 4.2.3 The Unperturbed Motion.- 4.2.4 Perturbed Motion.- 4.2.5 Governing Equation.- 4.2.6 Modal Solution.- 4.2.7 Amplification Functions.- 4.2.8 Approximate Solutions for Terminal Motion.- 4.2.9 Preferred Modes and Threshold Impulses.- 4.2.10 Displacement and Velocity Imperfections.- 4.2.11 Viscoplastic and Directional Moments.- 4.2.12 Comparison of Theory and Experiment.- 4.3 Critical Velocity for Collapse of Cylindrical Shells Without Buckling.- 4.3.1 Strain-Hardening Moments Only.- 4.3.2 Strain Rate Moments Only.- 5. Dynamic Buckling of Cylindrical Shells Under Axial Impact.- 5.1 Dynamic Buckling of Cylindrical Shells Under Elastic Axial Impact.- 5.1.1 Analytical Formulation.- 5.1.2 Static Buckling.- 5.1.3 Amplification Functions for Dynamic Buckling.- 5.1.4 Buckling From Random Imperfections.- 5.1.5 Impact Experiments.- 5.1.6 Formula for Threshold Buckling.- 5.1.7 Dynamic Buckling Under Step Loads.- 5.2 Axial Plastic Flow Buckling of Cylindrical Shells.- 5.2.1 Introduction.- 5.2.2 Unperturbed Motion.- 5.2.3 Perturbed Motion.- 5.2.4 Governing Equations.- 5.2.5 Modal Solutions.- 5.2.6 Amplification Functions.- 5.2.7 Preferred Mode and Critical Velocity Formulas.- 5.2.8 Directional and Hardening Moments.- 5.2.9 Description of Experiments.- 5.2.10 Comparison of Theory and Experiment.- 5.2.11 Slow Buckling.- 5.2.12 Axial Impact of Plates.- 5.3 Forces and Energy Absorption During Axial Plastic Collapse of Tubes.- 5.3.1 Axial Collapse Experiments.- 5.3.2 Theoretical Estimates of Collapse Forces.- 5.3.3 Comparison of Theory and Experiment.- 6. Plastic Flow Buckling of Rectangular Plates.- 6.1 Introduction.- 6.2 Perturbational Flexure.- 6.3 Governing Equation.- 6.3.1 General Loading.- 6.3.2 Uniaxial Compression.- 6.4 Uniaxial Compression of Simply Supported Plates.- 6.4.1 Modal Solution.- 6.4.2 Amplification Functions.- 6.4.3 Preferred Mode and Critical Velocity Formulas.- 6.4.4 Directional and Hardening Moments.- 6.5 Uniaxial Compression of Unsupported Plates.- 6.5.1 Governing Equation, Modal Solution, and Amplification Functions.- 6.5.2 Preferred Mode and Critical Velocity Formulas.- 6.6 Comparison of Theoretical and Experimental Results.- 6.7 Slow Buckling.