Guided Explorations of the Mechanics of Solids and Structures Book

Introduction 1

1 QED the Computer Laboratory 5

1.1 Brief Overview of the Mechanics of Structures 6

1.2 Installing and Running QED 13

1.3 Overview of QED 16

1.4 Supporting Programs 30

1.5 QED Guided Explorations 32

2 Static Analysis 35

2.1 Deformation of Structural Members 36

2.2 Stiffness Behavior of Thin-Walled Structures 49

2.3 Equilibrium of Beam and Frame Structures 59

2.4 Stress Analysis of Thin-Walled Structures 73

2.5 Stress Analysis of a Ring 92

2.6 Stress Concentrations and Singularities 102

3 Vibration of Structures 112

3.1 Introduction to Vibrations 113

3.2 Modes of Vibration 121

3.3 Prestressed Structures 130

3.4 Frequency Analysis of Signals 139

3.5 Effect of Mass and Gravity on Vibrations 147

3.6 Vibration of Shells 152

4 Wave Propagation 161

4.1 Introduction to Wave Propagation 163

4.2 General Exploration of Wave Speeds 173

4.3 Dispersion of Waves 183

4.4 Deep Waveguides 197

4.5 Relation Between Waves and Vibrations 206

4.6 Dynamic Stress Concentrations 213

5 Nonlinear Structural Mechanics 226

5.1 Nonlinear Geometric Behavior of Structures 227

5.2 Elastic-Plastic Response and Residual Stresses 246

5.3 Rubber Elasticity 253

5.4 Nonlinear Vibrations 264

5.5 Nonlinear Vibrations Under Gravity 275

5.6 Impact 283

6 Stability of the Equilibrium 297

6.1 Introduction to Elastic Stability 298

6.2 Eigenanalysis of Buckling 308

6.3 Stability and Load Imperfections 328

6.4 Elastic-Plastic Buckling 335

6.5 Stability of Motion in the Large 349

6.6 Dynamic Instability Under Follower Loads 364

7 Constructing Simple Analytical Models 376

7.1 Fundamentals of Solid Mechanics 377

7.2 Stationary Principlesin Mechanics 386

7.3 Models, Similitude, and Dimensional Analysis 397

7.4 Some Simple Models With the Ritz Method 404

7.5 Mechanical Models for Postbuckling 416

7.6 Simple Models for Loadings 425

7.7 QED's Gallery of ODEs 435

References 439

Index 445