Cover 1
Half-title 3
Series-title 5
Title 7
Copyright 8
Dedication 9
Contents 11
Introduction 15
Computer Simulation and Accelerated Experiences 16
Strategies for Solving Unfamiliar Problems 16
Outline of the Book 18
1 QED the Computer Laboratory 19
1.1 Brief Overview of the Mechanics of Structures 20
Types of Structures 20
Structural Analyses 21
I. Deformation and Compatibility 21
II. Stress and Equilibrium 22
III. Material Behavior 22
IV. Solution Procedure 23
V. Postprocessing 23
General Structural Analyses 24
I. Frame Element 25
II. Shell Element 25
III. Solid Element 26
Structural Analysis Programs 27
1.2 Installing and Running QED 27
Copying and Installing QED 27
Introductory Tour of QED 29
1.3 Overview of QED 30
Creating Models 31
I. Plate 33
II. Notch 33
III. Hole 33
IV. Open 34
V. Closed 34
VI. Frame 35
VII. Solid 35
VIII. General 36
Structure Data File 36
I. Boundary Conditions 36
II. Loads 37
III. Material Properties and Units 37
IV. Example Structure DataFile 38
Analyzing the Problem 39
I. Static 40
II. Buckling 40
III. Vibration 41
IV. Transient 41
V. Forced Frequency 41
VI. Nonlinear Implicit 42
VII. Nonlinear Explicit 42
VIII. Gallery of Nonlinear Ordinary Differential Equations (ODEs) 42
Viewing the Results 42
I. Deformed Shapes 43
II. Contours 43
III. Traction Distributions 44
IV. Traces 44
1.4 Supporting Programs 44
Mesh Generating with GenMesh 44
Analyses with StaDyn/NonStaD and Simplex 45
1.5 QED Guided Explorations 46
2 Static Analysis 49
2.1 Deformation of Structural Members 50
Partial Results 62
Background Readings 62
2.2 Stiffness Behavior of Thin-Walled Structures 63
Partial Results 73
Background Readings 73
2.3 Equilibrium of Beam and Frame Structures 73
Partial Results 87
Background Readings 87
2.4 Stress Analysis of Thin-Walled Structures 87
2.4.1 Open Section Thin-Walled Structures 88
Partial Results 97
2.4.2 Closed Thin-Walled Structures 98
Partial Results 105
Background Readings 105
2.5 Stress Analysis of a Ring 106
Partial Results 116
Background Readings 116
2.6 Stress Concentrations and Singularities 116
Partial Results 125
Background Readings 125
3 Vibration of Structures 126
3.1 Introduction to Vibrations 127
Partial Results 135
Background Readings 135
3.2 Modes of Vibration 135
Background Readings 144
3.3 Prestressed Structures 144
Partial Results 153
Background Readings 153
3.4 Frequency Analysis of Signals 153
Partial Results 160
Background Readings 161
3.5 Effect of Mass and Gravity on Vibrations 161
Partial Results 166
Background Readings 166
3.6 Vibration of Shells 166
Partial Results 173
Background Readings 174
4 Wave Propagation 175
4.1 Introduction to Wave Propagation 177
Partial Results 186
Background Readings 186
4.2 General Exploration of Wave Speeds 187
Partial Results 196
Background Readings 197
4.3 Dispersion of Waves 197
Partial Results 210
Background Readings 210
4.4 Deep Waveguides 211
Partial Results 219
Background Readings 219
4.5 Relation Between Waves and Vibrations 220
Part I. Transient Analyses 220
Partial Results 227
Background Readings 227
4.6 Dynamic Stress Concentrations 227
Partial Results 239
Background Readings 239
5 Nonlinear Structural Mechanics 240
5.1 Nonlinear Geometric Behavior of Structures 241
5.1.1 Large Deformations and Strains 241
Partial Results 249
5.1.2 Large Deflections of Plates 249
Partial Results 259
Background Readings 260
5.2 Elastic-Plastic Response and Residual Stresses 260
Partial Results 267
Background Readings 267
5.3 Rubber Elasticity 267
Partial Results 278
Background Readings 278
5.4 Nonlinear Vibrations 278
Partial Results 288
Background Readings 288
5.5 Nonlinear Vibrations Under Gravity 289
Partial Results 297
Background Readings 297
5.6 Impact 297
5.6.1 Contact Force Histories During Impact 297
Partial Results 303
5.6.2 Disk Impacting a Half-Plane 303
Partial Results 310
Background Readings 310
6 Stability of the Equilibrium 311
6.1 Introduction to Elastic Stability 312
Partial Results 321
Background Readings 322
6.2 Eigenanalysis of Buckling 322
6.2.1 Buckling of Closed Sections 322
Partial Results 330
6.2.2 Torsional Buckling of Open Sections 331
Partial Results 341
Background Readings 341
6.3 Stability and Load Imperfections 342
Partial Results 348
Background Readings 349
6.4 Elastic-Plastic Buckling 349
6.4.1 Buckling of Short Columns 349
Partial Results 356
6.4.2 Buckling of Long Columns 356
Partial Results 363
Background Readings 363
6.5 Stability of Motion in the Large 363
6.5.1 Stability of an Arched Structure 363
Partial Results 372
6.5.2 Stability of a Truss Structure 372
Partial Results 377
Background Readings 377
6.6 Dynamic Instability Under Follower Loads 378
Partial Results 388
Background Readings 389
7 Constructing Simple Analytical Models 390
7.1 Fundamentals of Solid Mechanics 391
Large-Deformation Measure of Strain 391
Stress and Equilibrium 393
Work and Strain Energy Concepts 395
Energies for Particular Systems 398
7.2 Stationary Principles in Mechanics 400
Principle of Virtual Work 400
Conservative Systems 403
Dynamical Systems 404
Ritz Method for Continuous Systems 406
Finite Element Formulation 408
7.3 Models, Similitude, and Dimensional Analysis 411
7.4 Some Simple Models With the Ritz Method 418
7.5 Mechanical Models for Postbuckling 430
7.6 Simple Models for Loadings 439
7.7 QED\u2019s Gallery of ODEs 449
References 453
Index 459