Page 9 - Introduction to Continuum Mechanics

viii Contents

4.11 Equations of Motion Written With Respect to the Reference
Configuration 201
4.12 Stress Power 203
4.13 Rate of Heat Flow Into an Element by Conduction 207
4.14 Energy Equation 208
4.15 Entropy Inequality 209
Problems 210

Chapter 5 The Elastic Solid 217
5.1 Mechanical Properties 217
5.2 Linear Elastic Solid 220
Part A Linear Isotropic Elastic Solid 225

5.3 Linear Isotropic Elastic Solid 225
5.4 Young's Modulus, Poisson's Ratio, Shear Modulus, and Bulk Modulus 228
5.5 Equations of the Infinitesimal Theory of Elasticity 232
5.6 Navier Equation in Cylindrical and Spherical Coordinates 236
5.7 Principle of Superposition 238
5.8 Plane Irrotational Wave 238
5.9 Plane Equivoluminal Wave 242
5.10 Reflection of Plane Elastic Waves 248
5.11 Vibration of an Infinite Plate 251
5.12 Simple Extension 254
5.13 Torsion of a Circular Cylinder 258
5.14 Torsion of a Noncircular Cylinder 266
5.15 Pure Bending of a Beam 269
5.16 Plane Strain 275
5.17 Plane Strain Problem in Polar Coordinates 281
5.18 Thick-walled Circular Cylinder under Internal and External Pressure 284
5.19 Pure Bending of a Curved Beam 285
5.20 Stress Concentration due to a Small Circular Hole in a Plate under Tension 287
5.21 Hollow Sphere Subjected to Internal and External Pressure 291

Part B Linear Anisotropic Elastic Solid 293
5.22 Constitutive Equations for Anisotropic Elastic Solid 293
5.23 Plane of Material Symmetry 296
5.24 Constitutive Equation for a Monoclinic Anisotropic Elastic Solid 299