Preface ....................................................... vii
Notation - A Short List ........................................ xv
Historical Note. Beginnings of Thermal Stresses Analysis ..... xvii
1 Basic Laws of Thermoelasticity ............................... 1
1 Introduction .............................................. 1
2 Stresses and Tractions .................................... 2
3 Equations of Motion ....................................... 4
4 Coordinate Transformation. Principal Axes ................. 6
5 Principal Stresses and Stress Invariants .................. 7
6 Displacement and Strain Tensor ........................... 10
7 Compatibility Equations. Simply Connected Region ......... 14
8 Compatibility Conditions. Multiply Connected Regions ..... 17
9 Constitutive Laws of Linear Thermoelasticity ............. 21
10 Displacement Formulation of Thermoelasticity ............. 23
11 Stress Formulation of Thermoelasticity ................... 24
12 Two-Dimensional Thermoelasticity ......................... 27
13 Michell Conditions ....................................... 35
14 Problems ................................................. 39
2 Thermodynamics of Elastic Continuum ......................... 43
1 Introduction ............................................. 43
2 Thermodynamics Definitions ............................... 44
3 First Law of Thermodynamics .............................. 45
4 Second Law of Thermodynamics ............................. 46
5 Variational Formulation of Thermodynamics ................ 48
6 Thermodynamics of Elastic Continuum ...................... 50
7 General Theory of Thermoelasticity ....................... 54
8 Free Energy Function of Hookean Materials ................ 57
9 Fourier's Law and Heat Conduction Equation ............... 60
10 Generalized Thermoelasticity, Second Sound ............... 61
11 Thermoelasticity without Energy Dissipation .............. 70
12 A Unified Generalized Thermoelasticity ................... 75
13 Uniqueness Theorem ....................................... 79
14 Variational Principle of Thermoelasticity ................ 88
15 Reciprocity Theorem ...................................... 91
16 Initial and Boundary Conditions .......................... 95
17 Problems ................................................. 98
3 Basic Problems of Thermoelasticity ......................... 105
1 Introduction ............................................ 105
2 Temperature Distribution for Zero Thermal Stress ........ 106
3 Analogy of Thermal Gradient with Body Forces ............ 110
4 General Solution of Thermoelastic Problems .............. 113
5 Solution of Two-Dimensional Navier Equations ............ 117
6 General Solution in Cylindrical Coordinates ............. 120
7 Solution of Problems in Spherical Coordinates ........... 123
8 Problems ................................................ 126
4 Heat Conduction Problems ................................... 131
1 Introduction ............................................ 131
2 Problems in Rectangular Cartesian Coordinates ........... 132
2.1 Steady State One-Dimensional Problems .............. 132
2.2 Steady Two-Dimensional Problems. Separation
of Variables ....................................... 135
2.3 Fourier Series ..................................... 137
2.4 Double Fourier Series .............................. 140
2.5 Bessel Functions and Fourier-Bessel Series ......... 142
2.6 Nonhomogeneous Differential Equations
and Boundary Conditions .................................... 153
2.7 Lumped Formulation ................................. 158
2.8 Steady State Three-Dimensional Problems ............ 163
2.9 Transient Problems ................................. 166
3 Problems in Cylindrical Coordinates ..................... 175
3.1 Steady-State One-Dimensional Problems (Radial
Flow) .............................................. 175
3.2 Steady-State Two-Dimensional Problems .............. 179
3.3 Steady-State Three-Dimensional Problems ............ 191
3.4 Transient Problems ................................. 194
4 Problems in Spherical Coordinates ....................... 199
4.1 Steady-State One-Dimensional Problems .............. 200
4.2 Steady-State Two- and Three-Dimensional
Problems ........................................... 201
4.3 Transient Problems ................................. 211
5 Problems ................................................ 216
5 Thermal Stresses in Beams .................................. 219
1 Introduction ............................................ 219
2 Thermal Stresses in Beams ............................... 220
3 Deflection Equation of Beams ............................ 223
4 Boundary Conditions ..................................... 225
5 Shear Stress in a Beam .................................. 226
6 Beams of Rectangular Cross Section ...................... 227
7 Transient Stresses in Rectangular Beams ................. 231
8 Beam with Internal Heat Generation ...................... 232
9 Bimetallic Beam ......................................... 234
10 Functionally Graded Beams ............................... 235
11 Transient Stresses in FGM Beams ......................... 240
12 Thermal Stresses in Thin Curved Beams and Rings ......... 242
13 Deflection of Thin Curved Beams and Rings ............... 243
14 Problems ................................................ 249
6 Disks, Cylinders, and Spheres .............................. 253
1 Introduction ............................................ 253
2 Cylinders with Radial Temperature Variation ............. 254
3 Thermal Stresses in Disks ............................... 258
4 Thick Spheres ........................................... 260
5 Thermal Stresses in a Rotating Disk ..................... 263
6 Non-axisymmetrically Heated Cylinders ................... 265
7 Method of Complex Variables ............................. 271
8 Functionally Graded Thick Cylinders ..................... 278
9 Axisymmetric Stresses in FGM Cylinders .................. 289
10 Transient Thermal Stresses in Thick Spheres ............. 295
11 Functionally Graded Spheres ............................. 303
12 Problems ................................................ 309
7 Thermal Expansion in Piping Systems ........................ 317
1 Introduction ............................................ 317
2 Definition of the Elastic Center ........................ 318
3 Piping Systems in Two Dimensions ........................ 322
4 Piping Systems in Three Dimensions ...................... 329
5 Pipelines with Large Radius Elbows ...................... 335
6 Problems ................................................ 346
8 Coupled and Generalized Thermoelasticity ................... 351
1 Introduction ............................................ 351
2 Governing Equations of Coupled Thermoelasticity ......... 352
3 Coupled Thermoelasticity for Infinite Space ............. 354
4 Variable Heat Source .................................... 357
5 One-Dimensional Coupled Problem ......................... 360
6 Propagation of Discontinuities .......................... 366
7 Half-Space Subjected to a Harmonic Temperature .......... 377
8 Coupled Thermoelasticity of Thick Cylinders ............. 380
9 Green-Naghdi Model of a Layer ........................... 385
10 Generalized Thermoelasticity of Layers .................. 394
11 Generalized Thermoelasticity in Spheres and
Cylinders ............................................... 402
12 Problems ................................................ 405
9 Finite and Boundary Element Methods ........................ 413
1 Introduction ............................................ 413
2 Galerkin Finite Element ................................. 414
3 Functionally Graded Layers .............................. 422
4 Coupled Thermoelasticity of Thick Spheres ............... 428
5 Generalized Thermoelasticity of FG Spheres .............. 440
6 Generalized Thermoelasticity of FG Disk ................. 451
7 Higher Order Elements ................................... 463
8 Functionally Graded Beams ............................... 466
9 Boundary Element Formulation ............................ 476
10 Creep Analysis ............................................. 499
1 Introduction ............................................ 499
2 Creep of Metals ......................................... 503
3 Constitutive Equation of Uniaxial Creep ................. 510
4 Creep Relaxation, Linear Rheological Models ............. 512
5 Three-Dimensional Governing Equations ................... 514
6 Creep Potential, General Theory of Creep ................ 518
7 Stress Function for Creep Problems ...................... 522
8 Creep Linearization ..................................... 525
9 Creep Relaxation of Axisymmetric Stresses ............... 531
10 Creep Relaxation of Non-axisymmetric Stresses ........... 536
11 Thermoelastic Creep Relaxation in Beams ................. 540
Index ......................................................... 553
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