Thermal Stresses -- Advanced Theory and Applications

1 Basic Laws of Thermoelasticity; 1 Introduction; 2 Stresses and Tractions; 3 Equations of Motion; 4 Coordinate Transformation. Principal Axes; 5 Principal Stresses and Stress Invariants; 6 Displacement and Strain Tensor; 7 Compatibility Equations. Simply Connected Region; 8 Compatibility Conditions. Multiply Connected Regions; 9 Constitutive Laws of Linear Thermoelasticity; 10 Displacement Formulation of Thermoelasticity; 11 Stress Formulation of Thermoelasticity; 12 Two-Dimensional Thermoelasticity; 13 Michell conditions; 2 Thermodynamics of Elastic Continuum; 1 Introduction; 2 Thermodynamics Definitions; 3 First Law of Thermodynamics; 4 Second Law of Thermodynamics; 5 Variational Formulation of Thermodynamics; 6 Thermodynamics of Elastic Continuum; 7 General Theory of Thermoelasticity; 8 Free Energy Function of Hookean Materials; 9 Fourier's Law and Heat Conduction Equation; 10 Generalized Thermoelasticity. Second Sound; 11 Thermoelasticity without Energy Dissipation; 12 Uniqueness Theorem; 13 Variational Principle of Thermoelasticity; 14 Reciprocity Theorem; 15 Initial and Boundary Conditions; 3 Basic Problems of Thermoelasticity; 1 Introduction; 2 Temperature Distribution for Zero Thermal Stress; 3 Analogy of Thermal Gradient with Body Forces; 4 General Solution of Thermoelastic Problems; 5 General Solution in Cylindrical Coordinates; 6 Solution of Two-Dimensional Navier Equations;7 Solution of Problems in Spherical Coordinates; 4 Heat Conduction Problems; 1 Introduction; 2 Problems in Rectangular Cartesian Coordinates; 2.1 Steady State One-Dimensional Problems; 2.2 Steady Two-Dimensional Problems. Separation of Variables; 2.3 Fourier Series; 2.4 Double Fourier Series; 2.5 Bessel Functions and Fourier-Bessel series; 2.6 Nonhomogeneous Differential Equations and Boundary Condition; 2.7 Lumped Formulation; 2.8 Steady State Three-Dimensional Problems; 2.9.Transient Problems; 3 Problems in Cylindrical coordinates; 3.1 Steady-State One-Dimensional Problems (Radial Flow); 3.2. Steady -State Two-Dimensional Problems 3.3 Steady-State Three-Dimensional Problems; 3.4 Transient Problems; 4 Problems in Spherical Coordinates; 4.1 Steady-State One-Dimensional Problems; 4.2 Steady-State Two- and Three-Dimensional Problems; 4.3 Transient Problems; 5 Thermal Stresses in Beams; 1 Introduction; 2 Elementary Theory of Thermal Stresses in Beams; 3 Deflection Equation of Beams; 4 Boundary Conditions; 5 Shear Stress in a Beam; 6 Beams of Rectangular Cross Section; 7 Transient Thermal Stresses in Rectangular Beams; 8 . Beam with Internal Heat Generation; 9 Bimetallic Beam; 10 Functionally Graded Beams; 11 Transient Thermal Stresses in Functionally Graded Beams; 12 Thermal Stresses in Thin Curved Beams and Rings; 13 Deflection of Thin Curved Beams and Rings; 6 Disks, Cylinders, and Spheres; 1 Introduction; 2 . Cylinders with Radial Temperature Variation; 3 Thermal Stresses in Disks; 4 Thick Spheres; 5 Thermal Stresses in a Rotating Disk; 6 Non-Axisymmetrically Heated cylinders; 7 Method of Complex Variables; 8 Functionally Graded Thick Cylinders; 9 Axisymmetric Thermal Stresses in FGM Cylinders; 10.Transient Thermal Stresses in Thick Spheres; 11 Functionality Graded Spheres; 7 Thermal Expansion in Piping Systems; 1 Introduction; 2 Definition of the Elastic Center; 3 . Piping Systems in Two Dimensions; 4 Piping Systems in Three-dimensions; 5 Pipelines with Large Radius Elbows; 8 Coupled and Generalized Thermoelasticity; 1 Introduction; 2 Governing Equations of Coupled Thermoelasticity; 3 Coupled Thermoelasticity for Infinite Space; 4 Variable Heat Source; 5 One-Dimensional Coupled Problem; 6 Propagation of Discontinuities; 7 Half-Space Subjected to a Harmonic Temperature; 8 Coupled Thermoelasticity of Thick Cylinders; 9 Green-Naghdi Model of a Layer; 10 Generalized Thermoelasticity of Layers; 11 Generalized Thermoelasticity of Spheres and Cylinders;