Thermal Stresses – Advanced Theory and Applications

Abstract

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