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