Theory of Thermal Stresses

"Note on Bibliographical References Part 1 BASIC THEORY Chapter 1. Mechanical and Thermodynamical Foundations 1.1 Introduction 1.2 Notation 1.3 Deformation; Small-Strain Tensor 1.4 Equations of Motion 1.5 Thermodynamics; Basic Definitions 1.6 Thermodynamics of Uniform Systems 1.7 Transition to Nonuniform Systems 1.8 Conservation of Energy in Nonuniform Systems 1.9 Preliminaries to the Second Law of Thermodynamics for Continua 1.10 Caratheodory's Statement of the Second Law of Thermodynamics and Its Consequences 1.11 Irreversible Theromodynamics; Entropy Production 1.12 Stress-Strain Relations and Energy Equation 1.13 Stress-Strain Relations and Energy Equation for an Isotropic Elastic Solid 1.14 Summary of Linear Coupled Thermoelastic Theory; Uniqueness Theorem Chapter 2. Uncoupled Quasi-Static Thermoelastic Theory 2.1 Introduction 2.2 General Remarks on the Effects of Coupling and Inertia 2.3 Solution of a Coupled Thermoelastic Problem 2.4 Discussion of Article 2.5 Effect of Inertia 2.6 Uncoupled Quasi-Static Foundation 2.7 ""Uniqueness Theorems for the Uncoupled, Quasi-Static Thermoelastic Theory"" Appendix Thermoelastic Damping Chapter 3. Alternate Formulations of Thermoelastic Problems 3.1 Introduction 3.2 Displacement Formulation 3.3 Body-Force Analogy 3.4 Reduction of the Thermoelastic Problem to One at Constant Temperature with No Body Forces; Goodier's Method 3.5 Use of Boussinesq-Papkovich Functions 3.6 Stress-Formulation 3.7 Necessity of Compatibility Equations 3.8 Stress-Formulation for Multiply Connected Bodies 3.9 Temperature Distributions Which Result in Zero Stress 3.10 Dislocations Chapter 4. Two-Dimensional Thermoelastic Formulations 4.1 Introduction 4.2 Plane-Strain Thermoelastic Problems 4.3 Boundary Conditions on the End Faces for the Case of Plane Strain 4.4 Stress Formulation of the Plane-Strain Problems 4.5 Stress Formulation in Terms of a Stress Function 4.6 Plane-Stress Thermoelastic Problems 4.7 Discussion of the Plane-Stress Solutions 4.8 Plane Stress as a Limiting Case of a Three-Dimensional State of Stress for Thin Slices 4.9 Steady-State Temperature Distributions 4.10 Dislocation Analogy Part 2 HEAT CONDUCTION Chapter 5. The Formulation of Heat Transfer Problems 5.1 Introduction 5.2 Modes of Heat Transfer 5.3 The Fourier Heat Conduction Equation 5.4 Initial and Boundary Conditions 5.5 Dimensionless Parameters 5.6 Discussion of the Boundary Conditions 5.7 Uniqueness Theorem 5.8 One-Dimensional Formulations for Thin Sections Chapter 6. Some Basic Problems in Heat Conduction 6.1 Introduction 6.2 Sources and Sinks in an Infinite Solid 6.3 A More General Solution of Eq. 6.2.3b 6.4 The Semi-Infinite Solid under Time-Dependent Boundary Conditions 6.5 Solutions Obtained by Superposition and Imaging of Sources Conditions 6.6 Alternative Forms of Series Solutions; Poisson's Formula 6.7 Temperatures Due to Sources Regarded as Fundamental Solutions (Green's Functions) 6.8 Saint-Venant's Principle in Heat Conduction Problems 6.9 Upper and Lower Bounds on the Temperature 6.10 Over-All Heat Balance; the Melting Slab Chapter 7. Methods of Solution of Heat Conduction Problems 7.1 Introduction 7.2 Separation of Variables (Method of Characteristic Functions) 7.3 Laplace Transforms 7.4 Conformal Mapping 7.5 Numerical Methods 7.6 Electrical Analogy 7.7 Approximate Analytical Procedures 7.8 Some Techniques for Extending Previous Solutions Part 3 THERMAL STRESS ANALYSIS FOR ELASTIC SYSTEMS Chapter 8. Summary of the Formulation of Thermoelastic Problems 8.1 Introduction 8.2 Thermoelastic Stress-Strain Relations 8.3 Equations of Equilibrium 8.4 Strain-Displacement Relations 8.5 Boundary Conditions 8.6 Mathematical Formulation of the Problem of Thermoelasticity 8.7 Principle Stresses and Strains 8.8 Separation of Stresses Due to Temperature and to External Loads 8.9 Alternative Formulations of the Problem of Thermoelasticity 8.10 Two-Dimensional Formulations 8.11 Energy Methods 8.12 Methods of Solution of Thermoelastic Problems Chapter 9. Some Basic Problems in Thermoelasticity 9.1 Introduction 9.2 Three-Dimensional Problems in Which the Stresses Are Zero 9.3 Three-Dimensional Problems in Which the Displacements Are Zero 9.4 Two-Dimensional Problems in which the Stresses in the Plane Are Zero 9.5 Free Plate with Temperature Variation through the Thickness Only 9.6 Rectangular Beam with Temperature Variation through the Depth Only 9.7 Discussion of Articles 9.5 and 9.6 9.8 Example for Articles 9.5 and 9.6 9.9 Slowly Heated Beam or Plate 9.10 Circular Disc or Cylinder with Radial Temperature Variation 9.11 Circular Disc or Cylinder with Plane-Harmonic Temperature Distribution 9.12 Additional References on Thermal Stresses in Cylinders 9.13 Circular Rectangular Beam with Radial Temperature Variation 9.14 Solid or Hollow Sphere under Radial Temperature Variation 9.15 Over-All Thermoelastic Deformation Chapter 10. Thermal Stresses in Beams 10.1 Introduction 10.2 Elementary Formulas for Normal Thermal Stresses in Free Beams 10.3 Thermal Deflections of Beams 10.4 Beam End-Conditions; Statically Indeterminate Beams 10.5 Thermal Shear Stresses in Thin-Walled Beams 10.6 Exact Two-Dimensional Thermoelastic Solution for Rectangular Beams under Arbitrary Temperature Distributions 10.7 Discussion of Article 10.6; Relation to Strength-of-Materials Theory 10.8 Exact Theory for Free Beams of Arbitrary Simply-Connected Cross Section with Linear Spanwise Temperature Distributions 10.9 Discussion of Article 10.8; Relation to Strength-of-Materials Theory 10.10 Use of Dummy Loads for the Calculation of Beam Deflections 10.11 Thermally Induced Vibrations of Beams Appendix The End-Problem in Beams; Saint-Venant's Principle ""Chapter 11. Thermal Stresses in Curved Beams, Rings, Trusses, Frames, and Built-up Structures"" 11.1 Introduction 11.2 Strength-of-Materials Theory for Thermal Stresses in Curved Beams 11.3 Discussion of Article 11.2; Relation to Exact and to Straight-Beam Analyses 11.4 Thermal Stresses in Rings 11.5 Thermal Stresses in Statically Determinate Trusses 11.6 Thermal Stresses in Statically Indeterminate Trusses 11.7 Thermal Stresses in Rigid Frames 11.8 Use of Influence Coefficients 11.9 References on the Analysis of Reinforced Sheet Structures Chapter 12. Thermal Stresses in Plates 12.1 Introduction 12.2 Basic Plate Equations 12.3 Plate Boundary Conditions 12.4 Solutions of Thermoelastic Plate Problems 12.5 Plates with Temperature Distributions Varying Through the Thickness Only 12.6 Relation of Thin-Plate Theory to Exact Thermoelastic Solutions 12.7 Thermally Induced Vibrations of Plates Chapter 13. Thermoelastic Stability and Related Problems 13.1 Introduction 13.2 Heated Beam-Columns with Ends Axially Unrestrained 13.3 Heated Beam-Columns with Ends Axially Restrained 13.4 Heated Beams under Axial Loads: General Theory 13.5 Discussion of Article 13.6 Bending and Buckling of Bimetallic Beams 13.7 Thermal Buckling of Plates 13.8 Buckling of Plates Subjected to Heat and No Transverse Loads with Edges Unrestrained in the Plane 13.9 Buckling of Plates Subjected to Heat and Loads in the Plane; Edges Unrestrained in the Plane 13.10 Plates with Their Edges Restrained in the Plane 13.11 Large Deflections and Post-Buckling Behavior of Plates Part 4 THERMAL STRESS ANALYSIS FOR INELASTIC SYSTEMS Chapter 14. The Formulation of Inelastic Thermal Stress Problems 14.1 Introduction 14.2 Stress Relaxation and Creep 14.3 Plastic Flow and Work-Hardening 14.4 Idealized Theories and Materials 14.5 Viscoelastic Stress-Strain Relations 14.6 Idealized Plasticity Theory: Work-Hardening Solid 14.7 Idealized Plasticity Theory: Perfectly Plastic Solid 14.8 Uniqueness Theorem for Perfectly Plastic Solid 14.9 The Mises Yield Condition 14.10 The Tresca Yield Condition 14.11 Combined Viscoelastic and Plastic Effects Chapter 15. Viscoelastic Stress Analysis 15.1 Introduction 15.2 Viscoelastic-Elastic Analogy 15.3 Discussion of the Viscoelastic-Elastic Analogy 15.4 Example for the Viscoelastic-Elastic Analogy 15.5 Linear Viscoelastic Strength-of-Materials Theory 15.6 Initial Conditions for a Linear Viscoelastic Solid 15.7 Nonlinear Viscoelastic Analyses 15.8 Nonlinear Viscoelastic Strength-of-Materials Theory; Creep Rupture in Tension 15.9 Creep Buckling 15.10 Further Investigations of Creep Buckling Chapter 16. Plastic Stress Analysis 16.1 Introduction 16.2 Elastoplastic Free Plate Analysis 16.3 Two Examples of Elastoplastic Plate Analysis 16.4 ""Free Plate Analysis, Including a Temperature-Dependent Yield Condition and Viscoelastic Effects"" 16.5 Elastoplastic Cylinder Analysis-Tresca Condition 16.6 Elastoplastic Cylinder Analysis-Mises Condition AUTHOR INDEX SUBJECT INDEX"