Theory of Thermal Stresses


Elevated temperatures and extreme temperature gradients arise in a large variety of engineering problems, and often produced thermal stresses and thermal deformations that crucially affect the life of the materials and the systems involved. Early examples arose with the advent of high-speed rocket-powered flight and the development of nuclear energy sources. More recent applications can be found in fields ranging from reentry heating and ablation in space flight to the localized heat generation in computer chips,...

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Theory of Thermal Stresses

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Elevated temperatures and extreme temperature gradients arise in a large variety of engineering problems, and often produced thermal stresses and thermal deformations that crucially affect the life of the materials and the systems involved. Early examples arose with the advent of high-speed rocket-powered flight and the development of nuclear energy sources. More recent applications can be found in fields ranging from reentry heating and ablation in space flight to the localized heat generation in computer chips, produced by high temperature during fabrication and by high current density during service.
This highly regarded text, aimed both at the researcher and the practicing engineer, as well as the student, presents a detailed discussion of fundamental aspects of the theory, accompanied by detailed solutions of typical and illustrative problems. The book is divided into four parts: Part I develops the fundamentals of thermoelasticity, starting with a presentation of the thermodynamic foundations of the subject and leading to various alternate formulations and methods of solutions of thermoelastic problems. Part II discusses the physical basis of heat transfer theory and methods of solution of heat conduction boundary-value problems. Part III covers more practical aspects of thermal stress analysis, mainly from the strength-of-materials viewpoint. Finally, Part IV presents the manner in which temperature effects can be included in inelasticity theory.
The result is an extremely useful resource which presents the salient features of the subject in a single volume from a unified and basic theoretical point of view.

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Table of Contents

Note on Bibliographical References
  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 Carath√©odory'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
  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
  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
  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
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