# Thermoelasticity

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Thermoelasticity, Second Edition reviews advances in thermoelasticity and covers topics ranging from stationary problems of thermoelasticity to variational theorems of stationary thermoelasticity; stresses due to the action of a discontinuous temperature field in an infinite elastic body; the action of heat sources in the elastic space; and thermal inclusions in an infinite disc and semi-infinite disc. Three different sets of differential equations describing the fields of strain and temperature are presented. This book is comprised of 12 chapters and begins with a discussion on basic relations and equations of thermoelasticity. Thermoelasticity is treated as a synthesis of the theory of elasticity and the theory of heat conduction. Some particular cases of thermoelasticity are then investigated, including stationary problems, the theory of thermal stresses, and classical dynamic elasticity. Dynamic effects due to the action of a non-stationary temperature field are examined, along with plane harmonic waves in an elastic space and thermal stresses in plates, shells, and viscoelastic bodies. The final chapter focuses on micropolar thermoelasticity, magnetothermoelasticity, and thermopiezoelectricity. This monograph will be of interest to physicists and mechanical engineers.

## Table of Contents

Preface to the First Edition

Preface to the Second Edition

Chapter I. Basic Relations and Equations of Thermoelasticity

1. Principle of Energy Conservation. Entropy Balance

2. The Fundamental Differential Equations of Thermoelasticity

3. The Wave Equations of Thermoelasticity

4. Uncoupling of the System of Differential Equations of Thermoelasticity

5. The Variational Theorems of Thermoelasticity

6. The Uniqueness Theorem for the Solution of the Problem of Thermoelasticity

7. Reciprocity Theorem of Work

8. Stationary Problems of Thermoelasticity

9. The Variational Theorems of Stationary Thermoelasticity

10. Theorem of Reciprocity of Work in Stationary Thermoelasticity

11. The Fundamental Equations of the Theory of Thermal Stresses

12. The Principle of Virtual Work in the Theory of Thermal Stresses. The Hamilton Principle

13. The Theorem of Reciprocity of Work for the Dynamic Problems of the Theory of Thermal Stresses

14. The Quasi-Static Problem of the Theory of Thermal Stresses

15. Equations of Classical Dynamic Elasticity

Chapter II. Stationary Three-Dimensional Thermoelastic Problems

1. Thermal Inclusions. Nucleus of Thermoelastic Strain

2. Stresses Due to the Action of a Discontinuous Temperature Field in an Infinite Elastic Body

3. Discontinuous Temperature Field in a Semi-Space and an Elastic Layer

4. The Nucleus of Thermoelastic Strain in an Infinite Cylinder

5. The Nucleus of Thermoelastic Strain in a Space with a Spherical Cavity, in a Solid Sphere and in a Shell

6. The Nucleus of Thermoelastic Strain in an Elastic Semi-Space with a Hemispherical Pit at the Free Surface

7. Stresses in the Elastic Semi-Space Due to a Heat Exposure on the Bounding Plane

8. Heat Exposure in Planes Bounding an Elastic Layer

9. Stresses Due to Heating of an Infinite Cylinder

10. Stresses Due to Heating of a Spherical Shell (Hollow Sphere)

11. Mixed Boundary Value Problems in Stationary Thermoelasticity

12. Heat Sources in an Elastic Space and Semi-Space

13. Heat Sources in an Infinite Cylinder and in a Sphere

Chapter III. Quasi-Static and Quasi-Stationary Spatial Thermoelasticity Problems

1. The Action of Heat Sources in the Elastic Space

2. Non-Stationary Heat Sources in an Elastic Semi-Space

3. Heat Exposure in a Plane Bounding an Elastic Semi-Space

4. Moving Heat Sources in an Elastic Space and Semi-Space

5. Non-Stationary State of Stress in a Sphere, Due to a Temperature Field of Spherical Symmetry

6. Non-Stationary Axisymmetric State of Stress in an Infinite Circular Cylinder

Chapter IV. Dynamic Effects Due to the Action of a Non-Stationary Temperature Field

1. Action of Plane Heat Sources in an Elastic Space and Semi-Space

2. Action of Concentrated Heat Sources in an Elastic Space and Semi-Space

3. Sudden Heating of a Spherical Cavity in the Infinite Space

4. Action of Heat Sources in the Vicinity of a Spherical Cavity

Chapter V. Dynamic Problems of Coupled Temperature and Strain Fields

1. Plane Harmonic Waves in an Elastic Space

2. Spherical Waves in the Infinite Thermoelastic Space

3. The Action of a Concentrated Force in the Infinite Space

Chapter VI. Stationary Plane Problems of Thermoelasticity

1. Plane State of Strain. Plane State of Stress

2. Thermal Inclusions in an Infinite Disc and Semi-Infinite Disc

3. Thermal Inclusions in a Disc Strip

4. Axisymmetric Thermal Inclusions in Hollow Infinite Cylinders and in Annular Discs

5. Discontinuous Temperature Field in a Circular Disc

6. Heat Sources in Discs

7. Discs Having Non-Free Boundaries

Chapter VII. Quasi-Static and Quasi-Stationary Two-Dimensional Thermoelastic Problems

1. Thermal Stresses Due to the Action of Heat Sources in an Infinite Space and an Infinite Disc

2. Thermal Stresses in Infinite Cylinders

3. Stresses Due to a Periodic Temperature Field

4. Moving Heat Sources on the Surface of a Disc

Chapter VIII. Two-Dimensional Dynamic Thermoelastic Problems

1. Action of Line Heat Sources in an Infinite Space

2. Action of Line Heat Sources in an Elastic Semi-Space

3. Rayleigh's Waves in a Thermoelastic Medium

4. Thermally Excited Vibrations of Solid Cylinders

Chapter IX. Thermal Stresses in Plates

1. Stationary Thermal Stresses in Plates

2. Solutions for Infinite Plates and for Plates of Rectilinear Contours

3. Stationary Stresses in Circular Plates

4. Plates Resting on Elastic Foundations

5. Simultaneous Bending and Compression of Plates. Buckling of Plates

6. State of Stress in Plates with Large Deflections

7. Non-Stationary Quasi-Static Stresses in Plates

8. Vibrations of Plates Due to Thermal Shock

Chapter X. Thermal Stresses in Shells

1. Thermal Stresses in Shells of Revolution

2. Thermal Stresses in an Open Cylindrical Shell

3. General and Engineering Bending Theory of Shells

Chapter XI. Thermal Stresses in Viscoelastic Bodies

1. Viscoelastic Bodies. Stress-Strain Relations

2. Quasi-Static Problems in Viscoelastic Bodies

3. Extension of Maysel's Method to Quasi-Static Problems for Viscoelastic Bodies

4. Dynamic Effects

Chapter XII. New Trends of Investigation in Thermoelasticity

1. Thermal Stresses in Anisotropic Bodies

2. Thermal Stresses in Isotropic Non-Homogeneous Bodies

3. Theory of Micropolar Thermoelasticity

4. Thermo-Piezoelectricity. Fundamental Relations and Differential Equations

5. Magneto-Thermoelasticity

Bibliography

Author Index

Subject Index

## Product details

- No. of pages: 578
- Language: English
- Copyright: © Pergamon 1986
- Published: January 1, 1986
- Imprint: Pergamon
- eBook ISBN: 9781483162485