Thermoelasticity

THERMOELASTICITY-the generalization of elasticity to nonisothermal deformations-has made considerable progress during the last two decades. Its basic theory is now well established, and many applications to problems in engineering have been successfully made. In writing this book it has been my aim to give, in a relatively small volume, an up-to-date presentation of those parts of thermoelasticity which, in my opinion, are of basic importance in the field. The theoretical back ground, together with the corresponding methods of solution, is developed first in each chapter and is followed by 'carefully selected examples intended to serve not only as illustrations of the theory but also as sources for useful results of engineering interest. Following a brief introductory chapter, the linearized, uncoupled theory is presented. Frequent reference is made here to the theory of isothermal elas ticity. A short review of the theory of heat conduction is included. The third and fourth chapters are concerned with special cases: plane thermo elastic stress and strain, and thermal bending and buckling of plates, respec tively. The real function method and the complex function approach are introduced simultaneously in Chapter 3 in order to exhibit and delineate the respective merits of the two procedures. In Chapter 5 the theory of thermo elasticity is developed in its most general form. Several particular cases are considered. This chapter also provides a rigorous foundation for the linearized theory of the preceding chapters.

Inhalt

1. Introduction.- 2. The Linearized Theory.- 2.1. Basic Equations.- 2.2. The Temperature Field.- 2.3. Stress-Free Temperature Fields.- 2.4. Methods of Solution. Thermoelastic Potential.- 2.5. Boundary Conditions. Uniqueness.- 2.6. Example: Instantaneous Point Source.- 2.7. Axisymmetrical Problems with Shearing Stresses Vanishing in a Plane.- 2.8. Green's Function I.- 2.9. Green's Function II 20 Problems.- 3. Two-Dimensional Problems.- 3.1. Plane Strain.- 3.2. Plane Stress.- 3.3. Method of Solution. Real Function Approach.- 3.4. Method of Solution. Complex Function Approach.- 3.5. Curvilinear Coordinates.- 3.6. Two-Dimensional Stress-Free Temperature Fields.- 3.7. Example: Plate with Circular Hole in Uniform Heat Flow.- 3.8. Example: Point Source in a Semi-Infinite Plate.- Problems.- 4. Thermal Bending and Buckling of Plates.- 4.1. Bending and Stretching.- 4.2. Equilibrium.- 4.3. Differential Equation for the Deflection.- 4.4. Boundary Conditions.- 4.5. Two Simple Cases.- 4.6. Axisymmetric Bending of a Circular Plate.- 4.7. Influence Function Method.- 4.8. Hot Area in an Infinite Plate.- 4.9. Rectangular Plate with Two Parallel Edges Simply Supported.- 4.10. Thermal Buckling.- 4.11. Example: Rectangular Plate.- Problems.- 5. General Thermoelastic Theory.- 5.1. Kinematic Relations.- 5.2. Analysis of Stress.- 5.3. Basic Equations.- 5.4. The Elastic Potential.- 5.5. Inversion of the Stress-Strain Law.- 5.6. Some Simple Cases.- 5.7. Isotropic Incompressible Material.- 5.8. Example: Torsion of an Incompressible Cylinder.- Problems.- 6. Wave Propagation.- 6.1. Jump Conditions.- 6.2. Example: Plane Waves in an Initially Stressed Medium.- 6.3. Example: Pressure Shock on the Surface of a Semi-Infinite Body.- Problems.- 7. Thermoelastic Stability.- 7.1. The Basic Relations.- 7.2. Construction of the Lyapunov Functional.- 7.3. Example: Column Stability.- Problems.