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Theory of thermoelasticity with applications

Although the theory of thermoelasticity has a long history, its foun- dations having been laid in the first half of the nineteenth century by Duhamel and Neumann, wide-spread interest in this field did not develop until the years subsequent to World War Two. There are good reasons for this sudden and continuing revival of interest. First, in the field of aeronautics, the high velocities of modern aircraft have been found to give rise to aerodynamic heating; in turn, this produces intense thermal stresses and, by lowering the elastic limit, reduces the strength of the aircraft structure. Secondly, in the nuclear field, the extremely high temperatures and temperature gradients originating in nuclear reactors influence their design and operation. Likewise, in the technology of modern propulsive systems, such as jet and rocket engines, the high temperatures associated with combustion processes are the origin of unwelcome thermal stresses. Similar phenomena are encountered in the technologies of space vehicles and missiles, in the mechanics of large steam turbines, and even in shipbuilding, where, strangely enough. ship fractures are often attributed to thermal stres- ses of moderate intensities. The investigations of these, and similar, problems have brol!ght forth a remarkable number of research papers, both theoretical and experimental, in which various aspects of thermal stresses in engineering structures are described.
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Table of Contents

1 Introduction.- 2 Mathematical groundwork.- 2.1 Tensor calculus.- 2.2 List of useful formulas.- 3 Fundamentals of thermodynamics.- 3.1 System. State. State parameters and functions.- 3.2 The laws of thermodynamics.- 3.3 Nonuniform systems.- 4 Thermodynamics of elastic deformations.- 5 Modes of heat transfer.- 5.1 Radiation.- 5.2 Convection.- 5.3 Conduction.- 6 Theory of heat conduction.- 6.1 Classical differential equation of heat conduction.- 6.2 Initial and boundary conditions.- 7 An hyperbolic equation of heat conduction.- 8 The linear thermoelastic solid.- 8.1 Anisotropy of materials.- 8.2 Certain types of thermoelastic coupling.- 9 The temperature field.- 9.1 Integral transforms.- 9.1a The Laplace transform.- 9.1b Fourier transforms.- 9.1c Hankel transforms.- 9.2 Separation of variables.- 9.3 Green's, or influence, functions.- 9.3a Steady states.- 9.3b Time-dependent states.- 9.4 Duhamel's superposition theorems.- 9.5 Solidification and melting.- 10 Stress and deformation fields.- 10.1 Goodier's thermoelastic potential.- 10.2 Method of biharmonic representations.- 10.3 Betti-Maysel reciprocal method.- 10.4 Thermoelastic-elastic correspondence principle.- 10.5 Method of Green's function.- 10.6 Method of a complex variable.- 10.6a General concepts and theorems.- 10.6b Series expansions.- 10.6c Conformai mapping.- 10.6d Applications to elasticity.- 10.6e Uniqueness of solution. Connectivity of regions.- 10.6f Cauchy integrals.- 10.7 The extended Boussinesq-Papkovich-Neuber solution.- 11 Uniqueness of solution. Stress-free thermoelastic fields.- 11.1 Uniqueness of solution.- 11.2 Stress-free thermoelastic fields.- 11.2a Three-dimensional regions.- 11.2b Two-dimensional regions.- 12 Anisotropic bodies.- 12.1 Correspondence principle for anisotropic bodies.- 12.2 Thermal stresses in an orthotropic hollow cylinder.- 12.3 Thermal stresses in a transversely isotropic half-space.- 13 Stresses due to solidification.- 14 Thermoelastic stresses in plates.- 14.1 General equations.- 14.2 Boundary conditions.- 14.3 Correspondence principle for isotropic plates.- 14.4 Two characteristic cases.- 14.5 Laminated composite plates.- 15 Thermoelastic stresses in shells.- 15.1 Deformation of shells of revolution under axisymmetric mechanical and thermal load.- 15.2 State of stress in shells of revolution deformed axisymmetrically.- 15.3 General theory of shells.- 15.4 Shells of revolution deformed arbitrarily.- 15.5 Donnell's theory of cylindrical shells.- 15.6 Boundary conditions.- 15.7 Equation of heat conduction for shells.- 16 Thermoelastic stresses in bars.- 16.1 Bars of solid cross-section.- 16.2 Bars of thin-walled open cross-section.- 16.3 Bars of thin-walled closed cross-section.- 16.4 Torsion of bars of thin-walled open cross-section.- 17 Thermoelastic stresses around cracks.- 18 Thermoelastic stability of bars and plates.- 18.1 Bars of solid and thin-walled closed cross-section.- 18.2 Bars of thin-walled open cross-section.- 18.3 Plates.- 18.4 Post-buckling behavior of plates.- 19 Moving and periodic fields.- 19.1 General remarks.- 19.2 Illustrative examples.- 20 Thermoelastic vibrations and waves.- 20.1 General concepts and equations.- 20.2 Thermoelastic harmonic waves in infinite media.- 20.3 Thermoelastic Rayleigh waves.- 20.4 Thermoelastic vibrations of a spinning disk.- 20.5 Wave discontinuities.- 21 Coupled thermoelasticity.- 22 Thermoelasticity of porous materials.- 23 Electromagnetic thermoelasticity.- 23.1 Basic concepts of electromagnetism.- 23.2 Maxwell's equations.- 23.3 Lorentz force. Maxwell stresses.- 23.4 Moving bodies.- 23.5 Electromagnetic energy.- 23.6 Electromagnetic thermoelastic equations.- 23.6a Thermoelasticity of dielectrics.- 23.6b Thermoelasticity of ferromagnetic bodies.- 23.6c Applications.- 24 Piezothermoelasticity.- 25 Random thermoelastic processes.- 25.1 General concepts and equations.- 25.1a Random variables.- 25.1b Random processes.- 25.2 Spectral density.- 26 Variational methods in thermoelasticity.- 26.1 General remarks.- 26.2 Virtual work.- 26.3 Principles of stationary energy of Hemp.- 26.4 Principle of Washizu.- 26.5 Principle of Biot.- Literature.- Author index.

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