Theory of thermoelasticity with applications

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.