ABSTRACT
The theory of linearized thermoelasticity for three-dimensional bodies is formulated. Stress, strain, and force equilibrium relations along with compatibility conditions are derived in Cartesian coordinates. The connection between the equations of linearized thermoelasticity and the Navier's governing equations, which are a set of vector partial differential equations, is established. The alternate formulation in terms of stresses leads to the Beltrami–Michell compatibility equations. Boundary conditions are derived for: prescribed surface stresses; prescribed surface displacements; prescribed stresses on part of the boundary surface, and prescribed displacements on the remainder of the boundary surface. A detailed analysis of the solution of the Navier's equations is carried out wherein the Goodier's thermoelastic displacement potential is used in conjunction with generalized Boussinesq harmonic functions. General solutions for the potential function are derived in the Cartesian coordinate system. Next, the equations of equilibrium and the formulas for strain in cylindrical and spherical coordinate systems are discussed and, the Navier's governing equations and associated solutions are derived.
