Transient Thermal Stresses in a Semi-Infinite Slab

Abstract

This investigation is concerned with the transient temperature and thermal-stress distribution generated in a semi-infinite slab if a finite segment of its edge is subjected to a sudden uniform change in temperature. The slab is supposed to be free from external loads and its faces are assumed to be insulated. Exact solutions in series form are obtained both for the heat-conduction problem and for the associated thermoelastic problem. The latter is treated quasi-statically within the classical two-dimensional theory of elasticity. The thermal stresses appropriate to the generalized plane-stress solution vanish identically in the limit as time tends to infinity. The space and time dependence of these stresses is examined in some detail with a view toward tracing the evolution of this well-known, steady-state degeneracy. Finally, the results corresponding to an instantaneous heating or cooling of a portion of the boundary are used to study the effect upon the stresses of gradual changes in the surface temperature.