Thermal stresses in a spherical shell under three thermoelastic models

The problem of dynamic thermoelastic stresses in a spherical shell with fix ed boundaries whose inner surface is subjected to a step jump in temperatur e is considered. The analysis is carried out in the uncoupled framework und er the classical Lord and Shulman (1967) and Green and Lindsay (1972) formu lations of thermoelasticity. Exact solutions for the temperature and displa cement equations are obtained using the Laplace transform and eigenfunction expansion method, respectively. Of particular interest is the propagation and nature of discontinuities in the temperature, displacement, and stress fields that are possible under the two nonclassical theor ies. Exact expres sions for the magnitudes of discontinuities in these quantities are also gi ven, and shock waves are noted Numerical results are presented graphically along with a comparison of the three models. In addition, special and limit ing cases of the physical parameters are investigated and the application o f this research to fuel vessels used in rocket engine testing are noted. La stly, a discussion concerning which of the three theories is the most physi cally acceptable is given, with the Lord and Shulman formulation emerging a s the clear overall choice, and conclusions are stated.