SPHERICALLY SYMMETRIC PROBLEM IN FINITE THERMO-ELASTOSTATICS
R. E. Craine · The Quarterly Journal of Mechanics and Applied Mathematics · 1968
The thermal stress problem in finite elasticity is considered for a hollow sphere with its internal and external surfaces maintained at constant temperatures. Comparison is made with the classical theory of thermal stress, using both constant and variable coefficients of heat conduction, for cases in which the maximum elastic strains are about 0.3% (above this strain plasticity occurs for most metals). It is found that the fractional errors in the solution are at most 0.01. Consequently the use of the classical solution is justified whenever an accuracy of 1% is sufficient provided that the material remains elastic.