Three-Dimensional Steady Thermal Stress Analysis of Functionally Graded Hollow Hemisphere

Abstract

Three-dimensional steady temperature field and the resulting thermal stress field are analyzed in a functionally graded hollow hemisphere (FG hollow hemisphere) subjected to unaxisymmetric heating at the inner and outer hemispherical surfaces. The FG hollow hemisphere whose thermal and mechanical properties vary arbitrarily in the radial direction is approximated as a multi-layered hollow hemisphere with distinct thermal and mechanical constants in each layer. An analytical solution to the three-dimensional heat conduction problem is obtained by introducing Fourier's cosine transform and Legendre transform. The associated three-dimensional thermal stress problem is estimated by the use of thermoelastic displacement potential and Papkovich-Neuber's displacement functions. Numerical calculations of the temperature and thermal stresses are carried out for SiC/Al-Alloy FG hollow hemisphere with three types of graded material composition expressed in the form of a power function. The effects of the graded composition, inner/outer radius ratio, and number of layers on relaxation characteristics of thermal stress are quantitatively discussed.