Analytical Study on Relaxation Behavior of Thermal Stresses in Nose Cones Composed of Functionally Graded Material Subjected to Three-Dimensional Transient Temperatures

Abstract

In this study, analytical solutions for the three-dimensional transient temperature fields and the resulting thermal stress fields in a space plane's nose cone composed of a functionally graded material (FGM) are derived by treating the nose cone as a multi-layered hollow hemisphere with distinct thermal and mechanical properties in each layer. The three-dimensional transient heat conduction problem can be solved by applying Fourier-cosine transform, Legendre transform, and Vodicka's method which is a type of integral transform for the one-dimensional multi-layer regions. The associated thermal stress problem can be analyzed by using thermoelastic displacement potential and Papkovich-Neuber's displacement functions. Numerical calculations for the thermal deformations and the thermal stresses are carried out for the FGM hollow hemisphere composed of SiC and Al-Alloy, which has a graded material composition of a power function expression. It is clarified that there is a specific thermal stress behavior in the FGM hollow hemisphere subjected to the three-dimensional transient temperature field, and the effects of the graded composition and number of layers on relaxation characteristics of thermal stress are quantitatively discussed.