Green's function approach to unsteady thermal stresses in an infinite hollow cylinder of functionally graded material

A Green's function approach based on the laminate theory is adopted for solving the two-dimensional unsteady temperature Field (r,z) and the associated thermal stresses in an infinite hollow circular cylinder made of a functionally graded material (FGM) with radial-directionally dependent properties. The unsteady heat conduction equation is formulated as an eigenvalue problem by making use of the eigenfunction expansion theory and the laminate theory. The eigenvalues and the corresponding eigenfunctions obtained by solving an eigenvalue problem for each layer constitute the Green's function solution for analyzing the unsteady temperature. The associated thermoelastic field is analyzed by making use of the thermoelastic displacement potential function and Michell's function. Numerical results are carried out and shown in figures.