This paper presents the analytical solution of one-dimensional mechanical and thermal stresses for a hollow cylinder made of functionally graded material. The material properties vary continuously across the thickness, according to power functions of radial direction. Temperature distribution is symmetric, and transient. The thermal boundary conditions may include conduction, flux, and convection for inside or outside of hollow cylinder. Thermoelasticity equation is transient, including the moving heat source. The heat conduction and Navier equations are solved analytically, using the generalized Bessel function. A direct method of solution of Navier equation is presented.

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