Dynamic analysis of functionally graded cylinders due to time-dependent heat flow

This study presents a numerical solution for a thermoelastic thick-walled hollow cylinder (or disk) with functionally graded, transversely isotropic properties, exposed to a thermal source. The material properties, such as density, elastic parameters, and thermal conductivity, are assumed to change along the thickness in a straightforward manner within the radial coordinates. The inner and outer surfaces of the hollow cylinder are assumed to be free of traction, with a heat flux applied to the inner surface to stimulate the body, while the outer surface is maintained at a constant temperature. Two coupled partial differential equations are combined to derive the general solution in the Laplace domain. To revert the transformation and obtain the solution in the physical domain, Durbin's modified inverse Laplace method is employed. The obtained results are compared with existing data from the literature at various stages and are presented graphically for a solid helium material. The influence of thermal relaxation time and the grading parameter on the stresses, strains, and temperature variations in the functionally graded cylinder is illustrated through graphs. A comparative analysis is carried out for the distribution of radial stress, hoop stress, radial strain, hoop strain, radial displacement, and temperature change with respect to time, thermal relaxation time, and cylinder thickness, considering both homogeneous and functionally graded materials. Keywords: Functionally graded, Laplace transform, Thermal relaxation, Thermoelastic, Temperature change