Dynamic response of functionally graded cylinders due to time-dependent heat flux

Abstract

In this paper, analytical solution has been obtained for a functionally graded, transversely isotropic, thermoelastic thick walled hollow cylinder (or disk) subjected to a thermal source. The linear theory of generalized thermoelasticity (Lord–Shulman model) has been employed to model the problem. The material stiffness and thermal conductivity have been assumed to vary as a simple power of the radial coordinate only. Keeping the inner and outer surfaces of the hollow cylinder traction free, a heat flux has been supplied on the inner surface to excite the body and outer surface is kept isothermal. The axisymmetry and plain strain (for cylinder) or plain stress (for disk) conditions have been considered here. The two coupled partial differential equations have been clubbed to obtain the general solution in Laplace domain. The residue calculus method has been employed to invert the transform to obtain the solution in physical domain. The solutions in case of classical coupled and uncoupled thermoelasticity; solid cylinder and infinite solid with cylindrical hole have been deduced as special cases of the present analysis. The results have also been validated with the existing one available in literature at various stages. The analytical results have been computed numerically and presented graphically for solid helium material. The effect of thermal relaxation time and grading parameter on the stresses, strains and temperature change produced in the FGM cylinder have been illustrated through the graphs. A comparative analysis has been done for homogeneous and functionally graded media for the distribution of radial stress, hoop stress, radial strain, hoop strain, radial displacement and temperature change with time, thermal relaxation time and thickness of the FGM cylinder.