Exact thermoelastic analysis of a thick cylindrical functionally graded material shell under unsteady heating using first order shear deformation theory

Abstract

In this article, a new analytical formulation is presented for an axisymmetric thick-walled functionally graded material cylinder with power-law variation in mechanical and thermal properties under transient heating using first order shear deformation theory. Equilibrium equations are derived by virtual work principles and the energy method. The unsteady heat conduction equation is solved using the method of separation of variables, generalized Bessel functions, and an Eigen-function method. Validation of the analytical solutions is conducted with a finite element method. The effects of time on stress and displacement distribution are studied in detail. The numerical values used in this study are selected based on earlier studies. The influence of effect of transient heat transfer on heterogeneous thick-walled cylinder elasticity is clearly demonstrated. In particular, the significant influence of time and the heterogenous constant on radial displacement, hoop stress, and temperature distributions is computed. The study is relevant to rocket chamber thermomechanics, propulsion duct thermophysical design, industrial thermal storage systems, and so forth.