<p>Graphene, a remarkable material, has numerous efficient applications due to its enhanced chemical, mechanical, electrical, and thermal properties. By gradually spreading graphene nanoplatelets into a matrix, graphene functionally graded materials combine remarkable strength and low weight. Thermoelastic analysis is crucial for forecasting performance and guaranteeing dependability in sophisticated structural applications since it assesses how they react to combined mechanical stresses and temperature changes. In the present work, we consider two functionally graded materials: one made of Graphene and Copper, and the other of Titanium and Zirconium. The problem is formulated for a spherical shell under two generalized thermoelastic theories to examine the thermoelastic behavior, specifically for the functionally graded material of Graphene. We use the Laplace transform technique to eliminate the time dependency from the governing equations and the finite element method to address the non-linearity of the governing equations, which is generated by the dependency of thermal parameters on spatial coordinates. A detailed comparative study of the results obtained is discussed to focus on the functionally graded material and the necessity of the finite element method for generalized thermoelasticity. The numerical values of the field variables are shown through different graphs to provide a more compact analysis of generalized thermoelasticity for functionally graded materials.</p>