The GDQ approach to thermally nonlinear generalized thermoelasticity of a hollow sphere

The present research deals with the thermoelastic response of a thick sphere based on the Lord-Shulman theory of generalized thermoelasticity. Unlike the other available works in which energy equation is linearized, the assumption of ignorance of temperature change in comparison to the reference temperature is not established in this research resulting in a nonlinear energy equation. Such nonlinearity is called thermally nonlinear. The one-dimensional radial equation of motion and energy equation are established for an isotropic homogeneous sphere. The resulting equations are discreted by means of the generalized differential quadrature in radial direction and traced in time by means of the Newmark time marching scheme. Numerical results are provided to demonstrate the discrepancies between the thermally linear and nonlinear results. As the numerical results reveal, thermally linear theory fails for precise analysis of structures under thermal loads especially at high temperature shocks, large coupling coefficient, and large relaxation time.