Radially symmetric response of an FGM spherical pressure vessel under thermal shock using the thermally nonlinear Lord-Shulman model

Abstract

In the present research, the coupled and non-linear thermo-mechanical response of a functionally graded material (FGM) hollow sphere under thermal shock is investigated. It is assumed that all of the properties of the sphere except for the thermal relaxation time are graded through the radial direction using an exponential representation. The formulation is based on the Lord and Shulman theory which contains a single relaxation time parameter to avoid the infinite speed of temperature wave propagation. Two coupled equations namely energy and motion equations are obtained. These two equations are written in terms of temperature change and radial displacement. The energy equation is kept in its non-linear form and the assumption of small temperature change in comparison to reference temperature is not established in this research. The obtained equations are provided in a dimensionless presentation. After that using the generalised differential quadrature (GDQ) method, nonlinear algebraic presentation of the governing equations is established. Using the successive Picard algorithm and the Newmark time marching scheme, the temporal evolution of the temperature and displacement are obtained. Numerical results are validated for the case of homogeneous sphere with the available data in the open literature. After that, novel numerical results are given to explore the effect of relaxation time, coupling parameter, exponential index and non-linearity of the energy equation.