Thermoelastic response of a nonhomogeneous elliptic plate in the framework of fractional order theory

This article aims to examine the thermoelastic problem for a medium with nonhomogeneous material properties within a finite-length elliptical plate. An analytical method is established under the assumption that the thermomechanical material inhomogeneity obeys the product form of power and exponential functions through the plate's thickness. At the same time, calorific capacity and Poisson's ratio are assumed to be constant. The fractional time derivative heat conduction differential equation with an internal heat source is solved using integral transformation technique in terms of generalized Laguerre polynomial, and Mathieu function in the Laplace domain. The Gaver–Stehfest approach is used to invert Laplace domain outcomes. The convergence of infinite series solutions has been discussed. In the specific case, the elliptic region that degenerates into the problem of the circular area by adding limiting conditions is also considered. As a numerical example, the temperature, displacement and thermal stress distributions are calculated, taking into account influence of inhomogeneity, and the numerical results are graphically demonstrated.