An exact analytical solution for fractional-order thermoelasticity in a multi-stacked elliptic plate

Abstract

Thermoelastic analysis of an isotropic homogeneous multi-stacked elliptical plate has been considered in this research. For which multi-layered plate is taken into consideration on a plane-parallel elliptic geometry perpendicular to the z-direction. The governing equations are considered in the context of time-fractional derivative of the order α with temperature distribution in each s layer of the stacked plate with time-dependent sectional heat supply on the lower and upper face. The multi-stacked profile consists of s discrete plates each of a different material with perfect thermal contact at each of its s-1 interface. The general solution, which perfectly satisfies the fundamental equation of heat conduction, is obtained using an integral transformation technique. It is solved using a type of quasi-orthogonality relationship by modifying Vodicka’s method and the Laplace transformation. The analysis is based on the small-deflection theory corresponding to the fundamental solutions for the fractional-order heat conduction equation. In addition to this, the intensities of bending moments, forces, maximum normal stresses and its associated stresses are formulated involving the Mathieu functions. As a special case, a multi-stacked circular plate is also discussed in detail as a limiting case. Numerical calculations are also performed, and the results are graphically illustrated.