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.

Keywords:

• Fractional-order
• integral transform
• multi-stacked plate
• transient responses

Acknowledgments

The authors are thankful to the reviewers and editors for their helpful feedback and positive comments that contributed to the revision of the paper in its present form.