2D hereditary thermoelastic application of a thick plate under axisymmetric temperature distribution

Abstract

In this work, we present a new theory of generalized fractional hereditary thermoelasticity associated with Mittag–Leffler relaxation function. We analyze a two‐dimensional problem of a thick plate of hereditary thermoelastic. The lower and upper surfaces of the plate are assumed to be traction free and subjected to a given axisymmetric temperature distribution. Direct approach together with Laplace and Hankel transform techniques is employed to obtain the solution in the transformed domain. Hankel transforms are inverted analytically while a numerical method is used for the Laplace transform inversion. The distributions of different fields like temperature, displacement, and stresses have been computed and shown graphically.