2D hereditary thermoelastic application of a thick plate under axisymmetric temperature distribution. (7th October 2021)

• Record Type: Journal Article
• Authors: Sherief, Hany H.; Abd El‐Latief, Abd El‐Latief M.; Fayik, Mohsen A.
• Is Part Of: Mathematical methods in the applied sciences. Volume 45:Number 2(2022)
• Page Start: 1080
• Page End: 1092
• Publication Date: 2021-10-07
• Subjects: Hankel transform -- hereditary thermoelasticity -- Laplace transform -- Mittag–Leffler relaxation function -- thick plate -- two‐dimensional application; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7837
• Languages: English
• ISSNs: 0170-4214

Abstract

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.