Thermoelastic Response of Thick Plates Using Fractional Calculus: Impact of Different Stress Measures and Boundary Configurations

This study examines the thermoelastic behavior of an isotropic, homogeneous thick plate with copper material with a height of 2h and infinite lateral dimensions with boundary conditions for temperature distribution θ (r, ±h, t) = θ 0 (r) sint − cost + e −t. The coordinate system is centred at the mid-plane of the plate, with the z-axis serving as the axis of symmetry. Employing cylindrical polar coordinates (r, ϕ, z), the analysis focuses on the transient temperature distribution T (r, z, t), assuming axial symmetry with respect to time t. To explore the coupled thermal and mechanical responses under various stress and boundary conditions, both analytical and numerical approaches are utilized. The analytical solution is derived using Laplace and Hankel transforms, providing insights into the temperature field and deformation characteristics. Additionally, numerical simulations are carried out to validate and complement the analytical results, offering a comprehensive understanding of the thermoelastic dynamics within the thick plate.