Bending analysis of circular plates under a refined Lord–Shulman fractional theory with variable thermal conductivity

This article examines the bending response of a circular plate under thermoelastic conditions using a refined Lord–Shulman fractional theory incorporating variable thermal conductivity. The analysis considers three theoretical frameworks: the simple classical thermoelasticity theory and its fractional extension, as well as Lord–Shulman’s simple and refined fractional formulation. Governing equations for the circular annular plate are obtained based on a fractional-order generalized thermoelasticity model. The solution is attained via the Laplace transform method, with numerical inversion employed for computational evaluation. Results are presented for key field variables—temperature, displacements, dilatation, and stresses—with comparative analysis illustrated through graphical distributions. The inquiry examines the influence of critical parameters, including relaxation time, fractional order, thermal conductivity variation, and ramp-type heat influences, on the thermoelastic bending response. The plots highlight radial and thickness-wise variations in field quantities under different theoretical assumptions. Special cases are also derived from the generalized framework, demonstrating the model’s versatility. This work contributes to the comprehension of thermoelastic plate behaviour under non-classical conditions, offering insights for applications requiring advanced thermo-mechanical modeling.