Analytical study of thermo‐elastic stresses in rotating disks considering material anisotropy and radial density variation

Abstract This study presents a nonlinear thermo‐mechanical framework for analyzing stress and deformation in shaft‐mounted rotating disks made of transversely isotropic materials with radially graded density. The model incorporates the combined effects of centrifugal forces, external radial traction, axial constraint, and a steady‐state thermal gradient. Utilizing Seth's transition theory, closed‐form analytical solutions are derived for radial displacement, radial stress, and hoop stress under axisymmetric conditions. The formulation is validated against classical isotropic solutions and finite element simulations, showing excellent agreement with deviations below 2%. Parametric studies reveal that positive density gradation (e.g., m = 2) reduces peak hoop stress by ∼14% and radial displacement by ∼12%, while negative gradation (e.g., m = −0.5) increases them by ∼9% and ∼8%, respectively. Axial loading significantly amplifies stress concentrations, particularly at the bore, and thermal gradients further elevate stress levels and advance the onset of yielding. It is conclusively shown that yielding initiates at the inner bore, with the critical angular velocity reduced by ∼15% under combined thermo‐mechanical loading. The proposed analytical model provides a robust tool for the design and optimization of advanced rotating components in aerospace, energy storage, and hydromechatronic systems.