This study presents a Physics-Informed Neural Network (PINN) framework for analyzing the nonlinear deformation of rotating variable-thickness hyperelastic disks made of both homogeneous and functionally graded materials (FGMs). The formulation incorporates large-deformation kinematics, the incompressibility constraint, and the neo-Hookean constitutive law within a hybrid loss function that combines physical residuals with sparse high-fidelity data. Three disk geometries—rectangular, trapezoidal, and parabolic profiles—are examined under steady-state rotation for both homogeneous and radially graded materials characterized by power-law variations in shear modulus and density. The hybrid PINN framework yields mesh-free and physics-consistent predictions for the displacement and stress fields. Quantitative comparison with finite element method (FEM) benchmarks demonstrates excellent agreement across all geometries: the relative differences remain below approximately 2% in radial displacement, the mean absolute deviation within about 3 MPa in the maximum principal stress, and the predicted shift in peak-stress location less than 3% of the outer radius for both positive and negative gradation indices (m = ±0.1). These results, derived directly from the validated graphical and numerical comparisons, confirm the accuracy, stability, and robustness of the proposed hybrid PINN formulation for the nonlinear analysis of rotating variable-thickness hyperelastic disks made of both homogeneous and graded materials.
Hamad et al. (Fri,) studied this question.