Modeling the Edge Warping in Large Strain Rotating Disks Accounting for Thickness Reduction Distribution

Rotating disks composed of hyperelastic materials, commonly utilized in high-speed machinery such as turbines and flywheels, are subjected to considerable deformation under centrifugal forces. Previous models assumed an initial stretch resulting from the normal force on the surface, followed by a rotational transformation that overconstrained the problem for this specific geometry and limited its applicability. In contrast, our model assumes zero stress in the [Formula: see text]-direction, effectively treating the problem as a plane stress condition. Additionally, we revised the assumption regarding the gradient of deformation in the [Formula: see text]-direction to reflect the physical behavior better. This simplification results in reduced accuracy in predicting deformation behavior and thickness variation. To address this limitation, a one-dimensional analytical framework has been developed that explicitly considers thickness variation along the radial direction. As a result, both the predictive accuracy and computational efficiency have been improved. Validation of the model has been performed through comparison with finite element simulations, yielding close agreement, particularly in the central region of the disk. For thin disks, in which the thickness reaches up to 8% of the radius, deformation errors have been found to remain below 0.2%. For thicker disks, where the thickness approaches forty percent of the radius, deviations increase to approximately 2%, reflecting a transition toward cylindrical deformation behavior. In hollow disk configurations, stress and strain distributions have been accurately captured, with the highest stress error occurring near the outer edge due to material redistribution, remaining under 7%. Nonuniform stress near the inner boundary has been accurately captured, demonstrating improved reliability over existing models. With thickness variation included and computational demands reduced, the proposed approach serves as an efficient and reliable tool for analyzing large deformations in hyperelastic rotating disks.