Rotating monoclinic classical and nano-disks: Analytical results

This research targets the mechanical behavior of rotating monoclinic disks, employing the principles of classical elasticity to derive precise analytical solutions under conditions of constant angular velocity. The primary focus is on understanding how these disks respond to rotational forces, specifically examining the resulting stress and displacement fields within their structures. Furthermore, the study extends its scope to the analysis of stress and displacement characteristics in nano-disks, utilizing both classical and gradient elasticity theories to provide a comprehensive perspective. The mathematical framework relies on the application of stress potential functions, a standard approach in elasticity, to facilitate the derivation of solutions. The investigation encompasses a variety of disk configurations, including annular disks, solid disks, and annular disks subjected to an external pressure. A significant part of the research is dedicated to visually representing the variations in stress and displacement, presenting these results graphically to enhance understanding and interpretation under both classical and gradient elasticity theories. Beyond homogeneous materials, the study explores the complexities introduced by inhomogeneity, specifically considering disks with radial variations in their elastic constants. The research meticulously investigates linear, exponential, and bi-exponential radial variations, deriving analytical solutions that account for these material property gradients. The findings are presented both analytically and graphically, enabling a comparative analysis between homogeneous and inhomogeneous isotropic and anisotropic materials, highlighting the influence of material composition on the overall mechanical response of the rotating disks. The graphical representations serve to illustrate the impact of varying material properties on the stress and displacement distributions within the disk structures.