Stress analysis of functionally graded hyperelastic variable thickness rotating annular thin disk: A semi-analytic approach

Functionally graded materials (FGMs) represent a promising class of advanced materials designed with tailored microstructures to achieve optimized mechanical, thermal, and functional properties across varying gradients. The strategic integration of distinct materials within functionally graded materials offers engineers unprecedented control over properties such as strength, thermal conductivity, and corrosion resistance, enabling innovative solutions for demanding applications in aerospace, automotive, and biomedical industries. This study investigates a rotating annular thin disk with variable thickness composed of incompressible hyperelastic material, made up of functionally graded properties under large deformations. To elucidate these phenomena, a power relation is employed to delineate the changes in cross-sectional geometry m, the material property n, and the angular velocity w of hyperelastic material. Constants used for hyperelastic material are obtained from the experimental data. Equations are solved semi-analytically for different values of m, n, and w, and the values of radial stresses, tangential stresses, and elongation are calculated and compared for different conditions. Results show that thickness and FG properties have a significant impact on the behavior of disk, so that the expected behavior of the disk can be obtained by an optimal selection of the disks geometry and material properties. By selecting the optimum values for these variables, the location of maximum stress can be controlled in large deformations, thereby furnishing significance advantages in structural design and material selection.