A three-dimensional elasticity solution for functionally graded rotating disks

A semi-analytical three-dimensional elasticity solution for rotating functionally graded disks for both of hollow and solid disks is presented. The aim is to generalize an available two-dimensional plane-stress solution to a three-dimensional one. Although for the thin disks problems the two-dimensional solution provides appropriate results, for the thick disks, a three-dimensional elasticity solution should be considered to avoid poor results. It is shown that although the plane-stress solution satisfies all the governing three-dimensional equations of motion and boundary conditions, it fails to give a compatible three-dimensional strain field. A valid three-dimensional solution has been introduced by modifying the plane-stress solution.