Elastic analysis of variable profile and polar orthotropic FGM rotating disks for a variation function with three parameters

Analytical solutions are developed for the analysis of elastic polar orthotropic functionally graded annular disks rotating with constant angular velocity. The formulations are carried out by presuming a state of plane stress and small deformations. The elasticity moduli and thickness are varied radially by a nonlinear function controlled by three parameters, while the radial variation of density may be defined by any form of continuous function. Poisson’s ratios are taken to be constant. Annular disks having traction-free inner and outer surfaces, and annular disks mounted on a circular rigid shaft having traction-free outer surface are studied separately. The analytical solutions are verified numerically by the use of a computational model based on the nonlinear shooting method. An analysis that inspects the effects of the degree of orthotropy is presented. Elastic limit angular velocities are determined according to Hosford’s yield criteria. Stress, displacement and strain profiles are compared within the elastic range.