A review of the three-dimensional elasticity analysis of a rotating annular disk

Abstract Novel stress-based derivations of three-dimensional elastic stress and displacement fields in an isotropic annular disk of uniform thickness, rotating around its axis of symmetry with constant angular speed, are presented, which complement other more involved derivations available in the literature. The first derivation is based on the direct integration of two partial differential equations for the sum and difference of the in-plane stresses, which are obtained by combining the equation of motion and the compatibility condition. In the second derivation the stresses are obtained by using a simple form of the stress function satisfying a first-order nonhomogeneous partial differential equation following from the Beltrami–Michell compatibility equations, which can be solved readily. The third derivation is based on Love’s stress function of axisymmetric three-dimensional elasticity, generalized to include a rotational inertia force. The resulting nonhomogeneous biharmonic partial differential equation is solved by two alternative methods of constructing its particular and complementary solution. The derived expression for Love’s function has not been reported in the literature before. The displacement-based derivation of elastic fields is also presented, including a construction of the corresponding Papkovich–Neuber potentials.