Stressed-deformed state of a rotating polar-orthotropic disk of constant thickness loaded with undistracted forces on the outer contour

Abstract

The work gives a solution of the plane elasticity problem for a rotating polar-orthotropic annular disk of a constant  thickness. The disk is loaded with a system of identical undistracted forces on the outer contour applied evenly along  the rim and symmetric concerning the diameter. The disk is seated with an interference fit on the flexible shaft so that  a constant contact pressure acts on the interior contour. The stresses and deformations arising in such a rotating anisotropic annular disk will be non-axisymmetric. A conclusion of a fourth-order partial differential equation for the Erie  stress function is drawn. Its general solution is searched out in the form of a Fourier series of cosines with even numbers.  The resulting infinite system of ordinary differential equations is solved by standard methods of the theory of differential  equations. Constants of integration are determined from the border conditions. Expressions for the stress components are  written through the stress function by the well-known formulas. We find the components of the displacement vector in the  disk by the integration of the Hooke’s law equations for the polar-orthotropic plate. It is easy to calculate the deformation  components in a ring anisotropic disk by Cauchy differential relations if we know the displacements. The case of a rotating solid polar-orthotropic disk of constant thickness loaded with undistracted forces on the outer contour is considered  separately. The obtained formulas for stresses and displacements completely describe the stress-deformed state in a rotating polar-orthotropic disc of constant thickness with a system of undistracted forces on the outer contour.