THE AXISYMMETRICAL DEFORMATION OF LINEARLY AND NONLINEARLY ELASTIC SPINNING TUBES UNDER END THRUSTS AND TORQUES

We consider the steady-state deformations of elastic tubes spinning st eadily and attached in various ways to rigid end plates to which end t hrusts and torques are applied. We assume that the tubes are made of h omogeneous linearly or nonlinearly anisotropic material and use Simmon ds' (1996) simplified dynamic displacement-rotation equations for shel ls of revolution undergoing large-strain large-l oration axisymmetric bending and torsion. To exploit analytical methods, we confine attenti on to the nonlinear theory of membranes undergoing small or large stra ins and the theory of strongly anisotropic tubes suffering small strai ns. Of particular interest are the boundary layers that appear at each end of the tube, their membrane and bending components, and the penet ration of these layers into the tube which, for certain anisotropic ma terials, may be considerably different from isotropic materials. Remar kably, we find that the behavior of a tube made of a linearly elastic, anisotropic material (having nine elastic parameters) can be describe d, to a first approximation, by just two combined parameters. The resu lts of the present paper lay, the necessary groundwork for a subsequen t analysis of the whirling of spinning elastic tubes under end thrusts and torques.