Abstract
We investigate axially symmetric localized bulging of an incompressible hyperelastic circular solid cylinder or tube that is rotating about its axis of symmetry with angular velocity omega. For such a solid cylinder, the homogeneous primary deformation is completely determined by the axial stretch lambda(z), and it is shown that the bifurcation condition is simply given by d omega/d lambda(z) = 0 if the resultant axial force F is fixed. For a tube that is shrink- fitted to a rigid circular cylindrical spindle, the azimuthal stretch lambda(a) on the inner surface of the tube is specified and the deformation is again completely determined by the axial stretch lambda(z) although the deformation is now inhomogeneous. For this case it is shown that with F fixed the bifurcation condition is also given by d omega/d lambda(z) = 0. When the spindle is absent (the case of unconstrained rotation), we also allow for the possibility that the tube is additionally subjected to an internal pressure P. It is shown that with P fixed, and omega and F both viewed as functions of lambda(a) and lambda(z), the bifurcation condition for localized bulging is that the Jacobian of omega and F should vanish. Alternatively, the same bifurcation condition can be derived by fixing omega and setting the Jacobian of P and F to zero. Illustrative numerical results are presented using the Ogden and Gent material models.