Existence of solutions to the linearized spinning wheel problem

Spinning wheels, or rather steady rolling cylinder-like deformable bodies occur in many mechanical (contact) problems, e.g. car- or aircraft-tires, gears or grinding processes. In order to avoid transient calculation for such problems and in order to obtain a steady-state formulation we make use of a model - advocated by Oden and Lin in [1] and further elaborated by Govindjee andMihalic in [2] - based on a spinning reference coordinate system. After developing the kinematics and deriving the weak formulation we will show the existence of a weak solution for the linearized spinning wheel problem by applying the Lax Milgram Lemma. The presented contribution will be concluded by some numerical examples.