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Existence of solutions to the linearized spinning wheel problem

: Staub, S.; Menzel, A.; Steinmann, P.


Proceedings in applied mathematics and mechanics. PAMM 6 (2006), No.1, pp.653-654
ISSN: 1617-7061
Gesellschaft für Angewandte Mathematik und Mechanik (GAMM Annual Meeting) <77, 2006, Berlin>
Journal Article, Conference Paper
Fraunhofer ITWM ()

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.