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Existence of Solutions to the Linearized Spinning Wheel Problem
Author(s) -
Ricker Sarah,
Menzel Andreas,
Steinmann Paul
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610307
Subject(s) - spinning , lemma (botany) , cylinder , kinematics , mechanical engineering , mechanics , mathematics , mathematical analysis , classical mechanics , computer science , control theory (sociology) , physics , engineering , artificial intelligence , ecology , poaceae , control (management) , biology
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. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)