Jeongho Ahn, Jon Calhoun
Abstract:
The motion of viscoelastic (Kelvin-Voigt model) bodies
between an upper and a lower obstacle is studied both mathematically and
numerically. The two obstacles are assumed to be stationary perfect
rigid, therefore, Signorini contact conditions are imposed at each
obstacle, which can be interpreted as a couple of complementarity
conditions (CCs). The convergence of numerical trajectories for general
dimensional problems is shown based on the box constrained
variational inequality (VI) which is equivalent to the two CCs. A
one-dimensional example is provided. Unlike higher dimensional cases,
different perspectives are used to prove the results of its existence.
Numerical results are also presented and discussed, showing a typical
behavior of the system
Submitted September 5, 2012. Published April 5, 2013.
Math Subject Classifications: 74M20, 74K10, 35L85.
Key Words: Dynamic contact; variational inequality;
signorini contact conditions; complementarity conditions;
strong pointedness; numerical scheme.
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Jeongho Ahn Department of Mathematics and Statistics Arkansas State University, PO Box 600 State University, AR 72846, USA email: jahn@astate.edu |
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Jon Calhoun Department of Computer Science University of Illinois, Urbana-Champaign 201 North Goodwin Avenue Urbana, IL 61801-2302, USA email: jccalho2@illinois.edu |
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