Mircea Sofonea, Meir Shillor
Abstract:
This article constructs and analyzes a mathematical model that describes
the quasistatic evolution of a 2D elastic bar that may come in frictional
contact with a deformable foundation. The model and the underlying
mechanical assumptions are described in detail and so are the assumptions
on the problem data.
The variational formulation of the problem is derived and,
since friction is taken into account, it is in the form of an evolutionary
variational inequality for the displacement field. Existence of solutions
for the problem is established by using arguments of evolutionary variational
inequalities.
Submitted January 30, 2017. Published May 8, 2018.
Math Subject Classifications: 74M10, 74M15, 74K20, 58E35, 35Q74.
Key Words: 2D bar; frictional contact; normal compliance; weak solution;
variational inequality.
Show me the PDF file (303 KB), TEX file for this article.
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Mircea Sofonea Laboratoire de Mathéematiques et Physique University of Perpignan Via Domitia 52 Avenue Paul Alduy, 66860 Perpignan, France email: sofonea@univ-perp.fr |
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Meir Shillor Department of Mathematics and Statistics Oakland University Rochester, MI 48309, USA email: shillor@oakland.edu |
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