Variational approach to contact problems in nonlinear elasticity |
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Authors: | Friedemann Schuricht |
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Institution: | Mathematisches Institut, Universit?t zu K?ln, Weyertal 86–90, 50931 K?ln, Germany (e-mail: fs@math.uni-koeln.de), DE
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Abstract: | We use variational methods to study problems in nonlinear 3-dimensional elasticity where the deformation of the elastic body
is restricted by a rigid obstacle. For an assigned variational problem we first verify the existence of constrained minimizers
whereby we extend previous results. Then we rigorously derive the Euler-Lagrange equation as necessary condition for minimizers,
which was possible before only under strong smoothness assumptions on the solution. The Lagrange multiplier corresponding
to the obstacle constraint provides structural information about the nature of frictionless contact. In the case of contact
with, e.g., a corner of the obstacle, we derive a qualitatively new contact condition taking into account the deformed shape
of the elastic body. By our analysis it is shown here for the first time rigorously that energy minimizers really solve the
mechanical contact problem.
Received: 20 October 2000 / Accepted: 7 June 2001 / Published online: 5 September 2002 |
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Keywords: | Mathematics Subject Classification (2000): 35D05 35Q72 49J45 49K20 74B20 74M15 |
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