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CONTACT PROBLEMS FOR NONLINEARLY ELASTIC MATERIALS: WEAK SOLVABILITY INVOLVING DUAL LAGRANGE MULTIPLIERS

Part of: Special kinds of problems Elliptic equations and systems

Published online by Cambridge University Press:  03 August 2011

A. MATEI  and
R. CIURCEA
A. MATEI*
Affiliation:
Department of Mathematics, University of Craiova, A.I. Cuza 13, 200585 Craiova, Romania (email: [email protected], [email protected])
R. CIURCEA
Affiliation:
Department of Mathematics, University of Craiova, A.I. Cuza 13, 200585 Craiova, Romania (email: [email protected], [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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A class of problems modelling the contact between nonlinearly elastic materials and rigid foundations is analysed for static processes under the small deformation hypothesis. In the present paper, the contact between the body and the foundation can be frictional bilateral or frictionless unilateral. For every mechanical problem in the class considered, we derive a weak formulation consisting of a nonlinear variational equation and a variational inequality involving dual Lagrange multipliers. The weak solvability of the models is established by using saddle-point theory and a fixed-point technique. This approach is useful for the development of efficient algorithms for approximating weak solutions.

Keywords

contact modelsnonlinearly elastic materialsdual Lagrange multipliersweak solutions

MSC classification

Secondary: 74M10: Friction 35J50: Variational methods for elliptic systems 35J66: Nonlinear boundary value problems for nonlinear elliptic equations
Type
Research Article
Information
The ANZIAM Journal , Volume 52 , Issue 2 , October 2010 , pp. 160 - 178
Copyright
Copyright © Australian Mathematical Society 2011

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