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http://bura.brunel.ac.uk/handle/2438/12032
Title: | Dual-dual formulation for a contact problem with friction |
Authors: | Maischak, M Stephan, EP |
Keywords: | Contact problems;Friction;Fenchel duality;Variational inequalities |
Issue Date: | 2015 |
Publisher: | De Gruyter |
Citation: | Computational Methods in Applied Mathematics, 16(1): pp.1–16, (2015) |
Abstract: | A variational inequality formulation is derived for some frictional contact problems from linear elasticity. The formulation exhibits a two-fold saddle point structure and is of dual-dual type, involving the stress tensor as primary unknown as well as the friction force on the contact surface by means of a Lagrange multiplier. The approach starts with the minimization of the conjugate elastic potential. Applying Fenchel's duality theory to this dual minimization problem, the connection to the primal minimization problem and a dual saddle point problem is achieved. The saddle point problem possesses the displacement field and the rotation tensor as further unknowns. Introducing the friction force yields the dual-dual saddle point problem. The equivalence and unique solvability of both problems is shown with the help of the variational inequality formulations corresponding to the saddle point formulations, respectively. |
URI: | http://www.degruyter.com/view/j/cmam.2016.16.issue-1/cmam-2015-0021/cmam-2015-0021.xml http://bura.brunel.ac.uk/handle/2438/12032 |
DOI: | http://dx.doi.org/10.1515/cmam-2015-0021 |
ISSN: | 1609-9389 |
Appears in Collections: | Dept of Mathematics Research Papers |
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