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Shape Optimization in Contact Problems with Coulomb Friction and a Solution-Dependent Friction Coefficient
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SYSNO ASEP 0434234 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Shape Optimization in Contact Problems with Coulomb Friction and a Solution-Dependent Friction Coefficient Author(s) Beremlijski, P. (CZ)
Outrata, Jiří (UTIA-B) RID, ORCID
Haslinger, J. (CZ)
Pathó, R. (CZ)Number of authors 4 Source Title SIAM Journal on Control and Optimization. - : SIAM Society for Industrial and Applied Mathematics - ISSN 0363-0129
Roč. 52, č. 5 (2014), s. 3371-3400Number of pages 30 s. Publication form Print - P Language eng - English Country US - United States Keywords shape optimization ; contact problems ; Coulomb friction ; solution-dependent coefficient of friction ; mathematical programs with equilibrium constraints Subject RIV BA - General Mathematics R&D Projects GAP201/12/0671 GA ČR - Czech Science Foundation (CSF) Institutional support UTIA-B - RVO:67985556 UT WOS 000344748000027 EID SCOPUS 84911059522 DOI 10.1137/130948070 Annotation The present paper deals with shape optimization in discretized two-dimensional (2D) contact problems with Coulomb friction, where the coefficient of friction is assumed to depend on the unknown solution. Discretization of the continuous state problem leads to a system of finite-dimensional implicit variational inequalities, parametrized by the so-called design variable, that determines the shape of the underlying domain. It is shown that if the coefficient of friction is Lipschitz and sufficiently small in the C0,1-norm, then the discrete state problems are uniquely solvable for all admissible values of the design variable (the admissible set is assumed to be compact), and the state variables are Lipschitzian functions of the design variable. This facilitates the numerical solution of the discretized shape optimization problem by the so-called implicit programming approach. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2015
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