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Shape Optimization in Three-Dimensional Contact Problems with Coulomb Friction
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SYSNO ASEP 0323859 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Ostatní články Title Shape Optimization in Three-Dimensional Contact Problems with Coulomb Friction Title Optimalizace tvaru třídimenzionálních těles s Coulobmovským kontaktem Author(s) Beremlijski, P. (CZ)
Haslinger, J. (CZ)
Kočvara, Michal (UTIA-B) RID, ORCID
Kučera, R. (CZ)
Outrata, Jiří (UTIA-B) RID, ORCIDSource Title SIAM Journal on Optimization. - : SIAM Society for Industrial and Applied Mathematics - ISSN 1052-6234
Roč. 20, č. 1 (2009), s. 416-444Number of pages 29 s. Publication form www - www Language eng - English Country US - United States Keywords shape optimization ; contact problems ; Coulomb friction Subject RIV BA - General Mathematics R&D Projects IAA100750802 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) IAA1075402 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) CEZ AV0Z10750506 - UTIA-B (2005-2011) DOI 10.1137/080714427 Annotation We study the discretized problem of the shape optimization of three-dimensional elastic bodies in unilateral contact. The aim is to extend existing results to the case of contact problems obeying the Coulomb friction law. Mathematical modeling of the Coulomb friction problem leads to an implicit variational inequality. It is shown that for small coefficients of friction the discretized problem with Coulomb friction has a unique solution and that this solution is Lipschitzian as a function of a control variable describing the shape of the elastic body. The two-dimensional case of this problem was studied by the authors in SIAM J. Optim.; there we used the so-called implicit programming approach combined with the generalized differential calculus of Clarke. The extension of this technique to the three-dimensional situation is by no means straightforward. The main source of difficulties is the nonpolyhedral character of the second-order (Lorentz) cone, arising in the 3D model. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2009
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