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Shape Optimization in Three-Dimensional Contact Problems with Coulomb Friction

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, ORCID}
Source Title	SIAM Journal on Optimization. - : SIAM Society for Industrial and Applied Mathematics - ISSN 1052-6234 Roč. 20, č. 1 (2009), s. 416-444
Number 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

Number of the records: 1