0434234 - ÚTIA 2015 RIV US eng J - Journal Article
Beremlijski, P. - Outrata, Jiří - Haslinger, J. - Pathó, R.
Shape Optimization in Contact Problems with Coulomb Friction and a Solution-Dependent Friction Coefficient.
SIAM Journal on Control and Optimization. Roč. 52, č. 5 (2014), s. 3371-3400. ISSN 0363-0129. E-ISSN 1095-7138
R&D Projects: GA ČR(CZ) GAP201/12/0671
Grant - others:GA MŠK(CZ) CZ.1.05/1.1.00/02.0070; GA MŠK(CZ) CZ.1.07/2.3.00/20.0070
Institutional support: RVO:67985556
Keywords : shape optimization * contact problems * Coulomb friction * solution-dependent coefficient of friction * mathematical programs with equilibrium constraints
Subject RIV: BA - General Mathematics
Impact factor: 1.463, year: 2014
http://library.utia.cas.cz/separaty/2014/MTR/outrata-0434234.pdf

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.
Permanent Link: http://hdl.handle.net/11104/0239356