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Statements

Subject Item
n2:RIV%2F61989100%3A27740%2F14%3A86091407%21RIV15-MSM-27740___
rdf:type
skos:Concept n5:Vysledek
rdfs:seeAlso
http://epubs.siam.org/doi/pdf/10.1137/130948070
dcterms:description
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. Our main results concern sensitivity analysis, which is based on the well-developed generalized differential calculus of B. Mordukhovich and generalizes some of the results obtained in this context so far. The derived subgradient information is then combined with the bundle trust method to compute several model examples, demonstrating the applicability and efficiency of the presented approach. 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. Our main results concern sensitivity analysis, which is based on the well-developed generalized differential calculus of B. Mordukhovich and generalizes some of the results obtained in this context so far. The derived subgradient information is then combined with the bundle trust method to compute several model examples, demonstrating the applicability and efficiency of the presented approach.
dcterms:title
SHAPE OPTIMIZATION IN CONTACT PROBLEMS WITH COULOMB FRICTION AND A SOLUTION-DEPENDENT FRICTION COEFFICIENT SHAPE OPTIMIZATION IN CONTACT PROBLEMS WITH COULOMB FRICTION AND A SOLUTION-DEPENDENT FRICTION COEFFICIENT
skos:prefLabel
SHAPE OPTIMIZATION IN CONTACT PROBLEMS WITH COULOMB FRICTION AND A SOLUTION-DEPENDENT FRICTION COEFFICIENT SHAPE OPTIMIZATION IN CONTACT PROBLEMS WITH COULOMB FRICTION AND A SOLUTION-DEPENDENT FRICTION COEFFICIENT
skos:notation
RIV/61989100:27740/14:86091407!RIV15-MSM-27740___
n6:aktivita
n19:P
n6:aktivity
P(ED1.1.00/02.0070)
n6:cisloPeriodika
5
n6:dodaniDat
n9:2015
n6:domaciTvurceVysledku
n8:2314738
n6:druhVysledku
n16:J
n6:duvernostUdaju
n7:S
n6:entitaPredkladatele
n14:predkladatel
n6:idSjednocenehoVysledku
44696
n6:idVysledku
RIV/61989100:27740/14:86091407
n6:jazykVysledku
n18:eng
n6:klicovaSlova
mathematical programs with equilibrium constraints; solution-dependent coefficient of friction; Coulomb friction; contact problems; shape optimization
n6:klicoveSlovo
n11:Coulomb%20friction n11:shape%20optimization n11:mathematical%20programs%20with%20equilibrium%20constraints n11:solution-dependent%20coefficient%20of%20friction n11:contact%20problems
n6:kodStatuVydavatele
US - Spojené státy americké
n6:kontrolniKodProRIV
[E99D8B8E28FE]
n6:nazevZdroje
SIAM JOURNAL ON CONTROL AND OPTIMIZATION. Volume 52
n6:obor
n20:BA
n6:pocetDomacichTvurcuVysledku
1
n6:pocetTvurcuVysledku
4
n6:projekt
n15:ED1.1.00%2F02.0070
n6:rokUplatneniVysledku
n9:2014
n6:svazekPeriodika
52
n6:tvurceVysledku
Pathó, Róbert Outrata, Jiří Haslinger, Jaroslav Beremlijski, Petr
n6:wos
000344748000027
s:issn
0363-0129
s:numberOfPages
30
n17:doi
10.1137/130948070
n10:organizacniJednotka
27740