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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F12%3A10127026%21RIV13-AV0-11320___
rdf:type
skos:Concept n16:Vysledek
rdfs:seeAlso
http://dx.doi.org/10.1007/s11228-011-0179-7
dcterms:description
The paper deals with shape optimization of elastic bodies in unilateral contact. The aim is to extend the existing results to the case of contact problems, where the coefficient of friction depends on the solution. We consider the two-dimensional Signorini problem, coupled with the physically less accurate model of given friction, but assume a solution-dependent coefficient of friction. First, we investigate the shape optimization problem in the continuous, infinite-dimensional setting, followed by a suitable finite-dimensional approximation based on the finite-element method. Convergence analysis is presented as well. Next, an algebraic form of the state problem is studied, which is obtained from the discretized problem by further approximating the frictional term by a quadrature rule. It is shown that if the coefficient of friction is Lipschitz continuous with a sufficiently small modulus, then the algebraic state problem is uniquely solvable and its solution is a Lipschitz continuous function of the control variable, describing the shape of the elastic body. For the purpose of numerical solution of the shape optimization problem via the so-called implicit programming approach we perform sensitivity analysis by using the tools from the generalized differential calculus of Mordukhovich. The paper is concluded first order optimality conditions. The paper deals with shape optimization of elastic bodies in unilateral contact. The aim is to extend the existing results to the case of contact problems, where the coefficient of friction depends on the solution. We consider the two-dimensional Signorini problem, coupled with the physically less accurate model of given friction, but assume a solution-dependent coefficient of friction. First, we investigate the shape optimization problem in the continuous, infinite-dimensional setting, followed by a suitable finite-dimensional approximation based on the finite-element method. Convergence analysis is presented as well. Next, an algebraic form of the state problem is studied, which is obtained from the discretized problem by further approximating the frictional term by a quadrature rule. It is shown that if the coefficient of friction is Lipschitz continuous with a sufficiently small modulus, then the algebraic state problem is uniquely solvable and its solution is a Lipschitz continuous function of the control variable, describing the shape of the elastic body. For the purpose of numerical solution of the shape optimization problem via the so-called implicit programming approach we perform sensitivity analysis by using the tools from the generalized differential calculus of Mordukhovich. The paper is concluded first order optimality conditions.
dcterms:title
Shape Optimization in 2D Contact Problems with Given Friction and a Solution-Dependent Coefficient of Friction Shape Optimization in 2D Contact Problems with Given Friction and a Solution-Dependent Coefficient of Friction
skos:prefLabel
Shape Optimization in 2D Contact Problems with Given Friction and a Solution-Dependent Coefficient of Friction Shape Optimization in 2D Contact Problems with Given Friction and a Solution-Dependent Coefficient of Friction
skos:notation
RIV/00216208:11320/12:10127026!RIV13-AV0-11320___
n16:predkladatel
n17:orjk%3A11320
n4:aktivita
n13:Z n13:I n13:P
n4:aktivity
I, P(IAA100750802), Z(AV0Z10750506)
n4:cisloPeriodika
1
n4:dodaniDat
n10:2013
n4:domaciTvurceVysledku
n8:3962458 n8:7616880
n4:druhVysledku
n7:J
n4:duvernostUdaju
n12:S
n4:entitaPredkladatele
n5:predkladatel
n4:idSjednocenehoVysledku
167693
n4:idVysledku
RIV/00216208:11320/12:10127026
n4:jazykVysledku
n18:eng
n4:klicovaSlova
Mathematical programs with equilibrium constraints; Solution-dependent coefficient of friction; Model with given friction; Signorini problem; Shape optimization
n4:klicoveSlovo
n6:Signorini%20problem n6:Solution-dependent%20coefficient%20of%20friction n6:Model%20with%20given%20friction n6:Mathematical%20programs%20with%20equilibrium%20constraints n6:Shape%20optimization
n4:kodStatuVydavatele
NL - Nizozemsko
n4:kontrolniKodProRIV
[9E10A4213037]
n4:nazevZdroje
Set-Valued and Variational Analysis
n4:obor
n22:BA
n4:pocetDomacichTvurcuVysledku
2
n4:pocetTvurcuVysledku
3
n4:projekt
n19:IAA100750802
n4:rokUplatneniVysledku
n10:2012
n4:svazekPeriodika
20
n4:tvurceVysledku
Haslinger, Jaroslav Outrata, Jiri V. Pathó, Róbert
n4:wos
000299962100003
n4:zamer
n21:AV0Z10750506
s:issn
1877-0533
s:numberOfPages
29
n9:doi
10.1007/s11228-011-0179-7
n11:organizacniJednotka
11320