"Tvarov\u00E1 optimalizace kontaktn\u00EDch probl\u00E9m\u016F s Coulombov\u00FDm t\u0159en\u00EDm"@cs . "Beremlijski, Petr" . "The paper deals with a discretized problem of shape optimization of elastic bodies in unilateral contact. The aim is to extend the existing results to the case of contact problems following the Coulomb friction law. Mathematical model of the Coulomb friction problem leads to a quasi-variational inequality. It is shown that for small coefficients of friction, the discretized problem with Coulomb friction has a unique solution and thatthis solution is Lipschitzian as a function of a control variable, describing the shape of the elastic body.The shape optimization problem belongs to a class of so-called mathematical programs with equilibrium constraints (MPECs). The uniqueness of the equilibria for fixed controls enables us to apply the so-called implicit programming approach. Its main idea consists in minimization of a nonsmooth composite function generated by the objective and the (single-valued) control--state mapping. In this paper, the control--state mapping is much more complicated than in most MP" . "P(GA101/01/0538), P(IAA1075005), Z(AV0Z1075907), Z(MSM 113200002), Z(MSM 272400019)" . . . "Haslinger, Jaroslav" . "Shape Optimization in Contact Problems with Coulomb Friction" . "4"^^ . . "[492C33C17A37]" . "1052-6234" . . . . "663430" . . . "The paper deals with a discretized problem of shape optimization of elastic bodies in unilateral contact. The aim is to extend the existing results to the case of contact problems following the Coulomb friction law. Mathematical model of the Coulomb friction problem leads to a quasi-variational inequality. It is shown that for small coefficients of friction, the discretized problem with Coulomb friction has a unique solution and thatthis solution is Lipschitzian as a function of a control variable, describing the shape of the elastic body.The shape optimization problem belongs to a class of so-called mathematical programs with equilibrium constraints (MPECs). The uniqueness of the equilibria for fixed controls enables us to apply the so-called implicit programming approach. Its main idea consists in minimization of a nonsmooth composite function generated by the objective and the (single-valued) control--state mapping. In this paper, the control--state mapping is much more complicated than in most MP"@en . . "US - Spojen\u00E9 st\u00E1ty americk\u00E9" . . . "SIAM Journal on Optimization" . "561-587" . "12/3" . "Outrata, Ji\u0159\u00ED" . . . "2002" . "Zab\u00FDvejme se diskretizovanou \u00FAlohou tvarov\u00E9 optimalizace pru\u017En\u00E9ho t\u011Blesa v\u00A0jednostrann\u00E9m kontaktu. Na\u0161\u00EDm c\u00EDlem je roz\u0161\u00ED\u0159it sou\u010Dasn\u00E9 v\u00FDsledky pro p\u0159\u00EDpad kontaktu se t\u0159en\u00EDm popsan\u00FDm Coulombov\u00FDm z\u00E1konem. Matematick\u00FD model probl\u00E9mu s\u00A0Coulombov\u00FDm t\u0159en\u00EDm vede na \u0159e\u0161en\u00ED kvazi-varia\u010Dn\u00ED nerovnosti. Pro mal\u00FD koeficient t\u0159en\u00ED bylo dok\u00E1z\u00E1no, \u017Ee diskr\u00E9tn\u00ED \u00FAloha s\u00A0Coulombov\u00FDm t\u0159en\u00EDm m\u00E1 jedin\u00E9 \u0159e\u0161en\u00ED a toto \u0159e\u0161en\u00ED je pops\u00E1no lipschitzovskou funkc\u00ED \u0159\u00EDd\u00EDc\u00ED prom\u011Bnn\u00E9 popisuj\u00EDc\u00ED tvar pru\u017En\u00E9ho t\u011Blesa. Tvarov\u011B optimaliza\u010Dn\u00ED probl\u00E9m pat\u0159\u00ED do t\u0159\u00EDdy \u00FAloh naz\u00FDvan\u00FDch MPEC. D\u00EDky jedin\u00E9mu \u0159e\u0161en\u00ED diskr\u00E9tn\u00ED \u00FAlohy pro fixovanou \u0159\u00EDd\u00EDc\u00ED prom\u011Bnnou, m\u016F\u017Eeme pou\u017E\u00EDt tzv. IPA. Jeho hlavn\u00ED my\u0161lenkou je minimalizace nehladk\u00E9 funkce slo\u017Een\u00E9 z\u00A0c\u00EDlov\u00E9 funkce a jednozna\u010Dn\u00E9ho zobrazen\u00ED, kter\u00E9 \u0159\u00EDd\u00EDc\u00ED prom\u011Bnn\u00E9 p\u0159i\u0159azuje stavovou prom\u011Bnnou. V\u00A0na\u0161em probl\u00E9mu je toto zobrazen\u00ED mnohem slo\u017Eit\u011Bj\u0161\u00ED ne\u017E ve v\u011Bt\u0161in\u011B MPEC \u00FAloh \u0159e\u0161en\u00FDch v\u00A0odborn\u00E9 literatu\u0159e. Zobecn\u011Bn\u00ED podobn\u00FDch v\u00FDsledk\u016F tud\u00ED\u017E nen\u00ED mo\u017En\u00E9. Na\u0161e numerick\u00E9 experimenty ukazuj\u00ED efektivnost a spolehl"@cs . . "RIV/61989100:27240/02:00012250!RIV06-GA0-27240___" . "Shape Optimization in Contact Problems with Coulomb Friction" . "27"^^ . . . . "Tvarov\u00E1 optimalizace kontaktn\u00EDch probl\u00E9m\u016F s Coulombov\u00FDm t\u0159en\u00EDm"@cs . . "Shape Optimization in Contact Problems with Coulomb Friction"@en . "Shape Optimization in Contact"@en . "Ko\u010Dvara, Michal" . "RIV/61989100:27240/02:00012250" . "Shape Optimization in Contact Problems with Coulomb Friction"@en . "27240" . "1"^^ .