Approximation, numerical realization and qualitative analysis of contact problems with friction
Aproximace, numerická realizace a kvalitativní analýza kontaktních úloh se třením.
dizertační práce (OBHÁJENO)

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Trvalý odkaz
http://hdl.handle.net/20.500.11956/47201Identifikátory
SIS: 46918
Kolekce
- Kvalifikační práce [11325]
Autor
Vedoucí práce
Konzultant práce
Janovský, Vladimír
Oponent práce
Segeth, Karel
Rohan, Eduard
Fakulta / součást
Matematicko-fyzikální fakulta
Obor
Vědecko-technické výpočty
Katedra / ústav / klinika
Katedra numerické matematiky
Datum obhajoby
12. 9. 2011
Nakladatel
Univerzita Karlova, Matematicko-fyzikální fakultaJazyk
Angličtina
Známka
Prospěl/a
Klíčová slova (česky)
kontaktní úloha, Coulombovo tření, lokálně lipschitzovská větev řešení, po částech hladká kontinuační metoda, metoda přerozdělení hmotnostiKlíčová slova (anglicky)
contact problem, Coulomb friction, local Lipschitz continuous branch of solutions, piecewise smooth continuation method, mass redistribution methodTitle: Approximation, numerical realization and qualitative analysis of contact problems with friction Author: Tomáš Ligurský Department: Department of Numerical Mathematics Supervisor: prof. RNDr. Jaroslav Haslinger, DrSc., Department of Numerical Mathe- matics Abstract: This thesis deals with theoretical analysis and numerical realization of dis- cretized contact problems with Coulomb friction. First, discretized 3D static contact prob- lems with isotropic and orthotropic Coulomb friction and solution-dependent coefficients of friction are analyzed by means of the fixed-point approach. Existence of at least one solution is established for coefficients of friction represented by positive, bounded and con- tinuous functions. If these functions are in addition Lipschitz continuous and upper bounds of their values together with their Lipschitz moduli are sufficiently small, uniqueness of the solution is guaranteed. Second, properties of solutions parametrized by the coefficient of friction or the load vector are studied in the case of discrete 2D static contact problems with isotropic Coulomb friction and coefficient independent of the solution. Conditions under which there exists a local Lipschitz continuous branch of solutions around a given reference point are established due to two variants of the...