Augmented lagrangian methods for a class of convex and nonconvex contact problems

• Autorzy: Telega J. J. , Gałka A. , Bielski W.
• Języki publikacji: EN

Abstrakty

EN

The aim of this contribution is threefold. First, we formulate unilateral contact problems for three models of plates and the Koiter shell model. Contact conditions have been formulated on the face being in contact with an obstacle and not on the mid-plane of the plate or the middle surface of the shell. Such a rigorous approach results in nonconvex minimization problems even in the case of thin, geometrically linear plates. Existence theorems are formulated for each model considered. Second, the Ito and Kunisch (1990, 1995) augmented Lagrangians methods have been extended to nonconvex problems. Third, nonconvex duality theory by Rockafellar and Wets (1998), valid for finite-degree-of-freedom systems has been extended to continuous systems. Specific examples have also been provided.

PL

Metody rozszerzonego lagranżianu dla pewnej klasy wypukłych i niewypukłych zagadnień kontaktowych. Cel pracy jest trojaki. Po pierwsze, sformułowane zostały jednostronne zagadnienia kontaktowe dla trzech modeli płyt oraz liniowego modelu powłok Koitera. Warunki kontaktu zostały sformułowane na powierzchni będące w kontakcie z podłożem, a nie na powierzchni środkowej płyty lub powłoki. Takie ścisłe podejście prowadzi do niewypukłych zadań minimalizacji, nawet w przypadku płyt cienkich. Dla każdego zagadnienia sformułowano twierdzenie o istnieniu rozwiązań. Po drugie, metody rozszerzonego lagranżianu Ito i Kunischa (1990, 1995) uogólnione zostały na przypadek zagadnień niewypukłych. Po trzecie, teoria dualności Rockafellara i Wetsa (1998), opracowana dla skończenie wymiarowych zagadnień niewypukłych, została rozszerzona na przypadek układów ciągłych. Podano również kilka przykładów.

Słowa kluczowe

EN

unilateral contact problems without friction; plates; Koiter's shell model; augmented Lagrangian methods; nonconvex duality

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2001
• Tom: Vol. 39 nr 3
• Strony: 741--768
• Opis fizyczny: Bibliogr. 48 poz., rys.

Twórcy

autor

Telega J. J.

• Institute of Fundamental Technological Research, Polish Academy of Science, Warsaw

autor

Gałka A.

• Institute of Fundamental Technological Research, Polish Academy of Science, Warsaw

autor

Bielski W.

• Institute of Geophysics, Polish Academy of Sciences, Warsaw

Bibliografia

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