Übersicht
In diesem Aufsatz werden einseitige Randwertprobleme der Elastizitätstheorie behandelt, die durch Randbedingungen eines einseitigen Kontaktes und durch Reibungsrandbedingungen formuliert werden können. Es wird bewiesen, daß diese Ungleichungsrandwertprobleme als variationelle Ungleichungen äquivalent formuliert werden können, und daß das Minimum-Theorem der potentiellen und der komplementären Energie für diese neuen Randbedingungen gültig ist. Diese Minimum-Theoreme ermöglichen es, die Probleme numerisch als Probleme der nichtlinearen Optimierung zu behandeln. Die Theorie wird durch numerische Beispiele von Konstruktionen mit gekoppelten einseitigen Kontakt-Randbedingungen und Reibungs-Randbedingungen erläutert.
Summary
In the present paper the elastic analysis of structures with “unilateral contact” — and “friction” — boundary conditions is considered. It is proved that the considered inequality boundary value problems can be formulated equivalently as variational inequalities, which permit the derivation of the theorems of minimum potential and complementary energy, to account for this type of boundary conditions. These minimum theorems are used to formulate the analysis as a nonlinear programming problem. Numerical examples on structures with coupled unilateral contact- and friction-boundary conditions illustrate the theory.
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The author would like to extend his grateful thanks to the “Alexander von Humboldt-Stiftung” for their financial support, to Prof. Dr. rer. nat. G. Rieder for his continuous encouragement, to Mr. B. R. Witherden, B. A., M. Sc. Oxon, for his help in the exposition of the paper, and to Dipl.-Ing. E. Mitsoponlou for the programming of the numerical examples.
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Panagiotopoulos, P.D. A nonlinear programming approach to the unilateral contact-, and friction-boundary value problem in the theory of elasticity. Ing. arch 44, 421–432 (1975). https://doi.org/10.1007/BF00534623
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DOI: https://doi.org/10.1007/BF00534623