Summary
In order to complete the existing theory of beams subjected to follower forces, an exact solution for the case of triangularly distributed loads is presented. The results obtained may be compared with those reported in the literature and which were based on approximate calculations by means of the Method of Galerkin and the Finite Difference Method. The conclusion is that there is good agreement between all these results, thus confirming the dependability of the approximate methods.
Übersicht
Zur Abrundung der bereits bekannten Ergebnisse-zur Theorie von Balken mit Folgelasten wird eine exakte Lösung für den Fall einer dreieckförmig verteilten Last angegeben. Die Ergebnisse können mit den in der Literatur angegebenen verglichen werden, die auf der Grundlage von Näherungen nach der Methode von Galerkin oder mit Hilfe von finiten Elementen erhalten wurden. Die gute Übereinstimmung bestätigt die Zuverlässigkeit der Näherungslösungen.
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References
Leipholz, H. H. E.; Madan, Om. P.: On the Solution of the Stability Problem of Elastic Rods Subjected to Uniformly Distributed, Tangential Follower Forces. Ing.-Arch. 44 (1975) pp. 347–357
Leipholz, H. H. E.: Stability Theory. New York and London, 1970, pp. 244–245
Sugiyama, Y.; Katayama, T.; Sekiya, T.: Studies on Nonconservative Problems of Instability of Columns by Difference Method. Proc. 19th Japan National Congress of Applied Mechanics, 1969
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The financial support of this research by NRC Grant A7297 is gratefully acknowledged.
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Leipholz, H.H.E., Bhalla, K. On the solution of the stability problem of elastic rods subjected to triangularly distributed, tangential follower forces. Ing. arch 46, 115–124 (1977). https://doi.org/10.1007/BF00538745
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DOI: https://doi.org/10.1007/BF00538745