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An approximate method of analysis of large deflections

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Zusammenfassung

Ein einfaches analytisches Näherungsverfahren zur Behandlung einer Klasse nichtlinearer Randwertaufgaben wird beschrieben und bei der Berechnung der grossen Biegeverformungen von schweren, dünnen Balken und Säulen angewandt. Das Wesen des Verfahrens beruht auf der Linearisierung (oder der Herabsetzung des Nichtlinearitätsgrades) der nichtlinearen Differentialgleichung mittels der Tschebyschewschen Polynome. Die Genauigkeit des Verfahrens beruht auf der Eigenschaft der Tschebyschewschen Entwicklungen, den absoluten Maximal-Fehler der polynomischen Annäherung an eine gegebene Funktion in einem vorgeschriebenen Intervall beinahe auf ein Mindestmass zu verringern.

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Authors and Affiliations

  1. Dept. of Physics, Wayne State University, Detroit, Michigan, USA

    Harry H. Denman

  2. Dept. of Eng. Mechanics, University of Detroit, Detroit, Michigan, USA

    Robert Schmidt

Authors
  1. Harry H. Denman
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  2. Robert Schmidt
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Denman, H.H., Schmidt, R. An approximate method of analysis of large deflections. Journal of Applied Mathematics and Physics (ZAMP) 21, 412–421 (1970). https://doi.org/10.1007/BF01627946

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  • DOI: https://doi.org/10.1007/BF01627946

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