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Geometrically nonlinear elastic toroidal shells with open profiles—stability analysis and a design concept

Geometrisch nichtlineare, elastische toroidale Schalen mit offenem Profil—Stabilitätsanalyse und ein Konzept der Gestaltung

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Summary

The paper deals with the stability and some aspects of optimal design with respect to stability of geometrically nonlinear, elastic toroidal shells with open profiles. Shells rotationally symmetric in the narrower sense (toroidal segments) as well as in the broader sense (toroidal shell-arches), subjected to external pressure or to a combined loading (pressure and overall bending), are considered. The influence of the pressure distribution on its critical value as well as the post-buckling behaviour are discussed for the toroidal segments with various boundary conditions. The instability modes of the shell-arches for linear trajectories of the combined loading are also analysed. A double step parametrical optimization consisting of a midsurface design (1st step) and a design with respect to the thickness of the wall (2nd step) is performed for a toroidal segment. Constant distance between the supports and constant area of the meridional cross-section are applied as the constraints, respectively

Übersicht

Die Stabilität und einige Aspekte der Optimierung in Hinblick auf die kritische Belastung, von geometrisch nichtlinearen, elastischen Toroidalschalen mit offenem Profil werden untersucht. Sowohl die rotationssymmetrischen Schalen im engeren Sinn (Toroidalsegmente) als auch im weiteren Sinn (toroidale Schalenbogen), unter Außendruck oder Außendruck und globaler biegung werden analysiert. Der Zusammenhang zwischen der Außendruck verteilung und dem kritischen Wert des Druckes, aber auch das nachkritische Verhalten werden für die Toroidalsegmente untersucht. Für lineare Trajektorien der komplexen Belastung lassen sich die Formen der Instabilität der toroidalen Schalenbogen ermitteln. Das Konzept der einfachen., zweistufigen, parametrischen Optimierung, derer Bestandteile die Mittelflächengestaltung (erste Stufe) und die optimale Wanddickeauslegung (zweite Stufe) bilden, wird entwickelt, Konstanter Abstand zwischen den Stützen und konstante Fläche des meridionalen Querschnitts bilden die entsprechenden geometrischen Beschränkungen.

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Authors and Affiliations

  1. Inst. of Mechanics and Machine Design, Cracow University of Technology, ul. Warszawska 24, 31-155, Kraków, Poland

    B. Skoczeń

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  1. B. Skoczeń
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Skoczeń, B. Geometrically nonlinear elastic toroidal shells with open profiles—stability analysis and a design concept. Arch. Appl. Mech. 62, 1–14 (1992). https://doi.org/10.1007/BF00786677

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  • DOI: https://doi.org/10.1007/BF00786677

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