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Geometrically nonlinear behavior of initially curved plane slender bars and frames

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Summary

Field equations for the geometrically nonlinear behavior of initially curved plane slender bars and frames comprising such bars are presented. Formulation originates from Continuum Solid Mechanics, allowing for exact expressions of axial deformation and curvature to be accounted for and unrestricted finite displacements to be considered within accepted assumptions regarding slenderness. Equilibrium equations are derived in terms of the curvature and displacements, in the form of second order nonlinear polynomial differential equations, governing the nonlinear behavior of the single bar. These equations combined with joint force and compatibility equations yield a system representing the nonlinear behavior of a complete plane frame.

Übersicht

Es werden Feldgleichungen für das geometrisch nichtlineare Verhalten von vorgekrümmten ebenen schlanken Balken sowie von Rahmen aus derartigen Balken abgeleitet. Mit Hilfe der in der Kontinuumsmechanik fester Körper gebräuchlichen Formulierungen lassen sich exakte Ausdrücke für die achsiale Verformung und Krümmung sowie für unbeschränkte Verschiebungen finden. Dabei müssen gewisse Annahmen in bezug auf die Schlankheit vorausgesetzt werden. Die Gleichgewichtsbedingungen werden durch Krümmung und Verschiebung ausgedrückt, durch eine Polynom-Differentialgleichung zweiter Ordnung wird das nichtlineare Verhalten des einzelnen Balkens beschrieben. Diese Gleichungen bestimmen zusammen mit den Kraft- und Verträglichkeits-Bedingungen das nichtlineare Verhalten des gesamten ebenen Rahmens.

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  1. Faculty of Civil Engineering, Technion, 32 000, Technion City, Haifa, Israel

    A. Pisanty (Senior Lecturer)

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  1. A. Pisanty
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Pisanty, A. Geometrically nonlinear behavior of initially curved plane slender bars and frames. Ing. arch 46, 235–244 (1977). https://doi.org/10.1007/BF00536959

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  • DOI: https://doi.org/10.1007/BF00536959

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