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Numerical Analysis of the Branched Forms of Bending for a Rod

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Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract

Nonlinear boundary–value problems of plane bending of elastic arches subjected to uniformly distributed loading are solved numerically by the shooting method. The problems are formulated for a system of sixth–order ordinary differential equations that are more general than the Euler equations. Four variants of rod loading by transverse and longitudinal forces are considered. Branching of the solutions of boundary–value problems and the existence of intersected and isolated branches are shown. In the case of a translational longitudinal force, the classical Euler elasticas are obtained. The existence of a unique (rectilinear) form of equilibrium upon compression of a rod by a following longitudinal force is shown.

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  1. Institute of Computer Modeling, Siberian Division, Russian Academy of Sciences, Krasnoyarsks, 660036

    L. I. Shkutin

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  1. L. I. Shkutin
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Shkutin, L.I. Numerical Analysis of the Branched Forms of Bending for a Rod. Journal of Applied Mechanics and Technical Physics 42, 310–315 (2001). https://doi.org/10.1023/A:1018840322477

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  • DOI: https://doi.org/10.1023/A:1018840322477

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