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<p>A general procedure is developed for solving geometrically nonlinear 3D problems of deformation of the beams based on the use of a helix-form basic solution. The main parameters and specific features of the “small” helix elements are analyzed and a technique of their iterative alignment into large 3D structures is thoroughly investigated. It is shown that the basic solution is self-consistent and can be applied solely for the analysis of simple geometries, e.g., cantilever beams. We analyze the cases known from the available literature, namely, (a) Bathe’s problem for an initially plane curvilinear beam loaded in the vertical direction; (b) Ibrahimbegovich’s problem for an initially straight beam loaded by a vertical bending moment and a vertical axial force; (c) Kirchhoff’s problem of creation of a helix from initially straight flexible beam by applying a vertical force and a moment to its end.</p>

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3D Analysis of Geometrically Nonlinear Deformation of the Beams by the Method of Basic Helical Elements

  • 期刊论文

  • 发表日期：

    2025年7月26日

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  • I. V. Orynyak,
  • K. A. Kulyk,
  • R. V. Mazuryk

摘要

A general procedure is developed for solving geometrically nonlinear 3D problems of deformation of the beams based on the use of a helix-form basic solution. The main parameters and specific features of the “small” helix elements are analyzed and a technique of their iterative alignment into large 3D structures is thoroughly investigated. It is shown that the basic solution is self-consistent and can be applied solely for the analysis of simple geometries, e.g., cantilever beams. We analyze the cases known from the available literature, namely, (a) Bathe’s problem for an initially plane curvilinear beam loaded in the vertical direction; (b) Ibrahimbegovich’s problem for an initially straight beam loaded by a vertical bending moment and a vertical axial force; (c) Kirchhoff’s problem of creation of a helix from initially straight flexible beam by applying a vertical force and a moment to its end.