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Large deformation analysis of a plane curved beam using Jacobi elliptic functions

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Abstract

In this paper, the large deformation equilibrium equation of the plane arc-curved beam is derived based on the radius of curvature and tangent slope angle of the curved beam. The Jacobi elliptic function solutions of tangent slope angle and geometric configurations of a general curved beam and a curved beam between plates are given, in which the modulus p (or k) of elliptic functions is determined by the vertical external force η and boundary conditions. The nonlinear large deformation characteristics and geometric configurations of the curved beam with different initial installation angles (initial tangent slope angles of beam end) are analyzed in detail. The results show that the force–deformation curve of the curved beam has obvious platform stage, which means that the curved beam can store more energy and produce less reaction force compared with the ordinary elastic structure, and can be used as an energy-absorbing structure for the system subjected to repeated shocks.

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Authors and Affiliations

  1. Department of Packaging Engineering, Henan University of Science and Technology, 263 Kaiyuan Road, Luoyang, 471000, China

    Yin-lei Huo, Xue-sheng Pei & Meng-yao Li

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  1. Yin-lei Huo
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  2. Xue-sheng Pei
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  3. Meng-yao Li
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Huo, Yl., Pei, Xs. & Li, My. Large deformation analysis of a plane curved beam using Jacobi elliptic functions. Acta Mech 233, 3497–3510 (2022). https://doi.org/10.1007/s00707-022-03279-3

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  • DOI: https://doi.org/10.1007/s00707-022-03279-3

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