Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (7): 909-920.doi: https://doi.org/10.1007/s10483-017-2213-6

• 论文 •    下一篇

Large deflection of curved elastic beams made of Ludwick type material

Hua LIU, Yi HAN, Jialing YANG   

  1. School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China
  • 收稿日期:2016-06-29 修回日期:2016-11-07 出版日期:2017-07-01 发布日期:2017-07-01
  • 通讯作者: Hua LIU, E-mail:liuhuarui@buaa.edu.cn E-mail:liuhuarui@buaa.edu.cn
  • 基金资助:

    Project supported by the National Natural Science Foundation of China (Nos. 11472035 and 11472034)

Large deflection of curved elastic beams made of Ludwick type material

Hua LIU, Yi HAN, Jialing YANG   

  1. School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China
  • Received:2016-06-29 Revised:2016-11-07 Online:2017-07-01 Published:2017-07-01
  • Contact: Hua LIU E-mail:liuhuarui@buaa.edu.cn
  • Supported by:

    Project supported by the National Natural Science Foundation of China (Nos. 11472035 and 11472034)

摘要:

The large deflection of an axially extensible curved beam with a rectangular cross-section is investigated. The elastic beam is assumed to satisfy the Euler-Bernoulli postulation and be made of the Ludwick type material. Through reasonably simplified integration, the strain and curvature of the axis of the beam are presented in implicit formulations. The governing equations involving both geometric and material nonlinearities of the curved beam are derived and solved by the shooting method. When the initial curvature of the beam is zero, the curved beam is degenerated into a straight beam, and the predicted results obtained by the present model are consistent with those in the open literature. Numerical examples are further given for curved cantilever and simply supported beams, and the couplings between elongation and bending are found for the curved beams.

关键词: flexural-torsional buckling, geometric equation, rotations, order, large deflection, nonlinearity, curved beam, Ludwick type material

Abstract:

The large deflection of an axially extensible curved beam with a rectangular cross-section is investigated. The elastic beam is assumed to satisfy the Euler-Bernoulli postulation and be made of the Ludwick type material. Through reasonably simplified integration, the strain and curvature of the axis of the beam are presented in implicit formulations. The governing equations involving both geometric and material nonlinearities of the curved beam are derived and solved by the shooting method. When the initial curvature of the beam is zero, the curved beam is degenerated into a straight beam, and the predicted results obtained by the present model are consistent with those in the open literature. Numerical examples are further given for curved cantilever and simply supported beams, and the couplings between elongation and bending are found for the curved beams.

Key words: order, flexural-torsional buckling, geometric equation, rotations, curved beam, Ludwick type material, large deflection, nonlinearity

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