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Large deflection of curved elastic beams made of Ludwick type material

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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.

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Abbreviations

b :

width of the cross-section

h :

height of the cross-section

κ 0 :

initial curvature of the beam

κ 1 :

curvature increment

s 0 :

initial arc length

s *0 :

arc length after deformation

u :

horizontal displacement

w :

vertical displacement

φ 0 :

initial slope

φ :

slope after deformation

φ 1 :

slope increment

V :

resultant force component along the y-axis

F :

concentrated force

q :

distributed load

E :

elastic modulus of the material

n :

material constant

L :

reference length

L 0 :

initial length of the beam

σ :

stress

ɛ :

strain

N :

resultant axial force

M :

resultant bending moment

H :

resultant force component along the x-axis

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Authors and Affiliations

  1. School of Aeronautic Science and Engineering, Beihang University, Beijing, 100191, China

    Hua Liu, Yi Han & Jialing Yang

Authors
  1. Hua Liu
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  2. Yi Han
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  3. Jialing Yang
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Corresponding author

Correspondence to Hua Liu.

Additional information

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

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Liu, H., Han, Y. & Yang, J. Large deflection of curved elastic beams made of Ludwick type material. Appl. Math. Mech.-Engl. Ed. 38, 909–920 (2017). https://doi.org/10.1007/s10483-017-2213-6

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  • DOI: https://doi.org/10.1007/s10483-017-2213-6

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

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