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Applied Mathematics and Mechanics

, Volume 38, Issue 7, pp 909–920 | Cite as

Large deflection of curved elastic beams made of Ludwick type material

  • Hua LiuEmail author
  • Yi Han
  • Jialing Yang
Article

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

large deflection curved beam Ludwick type material nonlinearity 

Abbreviations

b

width of the cross-section

h

height of the cross-section

κ0

initial curvature of the beam

κ1

curvature increment

s0

initial arc length

s0*

arc length after deformation

u

horizontal displacement

w

vertical displacement

φ0

initial slope

φ

slope after deformation

φ1

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

L0

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

Chinese Library Classification

O343.5 

2010 Mathematics Subject Classification

74B20 

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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of Aeronautic Science and EngineeringBeihang UniversityBeijingChina

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