Applied Mathematics and Mechanics

, Volume 36, Issue 8, pp 1005–1016 | Cite as

Theoretical analysis on quasi-static lateral compression of elliptical tube between two rigid plates

  • Ruirui Liu
  • Haibo Wang
  • Jialing Yang
  • Hua LiuEmail author
  • Yuxin Sun


Based on the rigid plastic theory, the load-deflection functions with and without considering the effect of strain hardening are respectively derived for an elliptical tube under quasi-static compression by two parallel rigid plates. The non-dimensional load-deflection responses predicted by the present theory and the finite element simulations are compared, and the favorable agreement is found. The results show that strain hardening may have a noticeable influence on the load-deflection curves of an elliptical tube under quasi-static compression. Compared with the circular counterpart, the elliptical tube exhibits different energy absorption behavior due to the difference between the major axis and the minor axis. When loaded along the major axis of a slightly oval tube, a relative even and long plateau region of the load-deflection curve is achieved, which is especially desirable for the design of energy absorbers.


elliptical tube strain hardening ovality quasi-static lateral compression 



initial horizontal semi-axis


initial collapse load


initial vertical semi-axis


mass density of material


initial radius of circular tube


elastic modulus of material

\(h = \frac{b}{a}\)

ovality of elliptical tube


Poisson’s ratio of material


thickness of tube wall


yield stress of material


breadth of tube wall


linear hardening modulus of material

Chinese Library Classification


2010 Mathematics Subject Classification

74C05 74S05 


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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Ruirui Liu
    • 1
    • 2
  • Haibo Wang
    • 1
  • Jialing Yang
    • 1
  • Hua Liu
    • 1
    Email author
  • Yuxin Sun
    • 1
  1. 1.School of Aeronautic Science and EngineeringBeihang UniversityBeijingChina
  2. 2.Jiuquan Satellite Launch CenterJiuquan, Gansu ProvinceChina

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