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

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Abstract

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.

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Abbreviations

a :

initial horizontal semi-axis

P 0 :

initial collapse load

b :

initial vertical semi-axis

ρ :

mass density of material

R :

initial radius of circular tube

E :

elastic modulus of material

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

ovality of elliptical tube

µ :

Poisson’s ratio of material

t :

thickness of tube wall

σ 0 :

yield stress of material

l :

breadth of tube wall

E P :

linear hardening modulus of material

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Authors and Affiliations

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

    Ruirui Liu, Haibo Wang, Jialing Yang, Hua Liu & Yuxin Sun

  2. Jiuquan Satellite Launch Center, Jiuquan, Gansu Province, 732750, China

    Ruirui Liu

Authors
  1. Ruirui Liu
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  2. Haibo Wang
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  3. Jialing Yang
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  4. Hua Liu
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  5. Yuxin Sun
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Corresponding author

Correspondence to Hua Liu.

Additional information

Project supported by the National Natural Science Foundation of China (No. 11472035)

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Liu, R., Wang, H., Yang, J. et al. Theoretical analysis on quasi-static lateral compression of elliptical tube between two rigid plates. Appl. Math. Mech.-Engl. Ed. 36, 1005–1016 (2015). https://doi.org/10.1007/s10483-015-1962-7

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  • DOI: https://doi.org/10.1007/s10483-015-1962-7

Keywords

Chinese Library Classification

2010 Mathematics Subject Classification

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