Crushing Response of Simple Structures

  • Jorge A. C. Ambrosio
Conference paper
Part of the International Centre for Mechanical Sciences book series (CISM, volume 423)


The explicit expression for the mean crushing force, P m , corresponding to a complete folding of a standing alone SE is derived by substituting expressions for contributing energy dissipation mechanisms, Eq. (8.5), into the governing minimum condition, Eq. (7.13). The complete derivation of the following result is given in [9.1]. The final form of the governing expression is
where A i = A i α*), i =1,2...5. The five terms in parenthesis on the right hand side of Eq. (9.1) describe, respectively, fractional contributions to the total energy dissipation resulting from five elementary deformation mechanisms, identified in Figure 8.5. The five factors, A i i =1,2...5 result from the surface-time integration. Factors. A 2 and A 4 , are easily calculated as a closed-form functions of geometrical parameters. The remaining factors A 1 , A 3 and A 5 , are functions of elliptic integrals and must be calculated numerically. The meaning of other variables appearing in Eq. (8.2) is explained in section 8.2.1.


Elliptic Integral Fractional Contribution Hinge Line Rolling Radius Complete Derivation 
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  1. [9.1]
    W. Abramowicz, Crush Resistance of ‘T’ ’Y’ and X’ Sections, Joint MIT-Industry Program on Tanker Safety, Massachusetts Institute of Technology, Report 24, 1994.Google Scholar
  2. [9.2]
    W. Abramowicz and T. Wierzbicki, Axial crushing of multi-corner sheet metal columns, J. App. Mech., 56 (1), 113–120, 1989.CrossRefGoogle Scholar
  3. [9.3]
    Wierzbicki, T., Abramowicz, W. The Manual of Crashworthiness Engineering,Vol. I - IV, Center for Transportation Studies, Massachusetts Institute of Technology, 1987–1989.Google Scholar
  4. [9.4]
    Abramowicz, W., Jones, N., Dynamic progressive buckling of circular and square tubes, Int. J. Impact Engng., 4 (4), 243–270, 1986.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 2001

Authors and Affiliations

  • Jorge A. C. Ambrosio
    • 1
  1. 1.Instituto Superior TécnicoPortugal

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