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Nonlinear dynamic buckling of pinned–fixed shallow arches under a sudden central concentrated load

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Abstract

The structural behavior of a shallow arch is highly nonlinear, and so when the amplitude of the oscillation of the arch produced by a suddenly-applied load is sufficiently large, the oscillation of the arch may reach a position on its unstable equilibrium paths that leads the arch to buckle dynamically. This paper uses an energy method to investigate the nonlinear elastic dynamic in-plane buckling of a pinned–fixed shallow circular arch under a central concentrated load that is applied suddenly and with an infinite duration. The principle of conservation of energy is used to establish the criterion for dynamic buckling of the arch, and the analytical solution for the dynamic buckling load is derived. Two methods are proposed to determine the dynamic buckling load. It is shown that under a suddenly-applied central load, a shallow pinned–fixed arch with a high modified slenderness (which is defined in the paper) has a lower dynamic buckling load and an upper dynamic buckling load, while an arch with a low modified slenderness has a unique dynamic buckling load.

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Acknowledgements

This work has been supported by the Australian Research Council through Discovery Projects (DP1096454 and DP1097096) awarded to first two authors and an Australian Laureate Fellowship (FL100100063) awarded to the second author.

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Authors and Affiliations

  1. Centre for Infrastructure Engineering and Safety, School of Civil and Environmental Engineering, The University of New South Wales, UNSW, Sydney, NSW, 2052, Australia

    Yong-Lin Pi & Mark Andrew Bradford

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  1. Yong-Lin Pi
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  2. Mark Andrew Bradford
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Correspondence to Yong-Lin Pi.

Appendix: Coefficients A 2, B 2 and C 2

Appendix: Coefficients A 2, B 2 and C 2

The coefficients A 2, B 2, and C 2 in Eq. (33) are given by

(47)
(48)

and

(49)

in which \(K'_{i}=\mbox{d}K_{i}/\mbox{d}\beta\) (i=2,3,4,5), K 6=2β+cos2βsin2β, K 7=3sinβ+2βcosβ+sin3β, K 8=5cosβ−2βsinβ+3cos3β, K 10=β−cosβsinβ, and K 11=β 2+βcosβsinβ−2sinβ 2.

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Pi, YL., Bradford, M.A. Nonlinear dynamic buckling of pinned–fixed shallow arches under a sudden central concentrated load. Nonlinear Dyn 73, 1289–1306 (2013). https://doi.org/10.1007/s11071-013-0863-2

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