Keywords: dynamic buckling, thin-walled structures, pulse loading, open cross-section, finite element method, analytical-numerical method.

The failure of thin-walled structures is usually determined by their stability. In real life the loads have a dynamic character. Dynamic pulse buckling occurs when the loading process is of intermediate amplitude and the pulse duration is close to the period of the fundamental natural flexural vibration (in the range of milliseconds). In such case the effects of dumping are neglected [1]. The dynamic buckling problem has frequently appeared in the literature.

To find the critical amplitude of pulse loads leading to dynamic buckling, first the analysis of the dynamic response should be performed and then the dynamic buckling criterion should be used. The most popular criteria are: the Volmir criterion [2] for plates; the Budiansky-Hutchinson criterion [3] for shell structures and also used for the plate structures [4]; four criteria formulated for plates by Ari-Gur and Simonetta [5] and the failure criterion proposed by Petry and Fahlbush [6].

The problem of the dynamic response of thin-walled beam-columns with open cross-sections subjected to different pulse loading is investigated. Two methods were employed: the finite element method and the proposed analytical-numerical method. Both methods of calculation gave comparable results. The applied analytical-numerical method is based on asymptotic Koiter theory [7] for a conservative system with a second order approximation. A plate model was adopted for the structures. The differential equations of motion have been obtained using Hamilton's Principle.

The analytical-numerical method as well as the finite element method allow the analysis of the dynamic response of thin-walled structures. The results of these responses make it possible to estimate the dynamic buckling based on one of the well-known criteria. Some of the criteria are more restrictive like the Volmir or the Budiansky-Hutchinson criterion, and some allow the use of higher loads (for example the Ari-Gur criteria).

1

A.N. Kounadis, C. Gantes, G. Simitses, "Nonlinear dynamic buckling of multi-dof structural dissipative system under impact loading", Int. J. Impact Engineering, 19 (1), 63-80, 1997. doi:10.1016/S0734-743X(96)00006-1

2

S.A. Volmir, "Nonlinear dynamics of plates and shells", Science, Moscow, 1972

3

J.W. Hutchinson, B. Budiansky, "Dynamic buckling estimates", AIAA Journal, 4(3), 525-530, 1966. doi:10.2514/3.3468

4

T. Kubiak, "Dynamic buckling of thin-walled composite plates with varying widthwise material properties", Int. J. Solid and Structures, 42(20), 2005. doi:10.1016/j.ijsolstr.2005.02.043

5

J. Ari-Gur, S.R. Simonetta, "Dynamic pulse buckling of rectangular composite plates", Composites Part B, 28B, 301-308, 1997. doi:10.1016/S1359-8368(96)00028-5

6

D. Petry, G. Fahlbusch, "Dynamic buckling of thin isotropic plates subjected to in-plane impact", Thin-Walled Structures, 38, 267-283, 2000. doi:10.1016/S0263-8231(00)00037-9

7

W.T. Koiter, "Elastic stability and post-buckling behaviour", Proceedings of the Symposium on Nonlinear Problems, Univ. of Wisconsin Press, Wisconsin, 257-275, 1963.

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