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Buckling of a column under a constant speed compression: a dynamic correction to the Euler formula

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Abstract

Dynamic buckling of an elastic column under compression at constant speed is investigated assuming the first buckling mode. Two cases are considered: (1) an imperfect naturally curved column (Hoff’s statement) and (2) a perfect column with an initial lateral deflection. The range of parameters where the maximum load supported by a column exceeds the Euler static force is determined. In this range, the maximum load is represented as a function of the compression rate, slenderness ratio, and imperfection/initial deflection. We answer the following question: “How slowly should the column be compressed in order to measure static load-bearing capacity?” This question is important for the proper setup of laboratory experiments and computer simulations of buckling. Additionally, we show that the behavior of a perfect column with an initial deflection differs significantly from the behavior of an imperfect column. In particular, for a perfect column the dependence of the maximum force on the compression rate is non-monotonic. The analytical results are supported by numerical simulations and available experimental data.

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Authors and Affiliations

  1. Institute for Problems in Mechanical Engineering RAS, Bolshoy pr. V.O. 61, Saint Petersburg, Russia

    Vitaly A. Kuzkin

  2. Peter the Great Saint Petersburg Polytechnical University, Polytechnicheskaya st. 29, Saint Petersburg, Russia

    Vitaly A. Kuzkin

  3. Institute of Mechanics and Computational Mechanics, Leibniz University Hanover, Appelstrasse 9a, 30167, Hannover, Germany

    Mona M. Dannert

Authors
  1. Vitaly A. Kuzkin
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  2. Mona M. Dannert
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Correspondence to Vitaly A. Kuzkin.

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Kuzkin, V.A., Dannert, M.M. Buckling of a column under a constant speed compression: a dynamic correction to the Euler formula. Acta Mech 227, 1645–1652 (2016). https://doi.org/10.1007/s00707-016-1586-5

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  • DOI: https://doi.org/10.1007/s00707-016-1586-5

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