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A simplified model of elastic column buckling under constant lateral force restraint

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Abstract

Buckling of a column under pre-load restraint has been found to differ from the conventional bifurcation problems and thus requires better understanding. To this end, a simple model consisting of two collinear rigid bars connected by a rotational spring, resting on a smooth surface, loaded by an axial force and restrained by a constant force at the common joint is investigated. The energy method is adopted to establish the equilibrium and stability conditions. The post-buckling response of the simple system indicates that the load-restrained buckling problem is a snap-through problem. The minimum possible buckling force and the buckling force based on the Maxwell construction are found to increase with the restraining force, and can be approximated by power-law functions. It is further shown that an energy barrier exists for the snap-through to occur and the buckling force depends on the perturbation energy. Sensitivity of this system to initial geometric imperfections is also investigated, and an energy barrier is also found to exist for the buckling of systems with imperfection amplitudes smaller than a certain critical value. The characteristic imperfection amplitude depends on the restraining force and, interestingly, transforms the snap-through problem into an eigenvalue problem identical to the conventional one, i.e., the one without imperfection and restraining force.

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Acknowledgements

This research was supported by NSF award CMMI-1727490. This support is acknowledged with thanks. The authors also acknowledge fruitful discussions with Alexander Breunig, Matt Esser, Prof. Peter Groche, Prof. Jinjin Ha and Prof. Brad Kinsey on the problem of wrinkling in deep-drawing of thin sheets.

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  1. Department of Integrated Systems Engineering, The Ohio State University, 1971 Neil Avenue, Columbus, OH, 43210, USA

    Kelin Chen & Yannis P. Korkolis

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  1. Kelin Chen
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  2. Yannis P. Korkolis
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Correspondence to Yannis P. Korkolis.

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Chen, K., Korkolis, Y.P. A simplified model of elastic column buckling under constant lateral force restraint. Arch Appl Mech 91, 2817–2832 (2021). https://doi.org/10.1007/s00419-021-01933-1

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