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An Improved Proof of Instability of Some Euler Elasticas

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Abstract

The analytical proof of instability of Euler elasticas proposed by ** and Bao (Mech. Res. Commun. 59:37–41, 2014) is improved. Without Sturm’s theory on the ordinary differential equation, conjugate points of Jacobi equation on the potential energy functional are detected by a comparison theorem. A corollary is proposed to prove instability of Euler elasticas with one clamped end and the other clamped in rotation.

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Acknowledgements

The project was supported by the Fund of Chinese Aviation Science through grant number 201109M5002, the Specialized Research Fund for the Doctoral Program of Higher Education of China (20120009110019).

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Authors and Affiliations

  1. Department of Mechanics, School of Civil Engineering, Bei**g Jiaotong University, Bei**g, 100044, P.R. China

    M. **

  2. School of Computer and Information Technology, Bei**g Jiaotong University, Bei**g, 100044, P.R. China

    Z. B. Bao

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  1. M. **
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  2. Z. B. Bao
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Correspondence to M. **.

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**, M., Bao, Z.B. An Improved Proof of Instability of Some Euler Elasticas. J Elast 121, 303–308 (2015). https://doi.org/10.1007/s10659-015-9529-2

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  • DOI: https://doi.org/10.1007/s10659-015-9529-2

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