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On the asymptotic reduction of a bifurcation equation for edge-buckling instabilities

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Abstract

Weakly clamped uniformly stretched thin elastic plates can experience edge buckling when subjected to a transverse pressure. This situation is revisited here for a circular plate, under the assumption of finite rotations and negligible bending stiffness in the pre-buckling range. The eigenproblem describing this instability is formulated in terms of two singularly perturbed fourth-order differential equations involving the non-dimensional bending stiffness \(\varepsilon >0\). By using an extension of the asymptotic reduction technique proposed by Coman and Haughton (Acta Mech 55:179–200, 2006), these equations are formally reduced to a simple second-order ordinary differential equation in the limit \(\varepsilon \rightarrow {0}^+\). It is further shown that the predictions of this reduced problem are in excellent agreement with the direct numerical simulations of the original bifurcation equations.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK

    Ciprian D. Coman

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  1. Ciprian D. Coman
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Coman, C.D. On the asymptotic reduction of a bifurcation equation for edge-buckling instabilities. Acta Mech 229, 1099–1109 (2018). https://doi.org/10.1007/s00707-017-2036-8

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  • DOI: https://doi.org/10.1007/s00707-017-2036-8

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