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 ε> 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 ε→ 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.

Original languageEnglish
Pages (from-to)1099-1109
Number of pages11
JournalActa Mechanica
Volume229
Issue number3
Early online date7 Oct 2017
DOIs
Publication statusPublished - Mar 2018
Externally publishedYes

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