On the asymptotic reduction of a bifurcation equation for edge-buckling instabilitiesTools Coman, Ciprian D. (2018) On the asymptotic reduction of a bifurcation equation for edge-buckling instabilities. Acta Mechanica, 229 (3). pp. 1099-1109. ISSN 1619-6937 Full text not available from this repository.AbstractWeakly 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.
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