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

Coman, Ciprian D.

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.

Citation

Coman, C. D. (2018). On the asymptotic reduction of a bifurcation equation for edge-buckling instabilities. Acta Mechanica, 229(3), 1099-1109. https://doi.org/10.1007/s00707-017-2036-8

• Journal Article Type: Article
• Acceptance Date: Sep 1, 2017
• Online Publication Date: Oct 7, 2017
• Publication Date: Mar 1, 2018
• Deposit Date: Jan 4, 2018
• Publicly Available Date: Oct 8, 2018
• Journal: Acta Mechanica
• Print ISSN: 0001-5970
• Electronic ISSN: 1619-6937
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 229
• Issue: 3
• Pages: 1099-1109
• DOI: https://doi.org/10.1007/s00707-017-2036-8
• Public URL: https://nottingham-repository.worktribe.com/output/962371
• Publisher URL: https://link.springer.com/article/10.1007%2Fs00707-017-2036-8
• Additional Information: This is a post-peer-review, pre-copyedit version of an article published in Acta Mechanica. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00707-017-2036-8.