On the asymptotic reduction of a bifurcation equation for edge-buckling instabilities
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 de...
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| Format: | Article |
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Springer
2018
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| Online Access: | https://eprints.nottingham.ac.uk/48940/ |
| _version_ | 1848797884551528448 |
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| author | Coman, Ciprian D. |
| author_facet | Coman, Ciprian D. |
| author_sort | Coman, Ciprian D. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:10:58Z |
| format | Article |
| id | nottingham-48940 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:10:58Z |
| publishDate | 2018 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-489402020-05-04T19:52:06Z https://eprints.nottingham.ac.uk/48940/ On the asymptotic reduction of a bifurcation equation for edge-buckling instabilities Coman, Ciprian D. 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. Springer 2018-03 Article PeerReviewed 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 https://link.springer.com/article/10.1007%2Fs00707-017-2036-8 doi:10.1007/s00707-017-2036-8 doi:10.1007/s00707-017-2036-8 |
| spellingShingle | Coman, Ciprian D. On the asymptotic reduction of a bifurcation equation for edge-buckling instabilities |
| title | On the asymptotic reduction of a bifurcation equation for edge-buckling instabilities |
| title_full | On the asymptotic reduction of a bifurcation equation for edge-buckling instabilities |
| title_fullStr | On the asymptotic reduction of a bifurcation equation for edge-buckling instabilities |
| title_full_unstemmed | On the asymptotic reduction of a bifurcation equation for edge-buckling instabilities |
| title_short | On the asymptotic reduction of a bifurcation equation for edge-buckling instabilities |
| title_sort | on the asymptotic reduction of a bifurcation equation for edge-buckling instabilities |
| url | https://eprints.nottingham.ac.uk/48940/ https://eprints.nottingham.ac.uk/48940/ https://eprints.nottingham.ac.uk/48940/ |