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Title: | An asymptotic membrane-like theory for long-wave motion in a pre-stressed elastic plate |
Authors: | Pichugin, A V Rogerson, G A |
Keywords: | Pre-stress;Elastic plates;Waves;Asymptotics;Membrane |
Issue Date: | 2002 |
Publisher: | Royal Society Publishing |
Citation: | Proceedings of the Royal Society of London, Series A, 458: 1447–1468, Nov 2002 |
Abstract: | An asymptotically consistent two-dimensional theory is developed to help elucidate dynamic response in finitely deformed layers. The layers are composed of incompressible elastic material, with the theory appropriate for long-wave motion associated with the fundamental mode and derived in respect of the most general appropriate strain energy function. Leading-order and refined higher-order equations for the mid-surface deflection are derived. In the case of zero normal initial static stress and in-plane tension, the leading-order equation reduces to the classical membrane equation, with its refined counterpart also being obtained. The theory is applied to a one-dimensional edge loading problem for a semi-infinite plate. In doing so, the leading- and higher-order governing equations are used as inner and outer asymptotic expansions, the latter valid within the vicinity of the associated quasi-front. A solution is derived by using the method of matched asymptotic expansions. |
URI: | http://bura.brunel.ac.uk/handle/2438/1575 |
DOI: | https://doi.org/10.1098/rspa.2001.0932 |
Appears in Collections: | Computer Science Dept of Mathematics Research Papers Mathematical Sciences |
Files in This Item:
File | Description | Size | Format | |
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2002prsoc.pdf | 265.05 kB | Adobe PDF | View/Open |
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