Discrete and non-local elastica

Challamel, Noël, Kocsis, Attila and Wang, C. M. (2015) Discrete and non-local elastica. International Journal of Non-Linear Mechanics, 77 128-140. doi:10.1016/j.ijnonlinmec.2015.06.012

Author Challamel, Noël
Kocsis, Attila
Wang, C. M.
Title Discrete and non-local elastica
Journal name International Journal of Non-Linear Mechanics   Check publisher's open access policy
ISSN 0020-7462
Publication date 2015-12-01
Year available 2015
Sub-type Article (original research)
DOI 10.1016/j.ijnonlinmec.2015.06.012
Open Access Status Not yet assessed
Volume 77
Start page 128
End page 140
Total pages 13
Place of publication Kidlington, Oxford, United Kingdom
Publisher Pergamon Press
Language eng
Formatted abstract
In this paper, the buckling and post-buckling behavior of an elastic lattice system referred to as the discrete elastica problem is investigated using an equivalent non-local continuum approach. The geometrically exact post-buckling analysis of the elastic chain, also called Hencky system, is first numerically solved using the shooting method. This discrete physical model is also mathematically equivalent to a finite difference formulation of the continuum elastica. Starting from the exact difference equations of the discrete problem, a continualization method is applied for approximating the difference operators by differential ones, in order to better characterize the discrete system by an enriched continuous one. It is shown that the new continuum associated with the discrete system exactly fits the discrete elastica post-buckling problem, where the non-locality is of Eringens type (also called stress gradient non-local model). An asymptotic expansion is performed for both the discrete and the non-local continuum models, in order to approximate the post-buckling branches of the discrete system. Some numerical investigations show the efficiency of the non-local approach, especially for capturing the scale effects inherent to the cell size of the lattice model.
Keyword Asymptotic expansion
Discrete model
Lattice model
Q-Index Code C1
Q-Index Status Provisional Code
Grant ID PD 100786
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Civil Engineering Publications
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Citation counts: TR Web of Science Citation Count  Cited 16 times in Thomson Reuters Web of Science Article | Citations
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