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Title: Asymptotic equivalence of homogenisation procedures and fine-tuning of continuum theories
Authors: Pichugin, AV
Askes, H
Tyas, A
Issue Date: 2008
Publisher: Elsevier
Citation: Journal of Sound and Vibration. 313(3–5): 858–874
Abstract: Long-wave models obtained in the process of asymptotic homogenisation of structures with a characteristic length scale are known to be non-unique. The term non-uniqueness is used here in the sense that various homogenisation strategies may lead to distinct governing equations that usually, for a given order of the governing equation, approximate the original problem with the same asymptotic accuracy. A constructive procedure presented in this paper generates a class of asymptotically equivalent long-wave models from an original homogenised theory. The described non-uniqueness manifests itself in the occurrence of additional parameters characterising the model. A simple problem of long-wave propagation in a regular one-dimensional lattice structure is used to illustrate important criteria for selecting these parameters. The procedure is then applied to derive a class of continuum theories for a two-dimensional square array of particles. Applications to asymptotic structural theories are also discussed. In particular, we demonstrate how to improve the governing equation for the Rayleigh-Love rod and explain the reasons for the well-known numerical accuracy of the Mindlin plate theory.
ISSN: 0022-460X
Appears in Collections:Dept of Mathematics Research Papers
Mathematical Sciences

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