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Pseudo spectral methods applied to problems in elasticity

Talbot, Chris J. and Crampton, Andrew (2006) Pseudo spectral methods applied to problems in elasticity. Journal of Scientific Computing, 27 (1-3). pp. 443-454. ISSN 1573-7691

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    Abstract

    Pseudo spectral methods offer an attractive alternative to finite element procedures for the solution of problems in elasticity. Especially for simple domains, questions involving both two and three dimensional elasticity (Navier’s Equations or their non-linear generalisations) would seem to be reasonable candidates for a pseudo spectral approach. This paper examines some simple vibrational eigenvalue type problems, demonstrating how Navier’s equations can be recast into pseudo- spectral format, including first derivative boundary conditions representing zero traction. Fourier–Chebyshev methods are shown to give solutions with typical spectral accuracy, with the addition of pole conditions being necessary for the case of a two dimensional disc. There is also consideration given to time-stepping solutions of elastodynamic problems, especially those involving non-linear friction effects, the authors particular interest being the study of disc brake noise. It is shown that, at least for relatively simple cases, it is possible to model systems in such a way that animated graphical output can be provided as the system of partial differential equations is numerically integrated. This provides a useful tool for engineers to rapidly examine the effect of parameter changes on a system model.

    Item Type: Article
    Additional Information: UoA 23 (Computer Science and Informatics) © 2005 Springer Science+Business Media,
    Subjects: Q Science > Q Science (General)
    Q Science > QA Mathematics > QA75 Electronic computers. Computer science
    Q Science > QA Mathematics
    Schools: School of Computing and Engineering
    School of Computing and Engineering > Automotive Engineering Research Group
    School of Computing and Engineering > Diagnostic Engineering Research Centre
    School of Computing and Engineering > Diagnostic Engineering Research Centre > Measurement System and Signal Processing Research Group
    School of Computing and Engineering > Informatics Research Group
    School of Computing and Engineering > Informatics Research Group > Knowledge Engineering and Intelligent Interfaces
    School of Computing and Engineering > Informatics Research Group > Software Engineering Research Group
    School of Computing and Engineering > Informatics Research Group > XML, Database and Information Retrieval Research Group
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    References:

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    Depositing User: Sara Taylor
    Date Deposited: 21 Jun 2007
    Last Modified: 10 Dec 2010 13:24
    URI: http://eprints.hud.ac.uk/id/eprint/237

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