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Equilibrium of Tchebychev Nets

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The Breadth and Depth of Continuum Mechanics

Abstract

Cloth is deformed mainly by changing the angle between the threads of the warp and woof. The additional deformation due to fiber-stretching is ordinarily negligible in comparison to the finite distortion that can be produced without stretching. In a lecture published only in summary, Tchebychev [1] suggested a continuum model for cloth in which the fibers are treated as continuously distributed and inextensible. Another summary of Tchebychev’S lecture appears in his collected works [2], but the manuscript was not published until 1951 [3]. Independently, Voss [4, 5] investigated the geometrical properties of the networks that are formed on curved surfaces by initially plane, orthogonal networks of inextensible fibers. Probably because of the influence of Darboux [6], such networks came to be known as Tchebychev nets (see also Bianchi [7, 8] for example).

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References

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Authors and Affiliations

  1. Division of Applied Mathematics, Brown University, Providence, Rhode Island, USA

    A. C. Pipkin

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  1. A. C. Pipkin
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For J. L. Ericksen, Geometer

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© 1986 Springer-Verlag Berlin Heidelberg

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Pipkin, A.C. (1986). Equilibrium of Tchebychev Nets. In: The Breadth and Depth of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61634-1_12

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  • DOI: https://doi.org/10.1007/978-3-642-61634-1_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16219-3

  • Online ISBN: 978-3-642-61634-1

  • eBook Packages: Springer Book Archive

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