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DRAPING WOVEN SHEETS

Part of: Hyperbolic equations and systems Equilibrium (steady-state) problems

Published online by Cambridge University Press:  07 January 2021

P. D. HOWELL Open the ORCID record for P. D. HOWELL [Opens in a new window] ,
H. OCKENDON Open the ORCID record for H. OCKENDON [Opens in a new window]  and
J. R. OCKENDON Open the ORCID record for J. R. OCKENDON [Opens in a new window]
P. D. HOWELL*
Affiliation:
OCIAM, Mathematical Institute, Andrew Wiles Building, OxfordOX2 6GG, UK; e-mail: ockendon@maths.ox.ac.uk, ock@maths.ox.ac.uk.
H. OCKENDON
Affiliation:
OCIAM, Mathematical Institute, Andrew Wiles Building, OxfordOX2 6GG, UK; e-mail: ockendon@maths.ox.ac.uk, ock@maths.ox.ac.uk.
J. R. OCKENDON
Affiliation:
OCIAM, Mathematical Institute, Andrew Wiles Building, OxfordOX2 6GG, UK; e-mail: ockendon@maths.ox.ac.uk, ock@maths.ox.ac.uk.
*
e-mail: howell@maths.ox.ac.uk
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Abstract

Motivated by the manufacture of carbon fibre components, this paper considers the smooth draping of loosely woven fabric over rigid obstacles, both smooth and nonsmooth. The draped fabric is modelled as the continuum limit of a Chebyshev net of two families of short rigid rods that are freely pivoted at their joints. This approach results in a system of nonlinear hyperbolic partial differential equations whose characteristics are the fibres in the fabric. The analysis of this system gives useful information about the drapability of obstacles of many shapes and also poses interesting theoretical questions concerning well-posedness, smoothness and computability of the solutions.

Keywords

drapingwoven fabricshyperbolic systemssingularity formation

MSC classification

Primary: 35L10: Second-order hyperbolic equations
Secondary: 74G99: None of the above, but in this section
Type
Research Article
Information
The ANZIAM Journal , Volume 62 , Issue 4 , October 2020 , pp. 355 - 385
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Copyright
© Australian Mathematical Society 2020

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