Draping woven sheets

Authors

DOI:

https://doi.org/10.21914/anziamj.v62.15884

Keywords:

draping, woven fabrics, hyperbolic systems, singularity formation

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.

doi:10.1017/S144618112000019X

Author Biographies

P. D. Howell, OCIAM, University of Oxford

OCIAM, Mathematical Institute, Andrew Wiles Building, Oxford, OX2 6GG, UK.

H. Ockendon, OCIAM, University of Oxford

OCIAM, Mathematical Institute, Andrew Wiles Building, Oxford, OX2 6GG, UK

J. R. Ockendon, OCIAM, University of Oxford

OCIAM, Mathematical Institute, Andrew Wiles Building, Oxford, OX2 6GG, UK.

Published

2021-04-25

Issue

Section

Special Issue for Renown Researcher