Motivated by the manufacture of carbon-fibre components, we consider the smooth draping of loosely woven fabric over rigid obstacles, both smooth and non-smooth. 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. This is joint work with Hilary and John Ockendon.
- Industrial and Applied Mathematics Seminar