title: Integrable structure in discrete shell membrane theory.
abstract: We present natural discrete analogues of two integrable classes of shell membranes. By construction, these discrete shell membranes are in equilibrium with respect to suitably chosen internal stresses and external forces. The integrability of the underlying equilibrium equations is proved by relating the geometry of the discrete shell membranes to discrete O surface theory. We establish connections with generalized barycentric coordinates and nine-point centres and identify a discrete version of the classical Gauss equation of surface theory.
authors.affiliation: School of Mathematics and Statistics and Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems , The University of New South Wales , Sydney, New South Wales 2052, Australia.
authors.forename: W K
authors.initials: WK
authors.lastname: Schief
keywords: discretization; integrability; membrane