A proposal for a membrane model for the small deformations of a spider orb-web

In this paper we propose a continuum membrane model for the infinitesimal deformation of a spider orb-web. The model is derived in the context of axially-symmetric webs formed by radial threads connected with circumferential threads belonging to concentric circles. The continuous model inherits a specific fibrous structure from the original discrete web. In particular, a singularity arises at the centre of the membrane as a consequence of the intensification of the density of radial threads towards the centre of the web. Under suitable assumption on the tensile pre-stress acting in the referential configuration, the out-of-plane free transverse vibrations of a circular orb-web supported at the boundary are studied in detail. The accuracy of the model in describing a discrete spider web is numerically investigated.