Inextensible Networks Deformed as Translation Surfaces

摘要

Cloth can be modelled as a network formed from inextensible fibres, with no resistance to changes of the angle between fibres of the warp and the woof. Rivlin has shown that in plane deformations of inextensible networks, initially parallel fibres must be congruent after the deformation. In three-dimensional deformations with this congruence property, the deformed surface is called atranslation surface. In the present paper we determine all translation surfaces that can be supported in equilibrium by edge tractions alone, and the corresponding stress fields. We show that the equilibrium configurations include all cases in which typical fibres of the warp and the woof lie along arbitrary plane curves, in planes that need not be parallel.