2023/01/24 by Sharifmoghaddam, Kiumars, Maleczek, Rupert, Nawratil, Georg · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2301.09969
We introduce an alternative way of constructing continuous flexible tubes and tubular structures based on a discrete, semi-discrete and smooth construction of surfaces known as T-hedra in the discrete case and profile-affine surfaces in the smooth setting, respectively. The geometric understanding of this method enables us to generalize discrete tubes with a rigid-foldability and to extend the construction to smooth and semi-discrete tubes with an isometric deformation. This achievement implies a unified treatment of continuous flexible structures, like surfaces and metamaterials, composed of tubes and it is the base for a deeper study of zipper tubes, and their generalization. Moreover, we discuss a potential application of the presented structures for the design of foldable bridges.