Navigating the space of Chebyshev nets

Andrew Sageman-Furnas (University Göttingen)

21-Apr-2020, 17:00-18:00 (4 years ago)

Abstract: Many materials are built from a grid of flexible but nearly inextensible rods that behaves as a shell-like structure. Everyday examples range from fabrics made of 1000s of interwoven yarns; to kitchen strainers made of 100s of plastically deforming wires; to architectural gridshells or medical stents made of 10s of elastically deforming rods. In this talk, I emphasize the geometric constraints common to these different physical systems. We build from a differential geometric model for woven fabric, initially introduced by Pafnuty Chebyshev in 1878, that directly encodes the inextensibility of the two families of rods.

We discuss the theory of Chebyshev nets through a series of applied, collaborative efforts in computational fabrication and inverse design. Theoretical obstructions expose the challenges in finding Chebyshev nets on surfaces with large amounts of curvature, suggesting a limited shape space. However, we show that a careful reformulation of the problem, combined with a discrete analog of Chebyshev nets, leads to computational tools that reveal a vibrant design space.

Mathematics

Audience: researchers in the topic


Online Seminar "Geometric Analysis"

Series comments: We discuss recent trends related to geometric analysis in a broad sense. The general idea is to solve geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals, discrete differential geometry, and numerical simulation.

Registration and links to videos available at blatt.sbg.ac.at/onlineseminar.php

Organizers: Simon Blatt*, Philipp Reiter*, Armin Schikorra*, Guofang Wang
*contact for this listing

Export talk to