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VOL. 21 | 2020 Explicit Parameterizations of Non-Bending Torus-Like Surfaces
Vladimir I. Pulov, Ivaïlo M. Mladenov

Editor(s) Ivaïlo M. Mladenov, Vladimir Pulov, Akira Yoshioka

Abstract

We explore an interesting three parametric family of essentially non-circular torus-like thin shells of revolution deforming under symmetrical loading without bending. It was found that these non-bending torus-like shells split naturally into two classes of shells lying either outside or inside of a given right circular cylinder. For each of these classes we obtain uniform parameterizations in terms of elliptic integrals. Explicit formulas for the aspect ratio of the non-bending toroids measuring their non-circularity are presented as well.

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Published: 1 January 2020
First available in Project Euclid: 14 October 2020

Digital Object Identifier: 10.7546/giq-21-2020-251-264

Rights: Copyright © 2020 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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