Version 1
: Received: 8 March 2020 / Approved: 10 March 2020 / Online: 10 March 2020 (03:19:02 CET)
Version 2
: Received: 25 May 2020 / Approved: 26 May 2020 / Online: 26 May 2020 (07:45:00 CEST)
How to cite:
Sun, B. On Symmetrical Deformation of Toroidal Shell with Circular Cross-Section. Preprints2020, 2020030156. https://doi.org/10.20944/preprints202003.0156.v2
Sun, B. On Symmetrical Deformation of Toroidal Shell with Circular Cross-Section. Preprints 2020, 2020030156. https://doi.org/10.20944/preprints202003.0156.v2
Sun, B. On Symmetrical Deformation of Toroidal Shell with Circular Cross-Section. Preprints2020, 2020030156. https://doi.org/10.20944/preprints202003.0156.v2
APA Style
Sun, B. (2020). On Symmetrical Deformation of Toroidal Shell with Circular Cross-Section. Preprints. https://doi.org/10.20944/preprints202003.0156.v2
Chicago/Turabian Style
Sun, B. 2020 "On Symmetrical Deformation of Toroidal Shell with Circular Cross-Section" Preprints. https://doi.org/10.20944/preprints202003.0156.v2
Abstract
By introducing a variable transformation $\xi=\frac{1}{2}(\sin \theta+1)$, the symmetrical deformation equation of elastic toroidal shells is successfully transferred into a well-known equation, namely Heun's equation of ordinary differential equation, whose exact solution is obtained in terms of Heun's functions. The computation of the problem can be carried out by symbolic software that is able to with the Heun's function, such as Maple. The Gauss curvature of the elastic toroidal shells shows that the internal portion of the toroidal shells has better bending capacity than the outer portion, which might be useful for the design of metamaterials with toroidal shells cells. Through numerical comparison study, the mechanics of elastic toroidal shells is sensitive to the radius ratio. By slightly adjustment of the ratio might get a desired high performance shell structure.
Keywords
toroidal shell; deformation; Gauss curvature; Heun's function; hypergeometric function; Maple
Subject
Physical Sciences, Applied Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Commenter: Bohua Sun
Commenter's Conflict of Interests: Author