Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

On Symmetrical Deformation of Toroidal Shell with Circular Cross-Section

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. Preprints 2020, 2020030156 (doi: 10.20944/preprints202003.0156.v2). Sun, B. On Symmetrical Deformation of Toroidal Shell with Circular Cross-Section. Preprints 2020, 2020030156 (doi: 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.

Subject Areas

toroidal shell; deformation; Gauss curvature; Heun's function; hypergeometric function; Maple

Comments (1)

Comment 1
Received: 26 May 2020
Commenter: Bohua Sun
Commenter's Conflict of Interests: Author
Comment: Added more info and numerical calculations
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