Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Geometry-Induced Rigidity in Elastic Torus from Circular to Oblique Elliptic Cross-Section

Version 1 : Received: 10 March 2021 / Approved: 12 March 2021 / Online: 12 March 2021 (20:00:46 CET)
Version 2 : Received: 16 May 2021 / Approved: 17 May 2021 / Online: 17 May 2021 (10:15:17 CEST)
Version 3 : Received: 24 November 2021 / Approved: 25 November 2021 / Online: 25 November 2021 (11:21:55 CET)

A peer-reviewed article of this Preprint also exists.

Journal reference: International Journal of Non-linear Mechanics ELSEVIER, 135, 103754
DOI: 10.1016/j.ijnonlinmec.2021.103754


For a given material, different shapes correspond to different rigidities. In this paper, the radii of the oblique elliptic torus are formulated, a nonlinear displacement formulation is presented and numerical simulations are carried out for circular, normal elliptic, and oblique tori, respectively. Our investigation shows that both the deformation and the stress response of an elastic torus are sensitive to the radius ratio, and indicate that the analysis of a torus should be done by using the bending theory of shells rather than membrance theory. A numerical study demonstrates that the inner region of the torus is stiffer than the outer region due to the Gauss curvature. The study also shows that an elastic torus deforms in a very specific manner, as the strain and stress concentration in two very narrow regions around the top and bottom crowns. The desired rigidity can be achieved by adjusting the ratio of minor and major radii and the oblique angle.


elliptic torus; oblique; nonlinear deformation; vibration; Gauss curvature; Maple



Comments (1)

Comment 1
Received: 17 May 2021
Commenter: Bohua Sun
Commenter's Conflict of Interests: Author
Comment: the principal radii of the oblique elliptic torus have been corrected
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