Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed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 of a built structure will be corresponding to different rigidity. In this paper, nonlinear displacement formulation is formulated and numerical simulations will be carried out for circular, normal elliptic, and oblique elliptic torus. Investigations show that both deformation and stress response of an elastic torus are sensitive to the radius ratio, and suggest that the analysis of a torus should be done by using the bending theory of a shell, and also reveal that the inner torus is stronger than the outer torus due to the property of their Gaussian curvature. The desired rigidity can be archived by adjusting the ratio of the minor and main radius and oblique angle.


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



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