Version 1
: Received: 10 March 2021 / Approved: 11 March 2021 / Online: 11 March 2021 (16:16:55 CET)
Version 2
: Received: 19 January 2022 / Approved: 25 January 2022 / Online: 25 January 2022 (10:04:29 CET)
How to cite:
Sun, B. Displacement Formulations for Deformation and Vibration of Elastic Circular Torus. Preprints2021, 2021030326. https://doi.org/10.20944/preprints202103.0326.v2
Sun, B. Displacement Formulations for Deformation and Vibration of Elastic Circular Torus. Preprints 2021, 2021030326. https://doi.org/10.20944/preprints202103.0326.v2
Sun, B. Displacement Formulations for Deformation and Vibration of Elastic Circular Torus. Preprints2021, 2021030326. https://doi.org/10.20944/preprints202103.0326.v2
APA Style
Sun, B. (2022). Displacement Formulations for Deformation and Vibration of Elastic Circular Torus. Preprints. https://doi.org/10.20944/preprints202103.0326.v2
Chicago/Turabian Style
Sun, B. 2022 "Displacement Formulations for Deformation and Vibration of Elastic Circular Torus" Preprints. https://doi.org/10.20944/preprints202103.0326.v2
Abstract
The formulation used by most of the studies on an elastic torus are either Reissner mixed formulation or Novozhilov's complex-form one, however, for vibration and some displacement boundary related problem of a torus, those formulations face a great challenge. It is highly demanded to have a displacement-type formulation for the torus. In this paper, I will carry on my previous work [ B.H. Sun, Closed-form solution of axisymmetric slender elastic toroidal shells. J. of Engineering Mechanics, 136 (2010) 1281-1288.], and with the help of my own maple code, I am able to simulate some typical problems and free vibration of the torus. The numerical results are verified by both finite element analysis and H. Reissner's formulation. My 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 outer torus due to the property of their Gaussian curvature. Regarding the free vibration of a torus, our analysis indicates that both initial in u and w direction must be included otherwise will cause big errors in eigenfrequency. One of the most intestine discovery is that the crowns of a torus are the turning point of the Gaussian curvature at the crown where the mechanics' response of inner and outer torus is almost separated.
Keywords
circular torus; deformation; vibration; Gauss curvature; Maple
Subject
Physical Sciences, Acoustics
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