Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Audoly-Pomeau Linear Law of the Gol'denveizer Torus

Version 1 : Received: 6 January 2022 / Approved: 10 January 2022 / Online: 10 January 2022 (11:27:25 CET)

How to cite: Song, G.; Sun, B. Audoly-Pomeau Linear Law of the Gol'denveizer Torus. Preprints 2022, 2022010100. https://doi.org/10.20944/preprints202201.0100.v1 Song, G.; Sun, B. Audoly-Pomeau Linear Law of the Gol'denveizer Torus. Preprints 2022, 2022010100. https://doi.org/10.20944/preprints202201.0100.v1

Abstract

The Gol'denveizer problem of a torus was studied analytically by Audoly and Pomeau (2002), and the accuracy of the Audoly and Pomeau linear law was confirmed numerically by Sun (2021). However, the law does not include the major radius R of the torus. To find the influence of the major radius, we used finite element numerical simulation to simulate different cases, and we propose a modified Audoly and Pomeau linear law for vertical deformation, which includes R. A linear law of horizontal deformation is presented as well. Our studies show that the Audoly and Pomeau linear law has high accuracy. With modified vertical and horizontal deformation, a displacement-compatible relation between them is formulated.

Keywords

circular torus; finite element method; analytical solution; Gaussian curvature

Subject

Engineering, Mechanical Engineering

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