Sun, B. H. Nonlinear Elastic Deformation of Mindlin Torus. Communications in Nonlinear Science and Numerical Simulation, 2022, 114, 106698. https://doi.org/10.1016/j.cnsns.2022.106698.
Sun, B. H. Nonlinear Elastic Deformation of Mindlin Torus. Communications in Nonlinear Science and Numerical Simulation, 2022, 114, 106698. https://doi.org/10.1016/j.cnsns.2022.106698.
Sun, B. H. Nonlinear Elastic Deformation of Mindlin Torus. Communications in Nonlinear Science and Numerical Simulation, 2022, 114, 106698. https://doi.org/10.1016/j.cnsns.2022.106698.
Sun, B. H. Nonlinear Elastic Deformation of Mindlin Torus. Communications in Nonlinear Science and Numerical Simulation, 2022, 114, 106698. https://doi.org/10.1016/j.cnsns.2022.106698.
Abstract
The nonlinear deformation and stress analysis of a circular torus is a difficult undertaking due to its complicated topology and the variation of the Gauss curvature. A nonlinear deformation (only one term in strain is omitted) of Mindlin torus was formulated in terms of the generalized displacement, and a general Maple code was written for numerical simulations. Numerical investigations show that the results obtained by nonlinear Mindlin, linear Mindlin, nonlinear Kirchhoff-Love, and linear Kirchhoff-Love models are close to each other. The study further reveals that the linear Kirchhoff-Love modeling of the circular torus gives good accuracy and provides assurance that the nonlinear deformation and stress analysis (not dynamics) of a Mindlin torus can be replaced by a simpler formulation, such as a linear Kirchhoff-Love theory of the torus, which has not been reported in the literature.
Keywords
circular torus; nonlinear deformation; shear deformation; Mindlin; 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.
