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.

圆环面的非线性变形和应力分析由于其复杂的拓扑结构和高斯曲率的变化而成为一项艰巨的任务。Mindlin环面的非线性变形（仅省略了一项应变）根据广义位移公式化，并编写了通用Maple代码进行数值模拟。数值研究表明，非线性Mindlin、线性Mindlin、非线性Kirchhoff-Love和线性Kirchhoff-Love模型得到的结果相互接近。该研究进一步表明，圆形环面的线性 Kirchhoff-Love 建模提供了良好的精度，并确保 Mindlin 环面的非线性变形和应力分析（不是动力学）可以用更简单的公式代替，例如线性 Kirchhoff-环面的爱情理论，