For a given material, different shapes correspond to different rigidities. In this paper, the radii of the oblique elliptic torus are formulated, a nonlinear displacement formulation is presented and numerical simulations are carried out for circular, normal elliptic and oblique tori, respectively. Our investigation shows that both the deformation and the stress response of an elastic torus are sensitive to the radius ratio, and indicate that the analysis of a torus should be done by using the bending theory of shells rather than membrane theory. Numerical study demonstrates that the inner region of the torus is stiffer than the outer region due to the Gauss curvature. The study also shows that an elastic torus deforms in a very specific manner, as the strain and stress concentration in two very narrow regions around the top and bottom crowns. The desired rigidity can be achieved by adjusting the ratio of minor and major radii and the oblique angle.

对于给定的材料，不同的形状对应不同的刚度。在本文中，公式化了斜椭圆环面的半径，提出了非线性位移公式，并分别对圆形、法向椭圆和斜环面进行了数值模拟。我们的研究表明，弹性环面的变形和应力响应都对半径比敏感，这表明环面的分析应该使用壳的弯曲理论而不是膜理论来进行。数值研究表明，由于高斯曲率，环面的内部区域比外部区域更硬。研究还表明，弹性环面以非常特殊的方式变形，因为应变和应力集中在顶部和底部冠部周围的两个非常狭窄的区域。