Axisymmetric buckling analysis of submerged hemi-elliptic toroidal shells

Toroidal shells have been widely used in various industrial applications for over a decade. Most studies on buckling behavior have focused on circular toroidal shells with uniform loads. In contrast, the existing literature on the shell buckling of a toroid with elliptical cross-sections has received limited attention. This study aims to present numerical solutions for axisymmetric buckling of hemi-elliptic toroidal shells under linearly hydrostatic pressure to append available data and results in this field. The thickness of the hemi-elliptic toroidal shells is assumed to be constant before and after the buckling state. Solution procedures for solving critical buckling loads dealt with eigenvalue problems and were formulated by an energy approach. All relevant parameters such as membrane and bending strain components and in-plane stress resultants were derived based on differential geometry. An in-house FEM program solved the weak formulation derived from a variational method. The buckling results for elliptic toroidal shells with various b/a ratios were established as the critical seawater depth and compared to the previously published results. Additionally, parametric studies on the effect of the variable b/a ratios and the major radius R of elliptic toroidal shells on the axisymmetric buckling loads and mode shapes were examined thoroughly and addressed in more detail herein.