Equatorial bending of an elliptic toroidal shell

• A formulation for the equatorial bending of elliptic toroidal shells is presented.
• Closed-form results for the state of stress in the mid-side zones are presented.
• Insights are shed on the effect of arbitrary edge actions on shell stresses.
• The accuracy of the formulation is demonstrated through numerical examples.

The exact differential equations for the axisymmetric bending of elliptic toroidal shells are difficult to solve. In this paper, and by considering a semi-elliptic toroid, we present an approximate bending solution that is valid in regions adjacent to the horizontal equatorial plane. The formulation accurately simulates edge effects which may arise from loading and geometric discontinuities located in the equatorial plane of elliptic toroids. In particular, the developed closed-form results provide a very effective means for evaluating the state of stress in the relatively narrow zones experiencing mid-side local effects in complete elliptic toroidal vessels subjected to hydrostatic loading, and for calculating the deformed shape of the shell midsurface.