Bending Behavior of Toroidal Shells

Axisymmetric stresses and deformations of an arbitrary toroidal sector of uniform thickness under both edge loads and uniform internal pressure were obtained by a numerical procedure. Solutions were generated using a transformation to the Reissner-Meissner governing differential equations to eliminate singularities at the crown of the toroid. It was found that edge effects for toroids extend over the entire meridional length of the shell when the ratio of the radius of revolution to that of ring cross section is approximately equal to or larger than three. The general bending characteristics are bounded respectively by those of spheres and cylinders. The general behavior of toroidal shells, including a complete quadrant for both positive and negative Gaussian curvature, has been computed for a wide range of shell parameters in terms of nondimensional influence coefficients and functions.