On the Linear Bending Theory of a Pressurized Torus

The intent of this note is to point out the role of initial displacements (due to manufacturing errors) in the analysis of toroidal shells by linear bending theory. It is shown that the stresses and displacement are very sensitive to small variations of the meridional curvature in the case of uniform pressure. On the other hand, the analysis is comparatively immune to these imperfections when the loading consists of forces or moments applied to the edges of the shell. These conclusions are drawn from the toroidal shell equations of Novozhilov and Zienova, which have been modified such as to include highest-order terms in initial displacements. No solution of the equations is attempted.