Fig 16. Geometry of the problem.

(a) Undeformed geometry: a spherical shell of radius R and thickness h ≪ R is characterised by its arclength s and distance from the axis of revolution ρ(s). (b) Deformed configuration characterised by arclength S(s) and distance r(s) from the axis of revolution. Intrinsic volume conservation sets the thickness H(s) of the sheet. A local basis (u_r,u_ϕ,u_z) describes the deformed surface. (c) Cross-section of the shell under the Kirchhoff hypothesis, with a coordinate ζ across the thickness of the shell, parallel to the normal n to the midsurface.