Fig. 3.

Indentation of a toroidal shell. (A) Schematic of a segment of a toroidal shell with radii R₁ and R₂. Three different parts of the shell are subject to point indentation. For all of the calculations, the shells with t/R₁ = 0.005, R₂/R₁ = 4 were clamped along the lateral edges. The other ends of the shells are free to displace and rotate. (B) Deformation caused by normal indentation of the outer surface, which has positive Gauss curvature. (C) Deformation caused by normal indentation along the nodal line, which has zero Gauss curvature. (D) Deformation caused by normal indentation of the inner surface, which has negative Gauss curvature. (E) Force–indentation response of the three shells under indentation. The inner part of the half-toroidal shell shows a much stiffer response under indentation compared with the other two shells, consistent with an extended region along which the deformation is felt. The normalized force is plotted on a logarithmic scale.