Lifting, Loading, and Buckling in Conical Shells
Daniel Duffy, Joselle M. McCracken, Tayler S. Hebner, Timothy J. White, John S. Biggins
Abstract
Liquid crystal elastomer films that morph into cones are strikingly capable lifters. Thus motivated, we combine theory, numerics, and experiments to reexamine the load-bearing capacity of conical shells. We show that a cone squashed between frictionless surfaces buckles at a smaller load, even in scaling, than the classical Seide-Koiter result. Such buckling begins in a region of greatly amplified azimuthal compression generated in an outer boundary layer with oscillatory bend. Experimentally and numerically, buckling then grows subcritically over the full cone. We derive a new thin-limit formula for the critical load, ∝t^{5/2}, and validate it numerically. We also investigate deep postbuckling, finding further instabilities producing intricate states with multiple Pogorelov-type curved ridges arranged in concentric circles or Archimedean spirals. Finally, we investigate the forces exerted by such states, which limit lifting performance in active cones.