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Lifting, Loading, and Buckling in Conical Shells.

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Duffy, Daniel 
McCracken, Joselle M 
Hebner, Tayler S 
White, Timothy J 
Biggins, John S 

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.

Description

Keywords

40 Engineering, 4017 Mechanical Engineering, 51 Physical Sciences

Journal Title

Phys Rev Lett

Conference Name

Journal ISSN

0031-9007
1079-7114

Volume Title

Publisher

American Physical Society (APS)
Sponsorship
MRC (MR/S017186/1)
Engineering and Physical Sciences Research Council (EP/L015552/1)