Multi-parameter actuation of a neutrally stable shell: a flexible gear-less motor

Abstract

We have designed and tested experimentally a morphing structure consisting of a neutrally stable thin cylindrical shell driven by a multi-parameter piezoelectric actuation. The shell is obtained by plastically deforming an initially flat copper disc, so as to induce large isotropic and almost uniform inelastic curvatures. Following the plastic deformation, in a perfectly isotropic system, the shell is theoretically neutrally stable, having a continuous set of stable cylindrical shapes corresponding to the rotation of the axis of maximal curvature. Small imperfections render the actual structure bistable, giving preferred orientations. A three-parameter piezoelectric actuation, exerted through micro-fibre-composite actuators, allows us to add a small perturbation to the plastic inelastic curvature and to control the direction of maximal curvature. This actuation law is designed through a geometrical analogy based on a fully nonlinear inextensible uniform-curvature shell model. We report on the fabrication, identification and experimental testing of a prototype and demonstrate the effectiveness of the piezoelectric actuators in controlling its shape. The resulting motion is an apparent rotation of the shell, controlled by the voltages as in a 'gear-less motor', which is, in reality, a precession of the axis of principal curvature.

Simple and extensible plate and shell finite element models through automatic code generation tools

“…The present work constitutes an instrumental step in a larger project on the mechanics and physics of shell structures, including the analysis of the nonlinear material behaviour and fracture of isotropic and anisotropic shells [6,8,7] through phase-field variational models [25,45,68], applications to multistable structures with embedded active materials [43,88], and for the understanding of singularities and energy scalings in plates and shells [33]. Current and future technical developments of FEniCS-Shells will be aimed at providing anisotropic adaptive remeshing tools [87,69] and coupling to advanced nonlinear solvers, such as asymptotic numerical continuation methods [93] and deflation techniques [36] to automatically detect multiple solutions of nonlinear systems.…”

“…FEniCS-Shells could provide users with efficient and simple tools to implement specific solvers for multilayered or other specific plate and shell models [85], shell models including multiphysical couplings or nonlinear material behaviour [84,52,43], as well as one atom thick shell structures such as nanotubes and graphene [11]. Because of its flexibility and the easiness in the development of user models and fine control of the different aspects of the solution process, it can conveniently complement the offer of commercial finite element packages and other open-source projects.…”

“…In the perfectly isotropic case, for k > k * T the plate is neutrally stable: all the shapes obtained by rotating the curvature axis are still solutions of the problem. This structure was a source of inspiration for several recent works on morphing plates and shells [89,90,43].…”

“…Their study has received renewed attention in the last decade because of their unique nonlinear behaviour, mainly caused by geometric effects [12], leading to d-cone singularities and crumpling [33], fracture [84], or multistability [89,90]. Examples of modern application fields in engineering include shape control through active materials [52,43], stretchable electronics [81], soft robotics [63], and thin nano-structures e.g. graphene sheets and nanotubes [11].…”

Constrained stability of conservative static equilibrium

“…Rafsanjani, Akbarzadeh and Pasini show how a meta-material with selected properties can be designed from geometrically non-linear effects in a non-homogeneous material [37]. Hamouche and co-workers derive closed-form expressions for bi-or tri-stability of thin shallow shells, and show how the shape of a structure can be controlled by active materials [25,26]. Emam and Inman give an extensive review of the morphing and energy harvesting potential in bi-stable composite laminates, where morphing is an "interesting feature of modern structures that enables them to change shape according to environmental or operational conditions" [14].…”