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Simon Guest: Lattice Structures

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Introduction

Morphing structures can change their shape to respond to or alter
their environment. Recently, there has been a great deal of interest
in using *lattice* structures as the microstructure of a new class
of morphing materials.
I have been working on actuation properties of lattice materials with Anthony Leung at the University of Cambridge, and Nathan Wicks and John Hutchinson at Harvard University. Others working closely on the same area include Norman Fleck, Digby Symons and Rob Hutchinson here at the University of Cambridge, and Tony Evans and Sergio Luis dos Santos e Lucato at the University of California Santa Barbara.

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Kagome Lattice

Our work has concentrated on the kagome lattice:

The kagome lattice has been shown to be one of the few
periodic, planar, single length scale lattice topologies that has
optimal passive stiffness. At the same time, if considered as
pin-jointed, any bar can be actuated without resistance. Although
practical micro-scale structures will necessarily be rigid-jointed
the additional resistance to actuation
from bar bending is small providing that the members are slender.
The rigid jointed planar Kagome lattice therefore has the required
properties for use in high authority shape morphing structures;
namely passive stiffness and low resistance to actuation.

We have considered the effect of actuating a single bar in an infinite lattice (Wicks and Guest 2004; Leung, Symons and Guest, 2004). The mode of actuation is shown for two structures, below: (a) is made of relatively thinner bars than (b); the deformation dies away with distance from the actuated bar more quickly in (b).

We define the * stockiness, s *, of the structure to be the ratio of the radius of gyration of the cross-section of a member to its length. For the kagome lattice, the work required to actuate a single member, relative to the work required to stretch a member, is proportional to *s*. This is different to both bending-dominated structures, where the work if proportional to *s*^{2}, and to stretching dominated, where the work done is independent of *s*. In fact, simple arguments show that for the kagome, the work done is absorbed approximately equally in bending and in stretching.

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See also

A recent poster by Anthony Leung

A recent presentation by Digby Symons
## Relevant Publications

Leung, A.C.H., Symons, D.D., and Guest,
S.D. (2004) "Actuation of Kagome Lattice Structures", in *Proceedings of the
45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials
Conference, Palm Springs, CA 19–22 April 2004*, paper no. AIAA 2004–1525. (pdf copy)
Wicks, N. and Guest, S.D. (2004), "Single member actuation in large repetitive truss structures." International Journal of Solids and Structures. 41(3-4), 965-978. doi:10.1016/j.ijsolstr.2003.09.029

Guest, S.D. and Hutchinson, J.W. (2003), "On the determinacy of repetitive structures." Journal of the Mechanics and Physics of Solids, 51(3), 383-391. doi:10.1016/S0022-5096(02)00107-2

Last updated on the 6th of July, 2004

S.D. Guest -
sdg@eng.cam.ac.uk