Actuation of Kagome Lattice Structures

Abstract

The kagome lattice has been shown to have promise as the basis of active structures, whose shape can be changed by linear actuators that replace some of the bars of the lattice. As a preliminary examination, this paper examines the effect of the actuation of a single bar in a large two-dimensional kagome lat- tice. Previous work has shown that interesting properties of the kagome lattice depend on the bars that are co-linear with the actuated bar being straight, but has also shown that actuation causes these bars to bend; this paper therefore explores the geometrically non-linear response of the structure. Numerical re- sults show that due to geometrically non-linear effects, the actuation stiffness is reduced from that predicted by linear models, while the peak elastic strain in the structure is increased. Individual actuators replace some of the members of the truss: altering the length of these actuators changes the macroscopic shape of the structure. In two dimensions, the kagome truss (Fig. 1) has been shown to be a promising solution for these structures. 3 It 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. As a preliminary investigation, this paper will examine the effect of the actuation of a single bar in a large two-dimensional kagome lattice, and will consider how the stockiness, s, of the members affects the response. The stockiness is a non-dimensional measure of the aspect ratio of each bar, defined as the ratio of the in-plane radius of gyration of the cross-section, k, to the length of the member, L. Practical structures have s in the range from 0.005 to 0.05, which is the range investigated here. Previous work 4 has examined the energy required to actuate a single bar in a large two-dimensional lattice by considering various linear analytical and computational models. However, the special properties of the kagome lattice are dependent on its geometry, and actuation imposes large geometric deformations. This paper therefore builds on the previous work by considering the geometrically non-linear response of the structure. The resistance of the structure to actuation will be considered, as well as the limitation on actuation imposed by material yield; the limiting actuation strain will be calculated for various values of material yield strain. The paper is structured as follows. Section II will describe the computational model used, and Section III will describe some generic features of the response of the kagome lattice to the actuation of a single bar. Section IV then goes on to explore the build-up of force in the actuated member as the bar is actuated. Section V explores the peak elastic strain anywhere in the structure due to the imposed actuation, and shows how the actuation strain is limited by yielding of the structure for varying values of stockiness and yield strain.