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Reticulated Tubes: Effective Elastic Properties and Actuation Response

S. P. Mai and N. A. Fleck
Proceedings: Mathematical, Physical and Engineering Sciences
Vol. 465, No. 2103 (Mar. 8, 2009), pp. 685-708
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/30243322
Page Count: 24
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Reticulated Tubes: Effective Elastic Properties and Actuation Response
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Abstract

The structural performance is explored for a reticulated circular tube made from a periodic lattice: triangulated; hexagonal; Kagome; and square lattices. The finite-element (FE) method is used to determine the macroscopic bending, torsional and axial rigidities of each tube. Additional insight is obtained by examining the structural mechanics of the pin-jointed version of each topology. For all pin-jointed lattices considered, no states of self-stress exist. However, collapse mechanisms do exist for all reticulated tubes, and for the Kagome and hexagonal lattices some of these mechanisms produce macroscopic generalized strain. These strain-producing collapse modes are additional to those observed in the planar version of these lattices. Consequently, the structural rigidities of tubes with walls made from the rigid-jointed Kagome lattice or hexagonal lattice are less than those predicted from the in-plane effective properties of these two lattices. The morphing capacity of reticulated tubes is also explored by replacing a single bar with an actuator in the FE simulations. The actuation stiffness of the structure is defined by the stiffness of the reticulated tube in resisting extension by the actuated bar. The actuation stiffness is explored as a function of the type of lattice, number of unit cells around the circumference, orientation of the actuated bar and of the bar stockiness. In all cases, the macroscopic shape change of the tube can be idealized as a combination of a local rotation, axial extension, axial twist and shear displacement of the cross-section.

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