Twist error response of periodic lattices to strain energy distribution

Abstract

Periodic lattices, when used as assembly scaffolds, can augment pre-existing 2D manufacturing techniques to fabricate 3D structures with heterogeneous materials, components and architecture such as human organs for transplant patients, and micro batteries. Periodic lattices are first preformed and then folded using externally actuating walls that properly constrain the lattice edges. Angular errors of the actuation walls cause the lattice to distort, misaligning components on the lattice panels. Research into the response of a lattice to geometric errors imposed on the lattice edges does not account for how much strain energy is put into the lattice during folding and its impact on the lattice distortion response and magnitude. This thesis shows how design parameters of the lattice can change the magnitude and shape of the twist response of the lattice when external geometric errors are applied to the lattice during folding. A Buckingham Pi analysis was used to show how the twist response of the lattice due to an external angular wall error depends on the torsional stiffnesses of the panels, the initial fold angle of the preformed accordion unit in the lattice and the angular wall error. A FEA simulation study quantified the Buckingham Pi results by varying the torsional stiffness ratio of the panels, the initial fold angle and the final lattice length after folding. The results showed that increasing the ratio of the torsional stiffnesses by two orders of magnitude decreases the magnitude of the response by as much as an order of magnitude and increases the asymmetry by 0.5 to 1.5 orders of magnitude. Increasing the initial fold angle by 50% increases the magnitude of the result by as much as 250% and decreases asymmetry by 26%.