Analysis and Optimization of a Shape Memory Alloy-Based Self-Folding Sheet Considering Material Uncertainties

Origami-inspired active structures have important characteristics such as reconfigurability and the ability to adopt compact flat forms for storage. A self-folding shape memory alloy (SMA)-based laminated sheet is considered in this work wherein SMA wire meshes comprise the top and bottom layers and a thermally insulating compliant elastomer comprises the middle layer. Uncertainty in various parameters (e.g. material properties) may affect the performance of the sheet, which is explored here. Different modeling approaches are studied in order to compare their accuracy and computational cost. A numerical approach based on the Euler-Bernoulli beam theory is selected due to its accuracy when compared to higher fidelity finite element simulations and its low computational cost, necessary to perform a large number of design evaluations as required for uncertainty analysis. Optimization is performed considering uncertainty in the material properties. Failure probabilities under mechanical constraints and expected values of fold curvature and blocking moment are considered during optimization of the self-folding sheet. The multiobjective genetic algorithm for technology characterization P3GA is used to obtain the Pareto dominant designs. Most designs forming the Pareto frontier have the same values for certain design parameters such as the distance between the wires in the SMA meshes non-dimensionalized by SMA wire thickness, elastomer layer thickness non-dimensionalized by SMA wire thickness, and applied temperature. The design parameter deciding the trade-off between fold curvature and blocking moment is found to be the SMA wire thickness.