Intelligent computational design of scalene-faceted flat-foldable tessellations

Abstract Origami tessellations can be folded from a given planar pattern into three-dimensional object with specific geometric properties, inspiring developments in various fields of science and engineering such as deployable structures, energy absorption devices, reconfigurable robots, metamaterials. However, the range existing origami patterns functional properties flat-foldability is rather scant, analytical solutions to constraint equations arising design process are generally highly complicated. In this paper, we tackle challenging problem automated scalene-faceted flat-foldable using an efficient metaheuristic algorithm. To end, study establishes curves based on compatibility conditions for all six-fold (i.e., degree-6) vertices. Subsequently, graphical method particle swarm optimization (PSO) adopted produce optimal patterns. Moreover, mountain-valley assignments obtained designs determined computational approach mixed-integer linear programming. It turns out that internal vertices each C2-symmetric unit fragment (UF) exist pairs about centroid UF. Furthermore, numerical experiments carried examine feasibility compare accuracy, efficiency, global convergence proposed methods. The results demonstrated that, comparison method, PSO has not only higher accuracy but also significantly lower cost, enabling us develop intelligent platform efficiently tessellations.