Design Optimization of Origami-Tunable Frequency Selective Surfaces

Recent studies demonstrate the benefit of integrating origami in many engineering applications, where computational methods facilitate the origami design process. An emerging concept utilizes origami design for physically and functionally flexible electromagnetic devices. However, coupled mechanical and electromagnetic design tools are needed to systematically navigate the complex spaces of fold topology and electromagnetic performance. In this article, we introduce topology optimization formulations that find origami fold-driven frequency selective surface designs possessing electromagnetic filtering properties at target frequencies. These formulations utilize a nonlinear mechanics analysis to simulate an origami folding process. A geometric mapping relates mechanically-relevant origami substrate properties and electromagnetically-relevant conductive element properties. Both gradient-based and genetic algorithm methods are used to find optimal origami crease patterns and folded configurations by optimizing fold stiffness and force distributions over a prescribed potential fold line network. Using nonlinear manifold learning techniques, we demonstrate the isolated nature of optimal design candidates in the design space and the complex interplay of fold topology and fold path selection through initial perturbation from the flat state. Collectively, this study provides an initial framework to design novel EM origami structures and also provides important insights on the complex nature of the design space, which can be leveraged to refine future tool development.