Parameterizing the stiffness of tubular hypar umbrellas using genetic programming

Thin-shell hyperbolic paraboloid (hypar) umbrellas have been widely used in architecture and structural art for their aesthetic appeal and structural efficiency. However, their reimagining as novel tubular structures can offer unique opportunities for creating efficient (micro)architectures with high stiffness-to-weight ratios to reduce material consumption and embodied energy. This research explores the mechanical performance of tubular cells inspired by F??lix Candela’s hypar umbrellas as an alternative to traditional prismatic structures (e.g., honeycombs). Symmetrical hypar tympans are merged to form polygonal umbrellas, which are then combined with their inverted counterparts to create repeatable tubular structures. Genetic programming (GP) was employed to develop closed-form solutions of their relative stiffness using over 1,100 datasets from finite element analysis (FEA). The equations are based on geometric properties including normalized rise, relative density, and number of edges, enabling the conceptual design and optimization of N-edged hypar cells subject to compression. This integrated approach enhances the ability to design ultra-light and ultra-stiff materials and structures, with potential applications in many engineering and construction industries.