Smooth poly-hypar membrane structure: A strut-and-membrane system based on combinations of hyperbolic paraboloids

This paper presents an innovative form-making method for membrane structures by combing hyperbolic paraboloid modules with G¹ continuity. The approach generates equilibrium forms with mainly axial forces by adhering to specific predefined geometric constraints, offering a detailed depiction of internal force distributions utilizing graphic statics, simplifying the calculation of structural behaviour both in the initial self-stressed state and under external loads. This paper introduces the two fundamental prototypes and outlines the form-making strategies for creating smooth poly-hypar surfaces for various design options based on these prototypes. It also showcases a practical application of this innovative structural system through an experimental project, the Hypar Umbrella. This project illustrates the aesthetic, structural, and fabrication advantages of smooth poly-hypar membrane structures. The prototype was designed with several standard components and identical joints, facilitating its low-tech manufacturing feature. The internal forces calculated by graphic statics is validated by a refined finite element (FE) model. Finally, physical loading tests and FE simulations were carried out to verify the load-bearing capacity of this structural system, indicating its potential for future applications.