Design of restrained pneumatic formwork – Inverse form finding and materialisation for free form geometries

This paper presents a method for the inverse design of restrained air-supported structures or pneumatic formwork. The proposed approach consists of two main steps. We first solve a best-fit optimisation using the force-density method. Considering the self-weight and air pressure, the optimisation determines an equilibrium force distribution in the membrane as a discrete network that closely approximates a given input surface. Subsequently, the force density results are materialised. By applying the finite element method, we tailor the material properties of the membrane, specifically adjusting its stiffness, to achieve the desired structural characteristics. To demonstrate the adaptability and effectiveness of our method, the paper concludes with a series of examples showcasing its application.