Form finding of non-minimal tensile membrane structures based on the general theory of curved interfaces using physics-informed neural networks

Tensile membrane structures (TMS) are growing in popularity for their ability to span vast regions, lightweight properties, and material utilisation efficiency. Given that the shape of the structure is unknown in advance and is dependent on the boundary and stress conditions, the designer must use an approach known as ‘form-finding’ which seeks to discover a static equilibrium configuration of TMS. Unfortunately, standard methods suffer from several convergence issues. Therefore, the authors propose an innovative approach for identifying the TMS form based on the theory of general curved interfaces by solving the generalised form of the Laplace equation, which stems from the mechanical and thermodynamic principles for describing the phenomena of curved interfaces. This theory is implemented to develop a novel form-finding equation that can incorporate non-minimal shapes and therefore is specifically tailored to fit a TMS’s structural requirements. The suggested methodology entails using a mesh-less framework called a physics-informed neural network to solve this newly obtained equation. Several numerical examples highlight the advantages of the proposed formulation.