Gradient enhanced physics-informed neural network for iterative form-finding of tensile membrane structures by potential energy minimization

Tensile membrane structures (TMS) are overwhelmingly popular as practical design solutions for large roofing structures. The TMS designer, however, has to perform a “form-finding” as the stable configuration of TMS are not known beforehand. Although many form-finding approaches are currently available, most suffer from various implementation complications, particularly with regards to convergence issues stemming from improper hyper-parameter selection, mesh distortion and the choice of initial reference configuration. In this study, a new iterative form-finding methodology is proposed and implemented by the direct minimization of a potential energy functional. A mesh-free approach based on gradient enhanced physics-informed neural network (gPINN) is employed, which expands the applicability to most common TMS types while eliminating the aforementioned issues faced by traditional mesh-based algorithms. Furthermore, a new method for selecting the initial reference configuration using transfinite interpolation is proposed that is significantly better suited to form-finding than conventional approaches. Additionally, approximate distance functions are employed to impose exact boundary conditions. Extensive numerical case studies on frame- and cable-supported TMS, along with multi-dimensional parametric variations, show the efficacy and robustness of the proposed form-finding framework.