Form-finding of tensile membrane structures with strut and anchorage supports using physics-informed machine learning

Due to their aesthetic appeal, light weight, and capacity to span vast expanses of space, tensile membrane structures (TMS) are very popular these days. TMS are usually supported by frames and boundary edge cables, but sometimes also by struts and anchorage supports. Traditional mesh-based form-finding algorithms, typically developed for the first two boundary types, suffer from convergence issues stemming from the choice of initial shape, choice of pseudo material properties, mesh distortion, hyper-parameter selection, etc. In order to address the issues with conventional mesh-based form-finding frameworks as stated above, a mesh-free form-finding framework for TMS is proposed utilizing a gradient-enhanced physics-informed neural network. The theory of functional connections is employed to precisely meet the TMS boundary conditions without depending on an additional penalty function used in conventional physics-informed neural network frameworks, thereby eliminating errors related to boundary constraints. The challenge of incorporating compressive strut supports in TMS form-finding is addressed by employing the principle of inverted forces, and modelling them as tension elements. 24 numerical studies, with a diverse set of TMS shapes and boundary supports, including benchmark problems, are presented demonstrating the effectiveness and accuracy of the proposed method. This method also allows the designer to explore various parametric (architectural) designs of TMS.