Physics-informed extreme learning machine for rapid form-finding of frame-supported lightweight tensile membrane structures

Abstract

Tensile membrane structures (TMS) are one of the most in-demand types of structures these days owing to their aesthetic appeal, light-weight nature, ability to span large distances with very little supports, high material usage efficiency, etc. They are mostly used as roofing structures in stadiums, airports, parking lots, facades, etc. However, the design of such TMS is not trivial. The initial shape of the TMS is not known beforehand unlike other traditional structures like steel, masonry, etc. and hence, the designer requires a form finding framework to find the equilibrium shape of the TMS subjected to a particular combination of prestress and boundary constraints. Conventional mesh-based approaches, although very popular, are known to encounter serious convergence issues especially for non-minimal TMS related to choice of initial reference configuration, hyper-parameter selection, mesh-distortion, deviation of the Cauchy stress distribution on the form found surface, etc. Hence, an alternative mesh-less form finding method is proposed which is devoid of the aforementioned limitations of these customary form finding techniques. The modified Laplace equation is explored for form finding of TMS in this study by employing a new framework in the domain of scientific machine learning called the physics-informed extreme learning machine (PIELM). Initially a vanilla PIELM based framework is used for validation of the proposed form finding approach. However, this approach is seen to be a victim of the curse of dimensionality. Subsequently a modified algorithm based on PIELM is proposed and it is seen that for real life high dimensional TMS, the proposed method performs significantly better than Physics informed neural network (PINN) based form finding approach and a conventional mesh-based form finding approach in terms of computational efficiency. The advantage of this PIELM-based form finding in comparison to traditional physics-informed neural networks (PINNs) is in its extremely fast convergence, which can be highly beneficial for form finding design. Extensive form finding case studies show the overall reliability and computational efficiency of the proposed framework. Additionally, it is evident that the PIELM-based form finding framework can help provide a solution that is inherently devoid of the existing shortcomings associated with conventional mesh-based methodologies. A computational speedup of 50–100 times is also observed for a certain case study compared to traditional methods using the proposed scientific machine learning framework.