Physics-informed neural networks for the form-finding of tensile membranes by solving the Euler–Lagrange equation of minimal surfaces

Abstract

The use of light-weight tensile membrane structures (TMS) has been widely accepted and their usage is continually increasing, particularly for covering large areas. Such structures result in high material usage efficiency as bending and buckling issues are absent. Their design begins with finding an initial equilibrium state of the structure, under given stress levels and boundary conditions, called ‘form-finding’. Although several form-finding algorithms are present in the literature, many of these conventional approaches are highly sensitive to the choice of parameters of the chosen method. Other problems, especially that of a proper selection of initial shape and non-convergence in case of large number of degrees of freedom, are also major issues in implementation. This article explores the applicability of a recently developed machine learning algorithm, known as the ‘physics-informed neural network’ (PINN), for the purpose of form-finding. The PINN is used to solve the Euler–Lagrange Equation of minimal surfaces which corresponds to a stable minimal shape of the TMS constrained by the prescribed boundary conditions and constant prestress. The accuracy of the proposed mesh-free method is illustrated using several form-finding case studies for frame-supported TMS. It is observed that the aforementioned issues faced by conventional approaches are efficiently avoided in the proposed framework. A step-by-step methodology is also provided, along with a practical guideline for implementation.