Form-finding of frame-supported non-minimal tensile membrane structures for anisotropic prestress using physics-informed neural networks

The use of light-weight tensile membrane structures (TMS) has gained widespread acceptance, especially for covering vast areas. Their tension only behavior leads to high efficiency in material utilization. Designing of TMS starts with ‘form-finding’ to find the membrane’s initial equilibrium state under specified prestress and boundary constraints. Existing techniques of form-finding are generally sensitive to the parameters of the selected method and the choice of initial shape; these methods pay high computational costs especially when the number of degrees of freedom is very high. In this paper, a new linear partial differential equation, defined as the ‘modified Laplace equation,’ is derived for form-finding of minimal and non-minimal TMS by extending the vibrating membrane analogy. This equation is solved using physics-informed neural network to determine the stable configuration of the TMS. Varied TMS case studies demonstrate the accuracy and efficacy of the proposed mesh-less framework. Issues of dependency on initial shape, arbitrariness in parameter selection, non-convergence due to high-dimensionality, and meshing complex geometries are mitigated in the proposed form-finding framework. However, this method is only applicable for frame-supported TMS.