Form-finding is a crucial process in architecture and structural engineering, used to identify the most efficient structural shapes by considering the specific materials, environmental factors, and external loads at play. Unlike conventional design approaches that start with a predetermined shape, form-finding is about discovering the optimal geometry that aligns with the unique demands of the materials and forces involved. This approach is particularly useful for designing lightweight structures like tensile membrane constructions, where the optimal shape isn’t always clear from the start. It’s especially effective for large-span roofs, such as those used for stadiums, pavilions, and public spaces, where the design must balance being lightweight and durable while efficiently handling forces and adapting to environmental factors. 

One of the main challenges in designing TMS lies in accurately analyzing the load behavior, as complications like membrane wrinkling, orientation of the fabric and the prestress value with consideration to practical design constraints. In response to these challenges, the focus is to provide a  load analysis formulation that incorporates a modified energy functional, accounting for the material fiber direction. Algorithms to detect membrane wrinkling and determine optimal fiber orientation are proposed, along with the development of a material seam partitioning method based on principal curvature. This integrated approach creates a practical optimization framework for TMS. The proposed methodology shows that the optimal fiber orientation results in stiffer and more stable structures while minimizing shear forces. This approach offers a robust, user-friendly tool for effectively designing and optimizing TMS.

In the conceptual design stage, structures—such as lightweight tensile membrane structures (TMS)—pose unique challenges, particularly when the initial shape is not predefined and must be discovered through ‘form-finding.’ To streamline this early design phase, a novel interactive generative framework has been developed. This framework allows designers to explore and experiment with various structural forms. For example, in TMS, it assists a designer to find shapes that are both aesthetic and structurally performant. This approach enables active participation in the design process, balancing qualitative aesthetics with quantitative performance for TMS. Adaptable to various conceptual structures, this tool empowers designers with greater control of the final structure right from the early-design stage.

Physics-Informed Neural Networks (PINNs) integrate physics and differential equations directly into the modeling process, offering powerful solutions for complex problems like tensile membrane structures (TMS) and other large-deformation challenges. Traditional methods often struggle with issues like mesh distortion and convergence in these scenarios, but PINNs provide a meshless approach, using a fixed neural network architecture that simplifies the problem’s dimensionality. This makes PINNs advantageous for simulations where accuracy, stability, and computational efficiency are essential.