Finite Deformation Analysis of Membranes Using Physics-Informed Neural Networks

The analysis of large deformations in membrane structures represents a pivotal area of research in contemporary engineering design, with significant implications across diverse fields such as aerospace engineering, architectural design and bioengineering. Conventional numerical methodologies, including the Finite Element Method (FEM), encounter substantial challenges in addressing inherent nonlinearities and achieving computational efficiency, particularly in scenarios involving extreme deformations. This investigation delves into the transformative potential of Physics-Informed Neural Networks (PINNs) as a novel computational paradigm to overcome these limitations. By integrating the fundamental governing equations of membrane mechanics directly into the loss function of the neural network, the proposed framework ensures rigorous adherence to physical principles while harnessing the flexibility and scalability of deep learning architectures. This study underscores the transformative potential of PINNs in advancing the field of computational mechanics and provides a robust methodological foundation for future explorations into the behavior of complex structural systems under nonlinear and large-deformation regimes.