Finite Element Network Analysis of the static response of 1D and 2D Structures

This study presents the concept of Finite element network analysis (FENA), which is a physics-constrained deep-learning-based computational framework for the simulation of physical systems. FENA leverages the unique transfer knowledge property of bidirectional recurrent neural networks (BRNN) and the extreme computational speed of trained neural networks to provide a powerful, flexible, and accurate computing platform. In FENA, each class of physical systems (e.g. fundamental structural elements such as beams and plates) is represented by a set of surrogate BRNN models, that are pre-trained and available in a library in a way that is conceptually analogous to finite element analysis. FENA has the ability to concatenate pre-trained network models in order to simulate large-scale multicomponent systems without the need for further training. More specifically, in this study FENA is developed and applied to the simulation of the static axial deformation of rods, as well as bending of slender beams and thin plates. The capabilities and performance of the platform will be illustrated via multiple sample cases. All the predictions are compared with numerical results produced via finite element analysis, showing an excellent agreement. The study also presents a variational-based network concatenation algorithm that allows the assembly of dissimilar elements (such as beam and plate networks) in order to form and simulate the response of stiffened plate systems. Although the framework is applied and numerically validated for structural analysis, the foundational concept of this FENA is extremely general and could be extended to a broad spectrum of physical simulations.