Two-dimensional finite element network analysis: Formulation and static analysis of structural assemblies. (1st July 2022) - Jokar, Mehdi; Semperlotti, Fabio
Highlights: Generalization of FENA to 2D structures and multi-element structural assemblies. Formulation of a variational concatenation strategy of surrogate network models. FENA database extended to include slender beams and thin plates. Numerical validation and performance assessment against established FEM solutions. Abstract: Finite element network analysis (FENA) is a physics-informed, deep-learning-based framework for the simulation of physical systems. FENA combines the conceptual flexibility of classical finite element methods with the computational power of pre-trained neural networks. A remarkable characteristic of FENA is the ability to simulate assemblies of physical elements by concatenating pre-trained networks serving as models of classes of physical systems. This characteristic places FENA in a new category of network-based computational platforms because, unlike other techniques, it does not require ad hoc training for problem-specific conditions. The present study significantly expands the concept and functionalities of FENA by including 1D slender beams and 2D thin plates and by further extending its concatenation functionality. Concatenation, which is a key property to create multicomponent assemblies without requiring training, is reformulated following an energy-based variational approach that significantly enhances accuracy and speed of convergence. The approach is numerically validated against finite element solutions for different configurations of structural assemblies, loads, and boundary conditions. Although presented in the context of one- and two-dimensional structures, the present framework is extremely general and provides a foundation to potentially simulate a broad range of physical systems.