Time transient Simulations via Finite Element Network Analysis: Theoretical Formulation and Numerical Validation

TL;DR

This paper develops a dynamic time-transient extension of finite element network analysis (FENA), introducing super finite network elements and network concatenation in time to enable efficient and accurate structural simulations beyond initial data windows.

Contribution

It introduces a novel time-transient formulation of FENA with super finite network elements and extends neural network concatenation to the time domain for dynamic simulations.

Findings

FENA accurately predicts transient responses with about 1% error.

The method significantly improves computational efficiency for dynamic simulations.

Validation against analytical and finite element solutions confirms its effectiveness.

Abstract

This paper extends the finite element network analysis (FENA) to include a dynamic time-transient formulation. FENA was initially formulated in the context of the linear static analysis of 1D and 2D elastic structures. By introducing the concept of super finite network element, this paper provides the necessary foundation to extend FENA to linear time-transient simulations for both homogeneous and inhomogeneous domains. The concept of neural network concatenation, originally formulated to combine networks representative of different structural components in space, is extended to the time domain. Network concatenation in time enables training neural network models based on data available in a limited time frame and then using the trained networks to simulate the system evolution beyond the initial time window characteristic of the training data set. The proposed methodology is validated by applying FENA to the transient simulation of one-dimensional structural elements (such as rods and beams) and by comparing the results with either analytical or finite element solutions. Results confirm that FENA accurately predicts the dynamic response of the physical system and, while introducing an error on the order of 1% (compared to analytical or computational solutions of the governing differential equations), it is capable of delivering extreme computational efficiency.