Physically constrained deep recurrent neural network for stiffness computation of plate structures

Abstract

AbstractIn the present study, we introduce two Neural Network (NN) enhanced methods to approximate the local tangent stiffness matrix and the internal force computation for a 2D Finite Element. The proposed model is based on Long‐Short Term Memory (LSTM), which inherently captures the required path‐dependent behavior through its internal parameters. Furthermore, we propose an enhanced training algorithm where an additional loss term corresponding to the derivative of the NN following the Sobolev training procedure is introduced. Such a learning algorithm combines the data‐driven approach with the necessary physical constraint to train the NN. Thus, the present work focuses on introducing the NN at an element level for plate structures taking physical non‐linearities into account. The performance of the proposed methods is demonstrated in an academic example showing a maximum of 90.564% boost in simulation speed.