An approach for displacement field prediction in structures combining the Finite Element Method and Deep Learning Techniques

Abstract

Recent advancements in machine learning have facilitated groundbreaking applications across different domains. In this study, we present a novel application of Deep Learning (DL) combined with the FEM for predicting nodal displacements in structures. The proposed approach retains all traditional FEM steps up to the formulation of the global system of equations, which includes the stiffness matrix, nodal load vector, and boundary conditions. However, instead of relying on classical numerical methods to solve the system, we employ a DL model capable of correlating applied loads and stiffness with the displacement field. This allows the model to act as an alternative solver for the discrete problem, offering the advantage of instantaneous and computationally efficient results. The methodology used in this study is divided into two stages: exploration and exploitation. In the exploration stage, we search for the DL architecture that performs best for the given problem by testing various models and configurations on an initial dataset. In the exploitation stage, the optimal model is applied to solve more complex structural problems. The outcomes underscore the significance of this approach; the proposed model demonstrates commendable performance in this task, exhibiting a maximum absolute mean error of approximately 2% and a maximum mean squared error of 0.2%, when contrasted with classical FEM solutions.