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

Resumo

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.