Selection of element-wise shell kinematics using neural networks

Abstract

This paper presents a novel approach to evaluate the role of non-classical effects, e.g., shear deformability, over a shell finite element model. Such an approach can identify the areas of a structural model in which the use of first-order shear deformation theories may lead to significant inaccuracies. Furthermore, it can indicate optimal distributions of structural theories over the finite element mesh to trade-off accuracy and computational costs. The proposed framework exploits the synergies among four methods, namely, the Carrera Unified Formulation (CUF), the Finite Element Method (FEM), the Node-Dependent Kinematics (NDK), and Neural Networks (NN). CUF generates the FE matrices for higher-order shell theories and provides numerical results feeding the NN for training. Via NDK, the shell theory is a property of the node; that is, a distribution of various shell theories over the FE mesh is attainable. The distributions of theories and the thickness of the structure are the inputs of multilayer NN to target natural frequencies. This work investigates the accuracy and cost-effectiveness of well-known NN. The results look promising as the NN requires a fraction of FE analyses for training, can evaluate the accuracy of FE models, and can incorporate physical features, e.g., the thickness ratio, that drives the complexity of the mathematical model. In other words, NN can inform on the FE modeling without the need to modify, rebuild, or rerun an FE model.