Best kinematics for shell finite elements using convolutional neural networks

The present work aims at exploring the capabilities of Convolutional Neural Networks (CNN) to identify the most influential generalized variables in 2D formulations for plates and shells. The outcome of CNN is the Best Theory Diagram (BTD), a graphical representation of the dependency between the model’s accuracy and nodal degrees of freedom (DOF). The networks are trained with data derived from Finite Element (FE) computations and samples of reduced theories obtained as combinations of a given set of generalized displacement variables. Such samples are obtained through the Carrera Unified Formulation (CUF), a generalized approach to generating the governing equations for any structural model. Furthermore, the Node-Dependent Kinematics(NDK) included local refinements to lead to Best Theory Distributions of structural theories over an FE mesh, that is, identifying areas of a shell in which higher-order models are most necessary. The training data can refer to different analyses, e.g., static or free-vibration, whereas the network’s input can include multiple structural parameters together with a sequence of expansion terms or theory distributions. The numerical results highlight a significant computational efficiency of CNN and its ability to identify the best models even for problem configurations not included in the training set