Mapping beam cross-section features to higher-order generalized variables using machine learning

The aim is to provide a numerical tool able to assess the accuracy of a set of generalized displacement variables for a given beam geometry. Furthermore, it can provide the most influential generalized variables for a given problem. The training dataset is built on the Carrera Unified Formulation and is based on a combination of fourth-order polynomial expansions. Convolutional and deep neural networks are used to correlate structural theories, geometries, materials, and accuracy. Dynamics problems are considered, and the accuracy is evaluated using natural frequencies. The trained network receives as inputs the problem features, such as the cross-section geometry and material, and a structural theory and estimates its accuracy. The results show that the proposed approach reliably predicts the accuracy of a structural theory. On the other hand, in evaluating the set of most influential generalized variables, the performance of the networks is poorer but still acceptable. In most cases, the accuracy of the natural frequencies is high if 60% of the total fourth-order terms are included; all terms up to the second-order are mandatory, and some third- and fourth-order terms are very influential.