Accuracy and Efficiency of Structural Theories for Free Vibration Analyses via Axiomatic/Asymptotic Method and Neural Networks

This paper presents novel approaches to investigate the accuracy and computational efficiency of 1D and 2D structural theories. The focus is on free vibration problems in metallic and composite structures. Refined theories are built via the Carrera Unified Formulation (CUF), and the influence of higher-order generalized variables is analysed via the Axiomatic/Asymptotic Approach (AAM). Best theory diagrams (BTD) are built by considering those models minimizing the computational cost and maximizing the accuracy. BTD can estimate the accuracy and efficiency of any structural models, including classical models and refined theories from literature. The construction of BTD can be a cumbersome task as multiple finite element (FE) problems are required. Machine learning through neural networks can significantly reduce such overhead. In other words, surrogate structural models are built using a limited number of FE analyses for training and having as input a structural theory and providing as output the natural frequencies without the need for finite element analyses. Finally, extensions to node-dependent kinematics (NDK) are presented for further optimization of the computational cost.