Optimal element-wise distributions of structural theories from neural networks

This paper presents a novel approach to developing refined structural theories for finite element models. The proposed methodology stems from the synergistic use of various methods. First, refined structural theories are built using the Carrera Unified Formulation, and 2D finite elements are used. Each element can be assigned a different structural theory through the Node-Dependent Kinematics approach. The axiomatic/asymptotic method is used to evaluate the accuracy of each structural theory distribution over a numerical mesh. Finally, neural networks are employed to obtain surrogate models, find optimal distributions of theories, and minimize computational costs. The numerical results consider free vibrations of composite shells with various stacking sequences and thickness ratios. Such input parameters are included as features of the surrogate models to avoid lengthy finite element simulations. The use of the proposed methodology provides guidelines on the proper modelling by indicating the areas of the structure in which refined models are most needed. Furthermore, the adoption of neural networks leads to significant reductions in computational overheads.