Accuracy Evaluation of Higher-Order Structural Theories for Stiffened Beams Using Neural Networks

Abstract

This paper presents a machine learning-based surrogate framework for predicting the accuracy of higher-order beam theories in the analysis of isotropic structures with longitudinal stiffeners and transverse ribs. The proposed approach maps the physical and geometric parameters of the beams directly to the accuracy of a selected structural theory, enabling the selection of the minimum set of generalized displacement variables required to achieve the desired accuracy for a given set of input parameters. The training dataset is generated using the Carrera Unified Formulation and comprises combinations of generalized variables stemming from polynomial expansions up to the fourth order. Unlike previous studies, the input space explicitly includes physical cross-sectional parameters, as well as the presence and positions of stringers and ribs. The full dataset, encompassing all combinations of the considered structural theories and cases, comprises millions of analyses; however, accurate predictions are achieved using Deep Neural Networks with only approximately 1% of the full dataset for training. The results show that the proposed surrogate model reliably predicts the accuracy of a structural theory with good generalization capabilities. Concerning the most influential generalized variables, high accuracy in natural frequency prediction is generally achieved when approximately 60% of the fourth-order expansion terms are retained; all second-order terms are essential, while selected third- and fourth-order terms significantly influence the response.