Elastic buckling analysis of CFS built-up plates under non-uniform loading: Integrated analytical method and machine learning

The elastic buckling behavior of screw-connected cold-formed steel (CFS) built-up plates under non-uniform in-plane loading is investigated by an integrated analytical-machine learning approach in this study. Based on the energy method and small-deflection theory, accounting for the screw shear-slip effect, an analytical expression for the critical buckling load with non-uniform in-plane loading of screw built-up plates is derived. The shear stiffness of self-drilling screws plays a crucial role in the buckling behavior of built-up plates. By conducting screw shear tests and analyzing the test results, a representative database of screw shear stiffness is established. Furthermore, symbolic regression (SR) is employed to learn from the dataset and develop a dimensionless empirical expression for the shear stiffness. Besides, to reduce the influence of the large distribution range and outliers of the labels, Logarithmic Scaling and RobustScaler are employed in the data preprocessing. The evaluation results indicate that the derived SR formula possesses high predictive accuracy and generalization capability. Moreover, the proposed analytical expression is validated through numerical simulations of varying geometric parameters and stress gradients. Analyses demonstrate that the proposed critical buckling load equation captures the buckling behavior accurately and consistently. This research not only extends theory for the design and optimization of screw built-up plates under non-uniform loading, but also provides a novel methodology for composite plate buckling analysis through combining analytical methods and machine learning.