A Gene Expression Programming Framework for Predicting the Buckling Coefficient of Rotationally-Restrained Mindlin Plates

Rotationally-restrained edges are increasingly common in structural applications, yet exact analytical buckling solutions for Mindlin plates under such boundary conditions have only recently become available, and no explicit, closed-form predictive equation has yet been developed for this class of problem. This study develops a Gene Expression Programming (GEP) framework that predicts the dimensionless buckling coefficient of rectangular Mindlin plates across fourteen boundary-conditions, spanning Lévy-type, non-Lévy classical, and non-classical rotationally-restrained families, as a single explicit function of the four edge rotational-restraint coefficients, the plate aspect ratio, the thickness-to-width ratio, and the biaxial in-plane load ratio. A machine-learning-ready dataset was compiled and verified directly from a recently published finite integral transform method analytical benchmark for rotationally-restrained Mindlin plates, then partitioned into stratified training, validation, and test subsets. Following the Gene Expression Programming methodology and presentation framework established for classical thin-plate buckling, a two-stage evolutionary search first reproduced a conventional, plain-addition GEP formulation before introducing a weighted, least-squares-fitted multigene linking function to meet a pre-defined accuracy target. The final ten-gene model achieves a coefficient of determination of 0.995, 0.992, and 0.987, and a mean absolute percentage error of 2.94%, 2.87%, and 5.37%, on the training, validation, and independent test subsets, respectively, a roughly four-fold reduction in error relative to the plain-addition baseline, and reproduces every qualitative trend established analytically, including the influence of boundary restraint, aspect ratio, thickness ratio, and load ratio on the buckling coefficient. Sensitivity analysis identifies the thickness ratio and the biaxial load ratio as the most influential parameters, and five-fold cross-validation confirms the model generalizes reliably beyond its training partition. The resulting explicit equation offers a computationally negligible, physically interpretable alternative to re-solving the governing eigenvalue problem for preliminary design, parametric studies, and structural-optimization workflows involving Mindlin plates with complex edge restraint.