Buckling behavior of orthotropic thin plates using analytical and machine learning methods

Designing plate structures poses challenges due to potential instabilities and the complexities involved in obtaining accurate analytical solutions, especially for non-Lévy-type boundary conditions. This study employs the finite integral transform method to analyze the buckling behavior of orthotropic thin plates with complex boundary conditions. In solution procedure, the governing high-order partial differential equations are transformed into a system of linear algebraic equations, yielding exact and rapidly converging analytical solution. The method is simple and general and does not need to predetermine the deflection function. The correctness of the method is validated by comparison with numerical simulations performed using the ABAQUS software. Furthermore, Gene Expression Programming (GEP) is utilized to develop empirical models that predict buckling coefficients of isotropic and orthotropic plates under classical and non-classical boundary conditions. Material properties, aspect ratio, rotating fixed coefficient, and boundary conditions are used as input parameters, with simplified mathematical formulations to predict the buckling coefficient. Model performance is assessed using parametric analysis and statistical tests to ensure accuracy and generalization. Further investigation shows aspect ratio and rotating fixed coefficient are significant variables influencing buckling coefficients under classical and non-classical boundary conditions, respectively, followed by boundary conditions and material property. The performance of the GEP model is further assessed by comparing with linear and non-linear regression models. The results show that GEP outperforms the regression models, showing its higher prediction accuracy. This study not only addresses the challenges of designing thin plates with complex boundary conditions, but it also presents an effective machine-learning method for predicting buckling behavior. The analytical solution can be used as a benchmark for validating new analytical and numerical methods. The equations developed using GEP to predict the buckling coefficient of plates provide a useful tool for extrapolating results beyond the scope of this study.