Size-Dependent Buckling and Data-Driven Optimization of Porous Laminated Nanoplates Using Nonlocal Higher-Order Shear Deformation Theory

Abstract

This study investigates the critical buckling behavior of porous laminated nanoplates resting on an elastic foundation using a nonlocal Higher-Order Shear Deformation Theory (HSDT). Size-dependent effects have been incorporated via nonlocal elasticity, and the governing equations are solved using the finite element method (FEM). The model is validated against benchmark results, showing excellent agreement. To improve computational efficiency, surrogate models—Artificial Neural Network (ANN), Random Forest (RF), and Gradient Boosting (GB)—are trained on FEM-generated data. The RF model exhibits superior predictive performance with higher R² and lower RMSE and is subsequently employed for parametric analysis and optimization. Parametric investigations reveal that the nonlocal parameter significantly reduces the critical buckling load (CBL) due to stiffness softening, whereas the elastic foundation (Winkler and Pasternak) enhances structural stability. The effects of material gradation, porosity, and geometric ratios are also quantified. Optimization using Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) yields a maximum CBL of 255.5834 at \({{E}_{1}}{\text{/}}{{E}_{2}} = 40\), \(a{\text{/}}h = 20\), \(\mu = 0.5\), \(\phi = 0.3\), \({{k}_{w}} = 100\), and \({{k}_{s}} = 100\). The developed framework enables rapid and accurate buckling prediction while providing an effective strategy for optimizing the structural performance of porous laminated nanoplates in advanced engineering applications.