Analytical and neural network-based approaches for mechanical postbuckling analysis of simply-supported functionally graded graphene origami-enabled auxetic metamaterial plates

This study investigates the nonlinear postbuckling behavior of functionally graded graphene origami-enabled auxetic metamaterial (FG-GOEAM) plates with a negative Poisson's ratio under in-plane compressive loads. The FG-GOEAM plates are modeled with layer-wise graphene origami (GOri) distributions across their thickness, utilizing genetic programming-assisted micromechanical models to accurately capture their complex material behavior. The theoretical framework is established based on Reddy's higher-order shear deformation theory and von Kármán's geometric nonlinearity, while Galerkin method and Airy's stress function are employed to determine the critical buckling loads and postbuckling load–deflection curves. An innovative approach was developed by integrating artificial neural networks (ANNs) with analytical modeling to enhance prediction accuracy and computational efficiency. Three advanced training algorithms—Bayesian Regularization (BR), Levenberg–Marquardt (LM), and Scaled Conjugate Gradient (SCG) backpropagation—are employed to develop ANN models capable of accurately predicting the nonlinear postbuckling load–deflection response. These models are trained on an extensive dataset generated from the analytical solution, ensuring robust generalization while mitigating overfitting. A comparative analysis between the analytical results and ANN predictions demonstrates exceptional agreement, validating the reliability of the proposed approach. Notably, errors for BR and LM consistently remain below 0.5%, with BR often yielding the smallest deviations, while SCG errors can approach 3% in certain cases. Additionally, an in-depth parametric analysis is conducted to elucidate the effects of thermal environments, material distributions, and geometric variations on the nonlinear postbuckling responses of FG-GOEAM plates. Increasing the GOri weight fraction markedly enhances both critical and postbuckling loads, whereas a higher degree of GOri folding reduces these loads by inducing auxetic behavior and increased deformability.