Hybrid Monte Carlo–Levenberg–Marquardt neural network for stochastic analysis of 3D-FGP microplates

This paper introduces a novel Monte Carlo–Levenberg–Marquardt neural network (MCS-LMNN) framework for efficient stochastic buckling and vibration analysis of tri-directional functionally graded porous (3D-FGP) microplates under material uncertainties. Deterministic frequencies and buckling loads are obtained via higher-order shear deformation theory (HSDT), modified couple stress theory (MCT), and Ritz method with hybrid orthogonal polynomial shape functions, achieving convergence with only five terms. The MCS-LMNN surrogate achieves R = 0.99 correlation to Ritz-MCS benchmarks (2000 samples) at 44% of the computational cost, representing a 2.25 × speedup. Parametric studies reveal that porosity degrades stiffness, steeper gradients amplify size effects, and boundary conditions significantly modulate dispersion (COV = 10–15%). Statistical analysis shows positive skewness (0.2–0.4) from lognormal stiffener dominance and kurtosis > 3 from porosity-induced heavy tails. New stochastic benchmarks for 3D-FGP microplates across porosity patterns, gradation profiles, and material length scale parameter ratios provide essential design data, validating the framework’s accuracy and efficiency for microplate analysis.