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<p>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 <i>R</i> = 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 &gt; 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.</p>

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

  • 期刊论文

  • 发表日期：

    2026年6月17日

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  • Van Thien Tran,
  • Trung Kien Nguyen,
  • Thuc P. Vo,
  • Armagan Karamanli

摘要

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.