Physics-based machine learning for modeling of laminated composite plates based on refined zigzag theory

Physics-based machine learning techniques have recently gained prominence for their ability to model complex material and structural behavior, particularly in laminated composite structures. This study introduces an innovative approach, being the first to employ physics-informed neural networks (PINNs) in conjunction with refined zigzag theory (RZT) for the stress analysis of laminated composite plates. A multi-objective loss function integrates governing partial differential equations (PDEs) and boundary conditions, embedding physical principles into the analysis. Using multiple fully connected artificial neural networks, called feedforward deep neural networks, tailored to handle PDEs, PINNs are trained using automatic differentiation. This training process minimizes a loss function that incorporates the PDEs governing the underlying physical laws. RZT, particularly suitable for the stress analysis of thick and moderately thick plates, simplifies the formulation by using only seven kinematic variables, eliminating the need for shear correction factors. The capability of the proposed method is validated through several benchmark cases in stress analysis, including 3D elasticity solutions, analytical solutions, and experimental results from a three-point bending test based on displacement measurements reported in the literature. These results show consistent agreement with the referenced solutions, confirming the accuracy and reliability of the proposed method. Comprehensive evaluations are conducted to examine the effects of softcore presence, elastic foundation, various lamination schemes, and differing loading and boundary conditions on the stress distribution in laminated plates.