In recent years, the increasing demand for lightweight, high-strength, and multifunctional materials has driven rapid advances in composite structures for modern engineering applications. Composite plates are now fundamental components in aerospace, civil, and mechanical systems, where structural stability, durability, and reliability under complex loading and support conditions are essential. Although their superior strength-to-weight characteristics make them attractive for advanced designs, most existing studies focus on idealized boundary conditions. In practice, however, composite plates are often subjected to non-Lévy and non-classical supports, including rotational restraints, welded edges, and partial clamping. These realistic boundary conditions introduce significant mathematical and computational challenges, limiting the applicability of conventional analytical and numerical techniques. Recent analytical solutions based on the finite integral transform method have provided rigorous benchmark results for bending and buckling responses of composite rectangular plates with non-Lévy and non-classical boundaries, offering insight into critical loads, mode shapes, and parametric effects. Nevertheless, such formulations become increasingly complex for generalized supports, while traditional numerical approaches, such as the finite element method, require extensive remeshing and incur high computational costs. To address these limitations, this study presents a physics-guided, mesh-free machine learning framework for analyzing the bending behavior of elastic and composite plates under complex boundary conditions. By embedding governing physics through energy minimization and flexible boundary enforcement, the proposed method serves as an efficient, data-free surrogate model. Validation against finite element benchmarks confirms its accuracy and robustness, demonstrating its potential for efficient stability analysis and design optimization of composite plate structures.