Effect of discontinuous elastic foundations on geometrically nonlinear bending and stress response of thick composite plates via energy-based physics-informed neural networks

This paper introduces a novel energy-based physics-informed neural network (EPINN) for the geometrically nonlinear analysis of thick composite plates interacting with discontinuous elastic foundations. Addressing the instability of conventional residual-based PINNs, our mesh-free framework minimizes the total potential energy, thereby eliminating the heuristic weighting of loss terms. The formulation integrates Reddy's higher-order shear deformation theory (HSDT) with von Kármán nonlinearity, while kinematic constraints are strictly satisfied through a hard enforcement strategy. A key innovation is the implementation of an analytical mask function that elegantly handles complex support geometries by decoupling the foundation layout from computational sampling. To ensure efficient convergence in the nonlinear regime, a continuation-based training strategy mirroring incremental loading is employed. The framework is rigorously validated against established benchmark solutions available in the open literature. The results demonstrate high precision in predicting full-field displacements and capturing sharp stress concentrations at support boundaries without the need for manual mesh refinement. Parametric investigations reveal that annular support offers superior stiffness compared to central support, triggering significant stress redistribution. This paper establishes the proposed EPINN as a robust, high-fidelity computational tool, offering a superior alternative to mesh-based methods for structures governed by strong nonlinearities and intricate boundary interactions.