An energy-based physics-informed neural network with optimized architecture for nonlinear bending of laminated composite plates via higher-order shear deformation theory

Accurate prediction of geometrically nonlinear bending in laminated composite plates remains a computational challenge in structural engineering. This paper presents a physics-informed neural network framework as a mesh-free approach to this problem. The methodology integrates Reddy’s higher-order shear deformation theory and von Kármán’s geometric nonlinearity to evaluate thick composites without relying on shear correction factors. To overcome the severe gradient pathologies and computational instability associated with the fourth-order spatial derivatives required by the strong-form governing equations, the loss function is formulated directly from the variational principle of minimum total potential energy. This energy-based objective reduces the required derivative order to the second degree, creating a mathematically stable optimization landscape that guides the network toward kinematically admissible equilibrium states. Furthermore, the neural network architecture and training hyperparameters are systematically evaluated using an automated hyperparameter optimization framework. The proposed framework was validated against established three-dimensional elasticity and finite element solutions, demonstrating consistent accuracy in capturing nonlinear responses and through-thickness stress distributions across diverse loading scenarios, boundary conditions, and laminate configurations. This article establishes a stable and data-efficient computational framework for the nonlinear analysis of laminated composite structures.