A PINN-based framework for the analysis of multiple plate theories

A single computational framework is proposed in which several plate kinematics are solved by training neural networks to minimize the discretized total potential energy of the laminate, so that residual-form governing equations are never assembled. The energetic contributions are integrated analytically using the symbolic package SymPy, which also enables the automatic generation of lambda functions from the symbolic expressions. The computational implementation was carried out in PyTorch, considering two equivalent single-layer plate models. The adopted models comprise the Reissner–Mindlin First Order Shear Deformation Theory (FSDT) and a Carrera Unified Formulation representation. Predicted displacement and stress fields are compared against finite element reference solutions, and the metrics used to evaluate this agreement are the RMSE and relative error.