Geometrically nonlinear bending analysis of laminated thin plates based on classical laminated plate theory and deep energy method

Abstract

This paper establishes a geometrically nonlinear bending analysis framework using the deep energy method and the classical laminated plate theory (CLPT) for laminated plates. Inspired by the transfer learning technique, a load applied to a laminated plate can be divided into multiple load steps. The network parameters for the current load step, with the exception of the initial step, are initialized by inheriting values from their preceding steps. Including both von Kármán and Green-Lagrange strains, the plate strains are computed using the automatic differentiation and integrated along the thickness direction per laminate plate based on the constitutive theory. By combining the outputs of neural network, the external potential energy can be obtained, and the optimized network parameters are given by minimizing the total system potential energy of the laminated plate. In order to validate the proposed approach, several numerical examples are calculated, and the present solutions are compared with those given by the literature and the Finite Element Analysis (FEA). The results show that the proposed approach is indeed feasible, can reach high levels of precision under varying loads while offering a simplified calculation strategy.