Automatic data-driven modeling of plate and beam elements based on the first principles of elasticity

The establishment of various basic mechanical elements is of great significance for qualitative analysis of the deformation mechanism of engineering structures with typical geometric features, as well as for rapid and accurate predictions of their mechanical behaviors. Although classical beam and plate models have been extensively developed and widely used in structural mechanics analysis, the expressions of the key parameter in shear deformation theories remain a topic of ongoing research, with no consensus yet reached. In this paper, the high-precision beam and plate models are established by the data-driven modeling method based on the first principles of elasticity. The governing equations of the data-driven models are automatically discovered from finite element simulation data without making any assumptions or approximations about the deformation of the structures. The established models are found to contain the high-order derivatives of the load, which are consistent with the shear deformation theories. The parameters of the governing equations are related to the position of the load, which has never been studied in previous work. Several representative numerical examples demonstrate that the established data-driven models are of higher accuracy compared to classical shear deformation models. This work provides an effective solution for establishing high-precision mechanical models of mechanical elements, and also offers a promising method for modeling and analyzing complex multiphysics systems and engineering structures.