Data-Driven Discovering Low-Dimensional Governing Equations for Mechanical Elements Based on the First Principles of Elasticity

It is of great scientific significance and application to establish simplified mechanical models for basic mechanical elements to effectively capture and analyze their deformation mechanisms and avoid solving complex equations of elasticity. This paper presents a novel data-driven modeling method of mechanical elements by discovering the low-dimensional governing equations from the simulation data based on the three-dimensional theory of elasticity. In this method, the data generated by directly solving the elasticity equations of specific mechanical structures are resorted to a system identification method of Seq-SVF, and the corresponding simplified mechanical models are established. The sparse structure of identified equations ensures the balance of precision and complexity. By applying this method to the mechanical modeling of slender structures, new homogeneous and heterogeneous beam models are established, where the conventional shear deformation theory is modified by these data-driven results. The numerical examples indicate that the constructed data-driven models are more accurate than classical models and greatly reduce the computational cost compared with solving the elasticity equations. This work provides an explicit strategy for modeling the simplified relationship between the input and output field functions. Compared with the commonly used system identification methods, the results are more interpretable.