Hybrid Modeling of Nonlinear-Jointed Structures via Finite-Element Model Reduction and Deep Learning Techniques

In engineering practice many structures are assembled by several linear components through nonlinear joints. A novel hybrid modeling method based on finite element model reduction and deep learning techniques is proposed to meet the ever-increasing requirements of efficient and accurate modeling for nonlinear jointed structures. The main idea of the hybrid modeling method for nonlinear jointed structures is summarized as follows: Firstly, finite element models of linear components are reduced to improve the computing efficiency using the free-interface mode synthesis method, as numerical integration of governing equations of nonlinear structures with large numbers of degrees-of-freedom is always time-consuming. Secondly, deep neural networks are used to equivalently represent the nonlinear joints which are difficult to describe by accurate and physically-motivated models, so as to avoid the errors caused by traditional mechanism modeling or system identification. Nonlinear joints are finally replaced with their equivalent neural networks and connected with the substructure models of linear components through the compatibility of displacements and equilibrium of forces at the interfaces. The performance of the proposed hybrid modeling method is tested and assessed via a case study focused on a cantilever plate with nonlinear joints. Comparative results demonstrate the capability of the proposed method for efficient and accurate modeling of nonlinear jointed structures and predicting their intrinsic nonlinear behavior.