Hybrid Modeling of Nonlinear-Jointed Structures via Finite-Element Model Reduction and Deep Learning Techniques
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ORIGINAL PAPER
Hybrid Modeling of Nonlinear‑Jointed Structures via Finite‑Element Model Reduction and Deep Learning Techniques Zhi‑Sai Ma1,2 · Qian Ding1,2 · Yu‑Jia Zhai1,2 Received: 23 June 2020 / Revised: 1 September 2020 / Accepted: 12 September 2020 © Krishtel eMaging Solutions Private Limited 2020
Abstract Purpose 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. Methods 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-offreedom 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. Results and Conclusions 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. Keywords Nonlinear jointed structures · Hybrid modeling · Finite element model reduction · Deep learning
Introduction In the past decades, finite element modeling has gradually become an effective numerical method for solving problems of structural dynamics, and been widely used in aerospace, civil, mechanical and other engineering fields. However, for complex structural systems with a number of nonlinear joints, it is usually difficult to efficiently and accurately model the system using the finite element method (FEM). On the one hand, numerical integration of governing equations of motion of complex structures is time-consuming due to their large numbers of degrees-of-freedom [1, 2]. On the other hand, the dynamic characteristics and parameters of * Qian Ding [email protected] 1
School of Mechanical Engineering, Tianjin University, Tianjin 300350, China
Tianjin Key Laboratory of Nonlinear Dynamics and Control, Tianjin 300350, China
2
nonlinear joints (such as friction, freeplay, collision, etc.) are difficult to determine, while linearized models of nonlinear joints are valid for a unique set of excitation parameters and fail to predi
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