FFT-Based Numerical Method for Nonlinear Elastic

作     者：Fei Guo Fan Wu Xinyong Li Yijie Huang Zhuo Wang Fei Guo;Fan Wu;Xinyong Li;Yijie Huang;Zhuo Wang

作者机构：State Key Laboratory of Tribology in Advanced EquipmentTsinghua UniversityBeijing 100084China Joint Research Center for Rubber and Plastic SealsTsinghua UniversityBeijing 100084China State Key Laboratory of Smart Manufacturing for Special Vehicles and Transmission SystemBaotou 014030China 

出 版 物：《Chinese Journal of Mechanical Engineering》 (中国机械工程学报（英文版）)

年 卷 期：2023年第36卷第5期

页      面：266-279页

核心收录：

学科分类：081406[工学-桥梁与隧道工程] 08[工学] 0814[工学-土木工程] 0701[理学-数学] 082301[工学-道路与铁道工程] 0823[工学-交通运输工程] 

基　　金：Supported by National Key R&D Program of China(Grant No.2019YFB1505301) National Natural Science Foundation of China(Grant No.U1937602) Aeronautical Science Foundation of China(Grant No.201907058001) Open Research Fund of State Key Laboratory of Smart Manufacturing for Special Vehicles and Transmission System(Grant No.GZ2019KF013) 

主　　题：Numerical method Elastoplastic contact Hyperelastic contact FEM FFT 

摘      要：In theoretical research pertaining to sealing, a contact model must be used to obtain the leakage channel. However, for elastoplastic contact, current numerical methods require a long calculation time. Hyperelastic contact is typically simplifed to a linear elastic contact problem, which must be improved in terms of calculation accuracy. Based on the fast Fourier transform, a numerical method suitable for elastoplastic and hyperelastic frictionless contact that can be used for solving two-dimensional and three-dimensional (3D) contact problems is proposed herein. The nonlinear elastic contact problem is converted into a linear elastic contact problem considering residual deformation (or the equivalent residual deformation). Results from numerical simulations for elastic, elastoplastic, and hyperelastic contact between a hemisphere and a rigid plane are compared with those obtained using the fnite element method to verify the accuracy of the numerical method. Compared with the existing elastoplastic contact numerical methods, the proposed method achieves a higher calculation efciency while ensuring a certain calculation accuracy (i.e., the pressure error does not exceed 15%, whereas the calculation time does not exceed 10 min in a 64 × 64 grid). For hyperelastic contact, the proposed method reduces the dependence of the approximation result on the load, as in a linear elastic approximation. Finally, using the sealing application as an example, the contact and leakage rates between complicated 3D rough surfaces are calculated. Despite a certain error, the simplifed numerical method yields a better approximation result than the linear elastic contact approximation. Additionally, the result can be used as fast solutions in engineering applications.