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Stable node-based smoothed finite element method for 3D contact problems

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Abstract

In this work, a stable node-based smoothed finite element method (SNS-FEM) is presented for curing temporal instability of NS-FEM in 3D contact problems. In present method, each node-based domain generated by NS-FEM is firstly equivalent to spherical region with the same volume. Then six temporary integral points are symmetrically distributed at the intersection of the equivalent spherical and the global Cartesian coordinate system to construct the stable terms related to the gradient of the smoothed shape function derivatives. It turns out the stable terms help the SNS-FEM obtain items of the ideal stiffness matrix and internal force vector. Meanwhile, by means of the basic boundary value equation of Coulomb friction contact, the SNS-FEM successfully maintains the stability of the load transfer between the master/slave surfaces and relaxes the sensitivity of the mesh deformation. Its effectiveness and potentialities can be well represented and clarified by several numerical examples containing benchmark case.

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Acknowledgements

The support of National Science Foundation of China (11872177), National Science Foundation of China (12002124), Changsha Municipal Natural Science Foundation (43386), and State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body (32065007) are gratefully acknowledged.

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  1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, People’s Republic of China

    Xiao Sun, Hong Yang, She Li & Xiangyang Cui

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Sun, X., Yang, H., Li, S. et al. Stable node-based smoothed finite element method for 3D contact problems. Comput Mech 69, 787–804 (2022). https://doi.org/10.1007/s00466-021-02114-1

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