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A novel node-to-segment algorithm in smoothed finite element method for contact problems

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Abstract

Studies have found that the widely-used one-pass node-to-segment (NTS) algorithm for contacts fails to pass the contact patch test. Solution errors at the contacting surfaces resulting from the classical NTS algorithm do not necessarily decrease with the mesh refinement. This paper presents a novel NTS with the explicit dynamic formulation in detail, which can pass the contact patch test. The proposed algorithm consists of the following technical ingredient: (1) A weighted smoothing technique is developed to accurately evaluate contact forces for contact problems; (2) The central difference time integration scheme is utilized for efficiency, to save storage space, and to avoid the use of tangent stiffness matrix; (3) the penalty method is used for ease in implementation; (4) Our NTS algorithm is coded in the smoothed finite element method (S-FEM). Two S-FEM models are adopted for the proposed NTS algorithm: the node-based smoothed finite element method (NS-FEM) and the edge-based smoothed finite element method (ES-FEM) so that automatically generable triangular elements can be used for excellent adaptation. Numerical examples of the proposed algorithm are presented to examine the performance. It is found that the present algorithm alleviates the nonuniformity of contact pressure on both flat and curve boundaries. ES-FEM and NS-FEM combined with the new NTS algorithm have higher convergence rates. In addition, the ES-FEM has more accurate displacement and stress solutions at the same grid level. NS-FEM can even provide an upper bound solution in the strain energy for contact problems.

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Acknowledgements

This work is financial supported by the National Natural Science Foundation of China (Grant Nos. 11832011, 52275184 and 12002395), and Natural Science Foundation of Hebei Province (Grant No. E2022202132).

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Authors and Affiliations

  1. School of Mechanical Engineering, Hebei University of Technology, Tianjin City, 300401, China

    Chao Sun, G. Wang, Chengjiao Yu & Zirui Li

  2. National Engineering Research Center for Technological Innovation Method and Tool, Hebei University of Technology, Tianjin, 300401, China

    Chao Sun, G. Wang, Chengjiao Yu & Zirui Li

  3. Department of Aerospace Engineering and Engineering Mechanics, University of Cincinnati, Cincinnati, OH, 45221, USA

    G. R. Liu

  4. College of Aeronautics and Astronautics, Taiyuan University of Technology, Taiyuan, 030024, China

    S. H. Huo

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  1. Chao Sun
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Sun, C., Liu, G.R., Huo, S.H. et al. A novel node-to-segment algorithm in smoothed finite element method for contact problems. Comput Mech 72, 1029–1057 (2023). https://doi.org/10.1007/s00466-023-02327-6

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