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Radial Basis Reproducing Kernel Particle Method for Damped Elastic Dynamics Problems

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Abstract

The reproducing kernel particle method (RKPM) is a widely used meshless method that has been extensively applied in numerical analysis. The drawback of RKPM is that when different kernel functions are chosen during the computation process, there are different calculation accuracy, and significant discreteness. To address this issue, the radial basis function is introduced to RKPM, and the radial basis reproducing kernel particle method (RB-RKPM) is proposed. The negative impacts of different kernel functions on calculation accuracy can be eliminated by RB-RKPM, which possesses some advantages, such as good convergence, high computational accuracy and efficiency. Furthermore, the RB-RKPM is applied to the damped elastic dynamics problems (DEDPs), the governing equations for the DEDPs are derived based on the weak integral formulation, and the time is integrated by using the Newmark-linear acceleration method. Finally, the correctness of the proposed method in analyzing the DEDPs is verified through numerical examples.

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Acknowledgements

The work is supported by the Natural Science Foundation of Shandong Province (Grant No. ZR2020MA059).

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Authors and Affiliations

  1. School of Mechanical Engineering, Qilu University of Technology (Shandong Academy of Sciences), Shandong, 250353, China

    Tengda Liu, Gaofeng Wei & Yijie Zhang

  2. Shandong Institute of Mechanical Design and Research, Shandong, 250353, China

    Tengda Liu, Gaofeng Wei & Yijie Zhang

Authors
  1. Tengda Liu
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  2. Gaofeng Wei
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  3. Yijie Zhang
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Contributions

TL: Methodology, Software, Formal Analysis, Writing-Original Draft. GW: Data Curation, Conceptualization, Writing–Review & Editing. YZ: Funding acquisition, Validation, Investigation.

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Correspondence to Gaofeng Wei.

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The authors declared no potential conflicts of interest with respect to the research, authorship, and publication of this article. The authors declare that they have no conflict of interest.

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Liu, T., Wei, G. & Zhang, Y. Radial Basis Reproducing Kernel Particle Method for Damped Elastic Dynamics Problems. Iran J Sci Technol Trans Mech Eng (2023). https://doi.org/10.1007/s40997-023-00701-6

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