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A Modified Radial Point Interpolation Method (M-RPIM) for Free Vibration Analysis of Two-Dimensional Solids

Author

Listed:
  • Tingting Sun

    (School of Road Bridge & Harbor Engineering, Nanjing Vocational Institute of Transport Technology, Nanjing 211188, China
    School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430063, China)

  • Peng Wang

    (Wuhan Second Ship Design and Research Institute, Wuhan 430205, China)

  • Guanjun Zhang

    (School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430063, China)

  • Yingbin Chai

    (School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430063, China
    State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China)

Abstract

The classical radial point interpolation method (RPIM) is a powerful meshfree numerical technique for engineering computation. In the original RPIM, the moving support domain for the quadrature point is usually employed for the field function approximation, but the local supports of the nodal shape functions are always not in alignment with the integration cells constructed for numerical integration. This misalignment can result in additional numerical integration error and lead to a loss in computation accuracy. In this work, a modified RPIM (M-RPIM) is proposed to address this issue. In the present M-RPIM, the misalignment between the constructed integration cells and the nodal shape function supports is successfully overcome by using a fixed support domain that can be easily constructed by the geometrical center of the integration cell. Several numerical examples of free vibration analysis are conducted to evaluate the abilities of the present M-RPIM and it is found that the computation accuracy of the original RPIM can be markedly improved by the present M-RPIM.

Suggested Citation

  • Tingting Sun & Peng Wang & Guanjun Zhang & Yingbin Chai, 2022. "A Modified Radial Point Interpolation Method (M-RPIM) for Free Vibration Analysis of Two-Dimensional Solids," Mathematics, MDPI, vol. 10(16), pages 1-20, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2889-:d:886530
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    References listed on IDEAS

    as
    1. Chai, Yingbin & Li, Wei & Liu, Zuyuan, 2022. "Analysis of transient wave propagation dynamics using the enriched finite element method with interpolation cover functions," Applied Mathematics and Computation, Elsevier, vol. 412(C).
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    4. You, Xiangyu & Li, Wei & Chai, Yingbin, 2020. "A truly meshfree method for solving acoustic problems using local weak form and radial basis functions," Applied Mathematics and Computation, Elsevier, vol. 365(C).
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