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<p>We study the quasi-consistent reproducing kernel particle method (QC-RKPM), which was recently introduced by Huang and Wei (Comput Mech 70(6):1211–1239, 2022). QC-RKPM (Huang and Wei 2022) was initially proposed to address the kernel instability arising in plate analysis when a quadratic basis is employed. Although QC-RKPM shows potential in overcoming this challenge, its formulation has not been fully derived, and the conditions ensuring the invertibility of the moment matrices remain unexplored. In this work, we present a detailed derivation of QC-RKPM within the framework of the moving least-squares RKPM and identify the requirements for moment matrix invertibility. In addition, we demonstrate that QC-RKPM can effectively mitigate the singularity caused by the linear dependence between RK basis functions and the shell surface function. The conditions under which moment matrices are non-singular in this case are established. A series of numerical examples is presented to verify the theoretical properties and effectiveness of QC-RKPM.</p>

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Regularized reproducing kernel particle method

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月23日

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  • Huy Anh Nguyen,
  • Satoyuki Tanaka

摘要

We study the quasi-consistent reproducing kernel particle method (QC-RKPM), which was recently introduced by Huang and Wei (Comput Mech 70(6):1211–1239, 2022). QC-RKPM (Huang and Wei 2022) was initially proposed to address the kernel instability arising in plate analysis when a quadratic basis is employed. Although QC-RKPM shows potential in overcoming this challenge, its formulation has not been fully derived, and the conditions ensuring the invertibility of the moment matrices remain unexplored. In this work, we present a detailed derivation of QC-RKPM within the framework of the moving least-squares RKPM and identify the requirements for moment matrix invertibility. In addition, we demonstrate that QC-RKPM can effectively mitigate the singularity caused by the linear dependence between RK basis functions and the shell surface function. The conditions under which moment matrices are non-singular in this case are established. A series of numerical examples is presented to verify the theoretical properties and effectiveness of QC-RKPM.