Analytical expression of RKPM shape functions

Lei Zhang, Shaoqiang Tang*, Wing Kam Liu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


In this paper, we derive an analytical expression for reproducing kernel particle method (RKPM) shape functions. Based on this, we propose a necessary and sufficient stability condition for general RKPM in arbitrary function space, and illustrate with degenerate cases. By selecting proper basis vectors and the support of the kernel functions, we demonstrate that the RKPM framework allows generating many kinds of shape functions, including the Lagrangian, B-spline and NURBS shape functions.

Original languageEnglish (US)
Pages (from-to)1343-1352
Number of pages10
JournalComputational Mechanics
Issue number6
StatePublished - Dec 2020


  • B-spline and NURBS
  • Lagrangian shape functions
  • Reproducing kernel particle method (RKPM)
  • Stability condition

ASJC Scopus subject areas

  • Computational Mechanics
  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


Dive into the research topics of 'Analytical expression of RKPM shape functions'. Together they form a unique fingerprint.

Cite this