An accelerated, convergent, and stable nodal integration in Galerkin meshfree methods for linear and nonlinear mechanics

Michael Hillman, Jiun Shyan Chen

Research output: Contribution to journalArticlepeer-review

55 Scopus citations

Abstract

Convergent and stable domain integration that is also computationally efficient remains a challenge for Galerkin meshfree methods. High order quadrature can achieve stability and optimal convergence, but it is prohibitively expensive for practical use. On the other hand, low order quadrature consumes much less CPU but can yield non-convergent, unstable solutions. In this work, an accelerated, convergent, and stable nodal integration is developed for the reproducing kernel particle method. A stabilization scheme for nodal integration is proposed based on implicit gradients of the strains at the nodes that offers a computational cost similar to direct nodal integration. The method is also formulated in a variationally consistent manner, so that optimal convergence is achieved. A significant efficiency enhancement over a comparable stable and convergent nodal integration scheme is demonstrated in a complexity analysis and in CPU time studies. A stability analysis is also given, and several examples are provided to demonstrate the effectiveness of the proposed method for both linear and nonlinear problems.

Original languageEnglish (US)
Pages (from-to)603-630
Number of pages28
JournalInternational Journal for Numerical Methods in Engineering
Volume107
Issue number7
DOIs
StatePublished - Aug 17 2016

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics

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