Continuous meshless approximations for nonconvex bodies by diffraction and transparency

D. Organ*, Mark A Fleming, T. Terry, T. Belytschko

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

254 Scopus citations


Continuous meshless approximations are developed for domains with non-convex boundaries, with emphasis on cracks. Two techniques are developed in the context of the element-free Galerkin method: a transparency method wherein smooth approximation are generated by making boundaries partially transparent, and a diffraction method, where the domain of influence wraps around a concave boundary. They are compared to the original method based on the visibility criterion in which the approximations are discontinuous in the vicinity of nonconvex boundaries. The performance of the methods is compared using two elastostatic examples: an infinite plate with a hole and a crack problem. The continuous approximations show only moderate improvement in accuracy over the discontinuous approximations, but yield significant improvements for enhanced bases, such as crack-tip singular functions.

Original languageEnglish (US)
Pages (from-to)225-235
Number of pages11
JournalComputational Mechanics
Issue number3
StatePublished - Jul 1 1996

ASJC Scopus subject areas

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

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