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A new support integration scheme for the weakform in mesh‐free methods
Author(s) -
Liu Yan,
Belytschko Ted
Publication year - 2009
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2780
Subject(s) - quadrature (astronomy) , numerical integration , exploit , divergence (linguistics) , construct (python library) , mathematics , scheme (mathematics) , computer science , mathematical optimization , algorithm , calculus (dental) , mathematical analysis , engineering , linguistics , philosophy , computer security , electrical engineering , programming language , medicine , dentistry
A new support integration technique is proposed, which is similar to those used in truly mesh‐free methods. The contribution of this paper is to exploit the divergence‐free condition for the support integrals to construct quadrature formulas that only require three integration points per particle in two dimensions. Numerical examples show that the proposed integration method can achieve results that agree with manufactured closed‐form solutions. Copyright © 2009 John Wiley & Sons, Ltd.