A modified Gaussian integration scheme in element free method

Jopan Sheng, Chung Yue Wang, Kuo Jui Shen

Research output: Contribution to journalArticlepeer-review


In this paper, a modified numerical integration scheme is presented that improves the accuracy of the numerical integration of the Galerkin weak form, within the integration cells of the analyzed domain in the element-free methods. A geometrical interpretation of the Gaussian quadrature rule is introduced to map the effective weighting territory of each quadrature point in an integration cell. Then, the conventional quadrature rule is extended to cover the overlapping area between the weighting territory of each quadrature point and the physical domain. This modified numerical integration scheme can lessen the errors due to misalignment between the integration cell and the boundary or interface of the physical domain. Some numerical examples illustrate that this newly proposed integration scheme for element-free methods does effectively improve the accuracy when solving solid mechanics problems.

Original languageEnglish
Pages (from-to)17-27
Number of pages11
JournalJournal of Mechanics
Issue number1
StatePublished - 2002


  • Element-free method
  • Meshfree
  • Quadrature rule
  • Weighting function


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