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A Modified Gaussian Integration Scheme in Element Free Method

Published online by Cambridge University Press:  05 May 2011

Jopan Sheng ,
Chung-Yue Wang  and
Kuo-Jui Shen
Jopan Sheng*
Affiliation:
Department of Civil Engineering, National Central University, Chungli, Tao-Yuan, Taiwan 32054, R.O.C.
Chung-Yue Wang*
Affiliation:
Department of Civil Engineering, National Central University, Chungli, Tao-Yuan, Taiwan 32054, R.O.C.
Kuo-Jui Shen*
Affiliation:
Department of Civil Engineering, Van Nung Institute of Technology, Chungli, Tao-Yuan, Taiwan 320, R.O.C.
*
*Associate Professor
**Professor
***Lecturer
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Abstract

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.

Keywords

Element-free methodMeshfreeQuadrature ruleWeighting function
Type
Articles
Information
Journal of Mechanics , Volume 18 , Issue 1 , March 2002 , pp. 17 - 27
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2002

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