An enriched radial point interpolation method (e-RPIM) for analysis of crack tip fields

Gu, YuanTong, Wang, Wenlong, Zhang, L.C., & Feng, X.Q. (2010) An enriched radial point interpolation method (e-RPIM) for analysis of crack tip fields. In Lu, Jane Wei-Zhen, Leung, Andrew Yee Tak, Lu, Vai Pan, & Mok, Kai Meng (Eds.) Proceedings of the 2nd International Symposium on Computational Mechanics and the 12th International Conference on the Enhancement and Promotion of Computational Methods in Engineering and Science, AIP - American Institute of Physics , Hong Kong, Macau, China , pp. 348-353.

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In this paper, an enriched radial point interpolation method (e-RPIM) is developed the for the determination of crack tip fields. In e-RPIM, the conventional RBF interpolation is novelly augmented by the suitable trigonometric basis functions to reflect the properties of stresses for the crack tip fields. The performance of the enriched RBF meshfree shape functions is firstly investigated to fit different surfaces. The surface fitting results have proven that, comparing with the conventional RBF shape function, the enriched RBF shape function has: (1) a similar accuracy to fit a polynomial surface; (2) a much better accuracy to fit a trigonometric surface; and (3) a similar interpolation stability without increase of the condition number of the RBF interpolation matrix. Therefore, it has proven that the enriched RBF shape function will not only possess all advantages of the conventional RBF shape function, but also can accurately reflect the properties of stresses for the crack tip fields. The system of equations for the crack analysis is then derived based on the enriched RBF meshfree shape function and the meshfree weak-form. Several problems of linear fracture mechanics are simulated using this newlydeveloped e-RPIM method. It has demonstrated that the present e-RPIM is very accurate and stable, and it has a good potential to develop a practical simulation tool for fracture mechanics problems.

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ID Code: 39851
Item Type: Conference Paper
Refereed: Yes
Additional URLs:
Keywords: Meshfree Method, Crack Tip, Enriched RBF, RPIM, Interpolation, Finite Element Analysis, Fracture Mechanics, Matrix Algebra, Elasticity
ISBN: 978-0-7354-0778-7
ISSN: 0094-243X
Subjects: Australian and New Zealand Standard Research Classification > ENGINEERING (090000) > MECHANICAL ENGINEERING (091300) > Numerical Modelling and Mechanical Characterisation (091307)
Divisions: Past > QUT Faculties & Divisions > Faculty of Built Environment and Engineering
Copyright Owner: 2010 American Institute of Physics
Copyright Statement: Permission is granted to quote from the AIP Conference Proceedings with the customary acknowledgement of the source. Republication of an article or portions thereof (e.g., extensive excerpts, figures, tables etc.) in original form or in translation, as well as other types of reuse (e.g., in course packs) require formal permission from AIP and may be subject to fees. As a courtesy, the author of the original proceeedings article should be informed of any request for republication/reuse. Permission may be obtained online using Rightslink. Locate the article online at, then simply click on the Rightslink icon/"Permission for Reuse" link found in the article Abstract. You may also address requests to: AIP Office of Rights and OPermissions, Suite 1NO1, 2 Huntington Quadrangle, Melville, NY 11747-4502, USA or Email:
Deposited On: 02 Feb 2011 23:08
Last Modified: 24 Jun 2017 14:34

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