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An enriched radial point interpolation method based on weak-form and strong-form

Gu, YuanTong (2011) An enriched radial point interpolation method based on weak-form and strong-form. Mechanics of Advanced Materials and Structures, 18(8), pp. 578-584.

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Abstract

In this article, an enriched radial point interpolation method (e-RPIM) is developed for computational mechanics. The conventional radial basis function (RBF) interpolation is novelly augmented by the suitable basis functions to reflect the natural properties of deformation. The performance of the enriched meshless RBF shape functions is first investigated using the surface fitting. The surface fitting results have proven that, compared with the conventional RBF, the enriched RBF interpolation has a much better accuracy to fit a complex surface than the conventional RBF interpolation. It has proven that the enriched RBF shape function will not only possess all advantages of the conventional RBF interpolation, but also can accurately reflect the deformation properties of problems. The system of equations for two-dimensional solids is then derived based on the enriched RBF shape function and both of the meshless strong-form and weak-form. A numerical example of a bar is presented to study the effectiveness and efficiency of e-RPIM. As an important application, the newly developed e-RPIM, which is augmented by selected trigonometric basis functions, is applied to crack problems. It has been demonstrated that the present e-RPIM is very accurate and stable for fracture mechanics problems.

Impact and interest:

2 citations in Scopus
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2 citations in Web of Science®

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ID Code: 47110
Item Type: Journal Article
Additional Information: Special Issue: The Second International Symposium on Computational Mechanics (ISCM II) and the Twelfth International Conference on the Enhancement and Promotion of Computational Methods in Engineering and Science (EPMESC XII) 2009
Keywords: meshfree, meshless, surface fitting, enriched RBF, RPIM
DOI: 10.1080/15376494.2011.621832
ISSN: 1537-6532
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
Past > Schools > School of Engineering Systems
Deposited On: 20 Nov 2011 22:48
Last Modified: 20 Nov 2011 22:48

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