Open Access

ARTICLE

RKPM with Augmented Corrected Collocation Method for Treatment of Material Discontinuities

H.M. Shodja^1,2,3, M. Khezri⁴, A. Hashemian¹, A. Behzadan¹

1 Center of Excellence in Structures and Earthquake Engineering, Department of Civil Engineering, Sharif University of Technology, P.O. Box 11155-9313, Tehran, Iran
2 Institute for Nanoscience and Nanotechnology, Sharif University of Technology, P.O. Box 11155-9161, Tehran, Iran
3 Corresponding author.Tel: (+98-21) 66164209; Fax: (+98-21) 66072555. E-mail: shodja@sharif.edu (H. M. Shodja)
4 School of Civil and Environmental Engineering, The University of New South Wales, Sydney, Australia

Computer Modeling in Engineering & Sciences 2010, 62(2), 171-204. https://doi.org/10.3970/cmes.2010.062.171

Abstract

An accurate numerical methodology for capturing the field quantities across the interfaces between material discontinuities, in the context of reproducing kernel particle method (RKPM), is of particular interest. For this purpose the innovative numerical technique, so-called augmented corrected collocation method is introduced; this technique is an extension of the corrected collocation method used for imposing essential boundary conditions (EBCs). The robustness of this methodology is shown by utilizing it to solve two benchmark problems of material discontinuities, namely the problem of circular inhomogeneity with uniform radial eigenstrain, and the problem of interaction between a crack and a circular inhomogeneity. Moreover, an efficient algorithm for computing the area associated to each particle for performing nodal quadrature in 2D in the context of RKPM is proposed. The efficacy of this algorithm in determination of the elastic fields within a plate weakened by a hole under uniform far-field tension is demonstrated. This algorithm combined with augmented corrected collocation method provides a powerful tool for treating problems with material discontinuities.

---

Keywords

---