RKPM with Augmented Corrected Collocation Method for Treatment of Material Discontinuities
H.M. Shodja; M. Khezri; A. Hashemian and A. Behzadan

doi:10.3970/cmes.2010.062.171
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 62, No. 2, pp. 171-204, 2010
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Keywords reproducing kernel particle method (RKPM), material discontinuity, augmented corrected collocation method, crack inhomogeneity interaction, nodal quadrature
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.
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