A mesh-free collocation method based on enriched differential reproducing kernel (DRK) approximations is developed for the analysis of two-dimensional cracks. DRK approximants are developed based on reproducing kernel (RK) approximations. The advantage of the present DRK approximants is that the derivatives of the shape functions can be determined using a set of differential reproducing conditions without involving the differentiation towards the RK approximants. This circumvents the need for the complicated calculations necessary to determine the derivatives of the shape functions in conventional RK methods. To take advantage of the DRK, the approximation is applied in a collocation method with weighted least squares. In the DRK collocation method, only a scattered set of nodal points is required in the domain of interest; no element connectivity data are needed, and the system equations are easy to establish directly from the governing partial differential equations and the associated boundary conditions. In order to accurately calculate the stress intensity factor (SIF) for cracks, we incorporate the singular asymptotic field in the approximate functions near the crack tip, and thus the SIF can be calculated directly from the coefficients of the asymptotic terms. Numerical examples are presented for a number of examples to demonstrate the accuracy of the method for the analyses of cracking problems.
|頁（從 - 到）||359-370|
|期刊||Journal of the Chinese Institute of Civil and Hydraulic Engineering|
|出版狀態||Published - 2011 十二月 1|
All Science Journal Classification (ASJC) codes
- Civil and Structural Engineering