Abstract
In this paper, we derive an analytical expression for reproducing kernel particle method (RKPM) shape functions. Based on this, we propose a necessary and sufficient stability condition for general RKPM in arbitrary function space, and illustrate with degenerate cases. By selecting proper basis vectors and the support of the kernel functions, we demonstrate that the RKPM framework allows generating many kinds of shape functions, including the Lagrangian, B-spline and NURBS shape functions.
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