ON SOME ENRICHMENTS OF REPRODUCING KERNEL PARTICLE METHOD

Abstract

In this paper efforts are made to enrich Reproducing Kernel Particle Method (RKPM). Firstly, the RKPM shape functions are expressed explicitly in terms of kernel function moments. This avoids numerical matrix inversions and solutions of linear algebraic equations which are involved in classical RKPM, and thus makes RKPM more accurate, faster and more efficient. Then, a recently developed truly meshless body integration technique is introduced into RKPM. It is based on a partition of unity by a set of overlapping patches covering the domain and eliminates background cells completely. We borrow an idea from computational geometry and propose a sweeping-line method to determine the quadrature points inside the domain. The method is robust and effective even for domain with complicated shapes. The truly meshless integration technique in combination with this sweeping-line method make implementation of RKPM quite simple, smart and especially very advantageous when nodes are irregularly scattered. Numerical results presented herein demonstrate that these enrichments make RKPM more efficient, versatile and particularly truly meshless.