This paper presents an innovative formulation of the RKPM (reproducing kernel
particle method) pioneered by Liu. A major weakness of the conventional RKPM is
in dealing with the derivative boundary conditions. The EFGM (element free
Galerkin method) pioneered by Belytschko shares the same difficulty. The
proposed RKPM referred to as GRKPM (gradient RKPM), incorporates the
first gradients of the function in the reproducing equation. Therefore in
three-dimensional space GRKPM consists of four independent types of shape
functions. It is due to this feature that the corrected collocation method can
be readily generalized and combined with GRKPM to enforce the EBCs
(essential boundary conditions), involving both the field quantity and its
first derivatives simultaneously. By considering several plate problems it
is observed that GRKPM yields solutions of higher accuracy than those
obtained using the conventional approach, while for a desired accuracy the
number of particles needed in GRKPM is much less than in the traditional
methodology.
Center of Excellence in Structures
and Earthquake Engineering
Department of Civil Engineering
Sharif University of Technology
P.O. Box 11365-9311
Tehran, Iran
Center of Excellence in Structures
and Earthquake Engineering
Department of Civil Engineering
Sharif University of Technology
P.O. Box 11365-9311
Tehran, Iran
