A node-based consistent non-conforming gradient smoothing scheme for highly efficient Galerkin meshfree formulation

Abstract

The stabilized conforming nodal integration (SCNI) is currently widely employed in Galerkin meshfree formulation. A key ingredient of SCNI is the strain or gradient smoothing defined within a set of conforming nodal representative domains, which usually are formed by the auxiliary points in addition to the meshfree nodes. Nonetheless, these auxiliary points may significantly increase the storage requirement and computational cost of SCNI, in comparison with the direct nodal integration. In order to address this issue, a purely node-based consistent non-conforming gradient smoothing (CNGS) scheme is proposed herein to accelerate the Galerkin meshfree computation. In the proposed method, only the meshfree nodes are employed to construct overlapping and non-conforming nodal representative domains, which are then adopted for the nodal gradient smoothing operation. However, unlike the existing non-conforming gradient smoothing algorithms that commonly violate the integration consistency, the proposed method maintains the desirable integration consistency through a proportional separation between the nodal gradient smoothing domains and the nodal integration domains, which essentially ensures the meshfree solution accuracy. Meanwhile, due to the absence of auxiliary points in the gradient smoothing evaluation, the computational efficiency is substantially improved by the proposed method of CNGS compared with SCNI. The effectiveness of the proposed methodology is well demonstrated by numerical results.