A local gradient smoothing method for solving strong form governing equation

Abstract

The gradient smoothing method(GSM) is used to approximate the derivatives of the meshfree shape function and it usually generates the smoothing domain by connecting the midpoints of sides and centroids of elements around the interested node. In order to simplify the generating process and geometric computation of smoothing domain, a local gradient smoothing method (LGSM) has been proposed in which the local smoothing domains corresponding to the nodes are independent of each other. The proposed method is very flexible to generate the smoothing domain, which can have a simple and regular shape. The derivatives of the meshfree shape function approximated by the proposed method was applied to the governing strong from of system equations at all nodes of problem domain. The convergence and accuracy of the proposed method according to the size of smoothing domain are examined. Numerical examples to some typical benchmark problems illustrated the efficiency of the proposed method.