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A local gradient smoothing method for solving strong form governing equation
European Journal of Mechanics - A/Solids ( IF 4.1 ) Pub Date : 2020-07-01 , DOI: 10.1016/j.euromechsol.2020.104073
Songhun Kwak , Kwanghun Kim , Kwangnam Choe , Kumchol Yun

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.



中文翻译:

求解强形式控制方程的局部梯度平滑方法

梯度平滑法(GSM)用于近似无网格形状函数的导数,通常通过连接感兴趣节点周围元素的边和质心的中点来生成平滑域。为了简化平滑域的生成过程和几何计算,提出了一种局部梯度平滑方法(LGSM),其中与节点相对应的局部平滑域彼此独立。所提出的方法在生成平滑域方面非常灵活,该平滑域可以具有简单且规则的形状。将所提方法近似的无网格形状函数的导数应用于问题域所有节点处系统方程的控制强。根据平滑域的大小,检验了所提方法的收敛性和准确性。几个典型基准问题的数值例子说明了该方法的有效性。

更新日期:2020-07-05
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