当前位置: X-MOL 学术Int. J. Numer. Meth. Eng. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
A nodal integration scheme for meshfree Galerkin methods using the virtual element decomposition
International Journal for Numerical Methods in Engineering ( IF 2.9 ) Pub Date : 2020-05-30 , DOI: 10.1002/nme.6304
R. Silva‐Valenzuela 1, 2, 3 , A. Ortiz‐Bernardin 1, 2 , N. Sukumar 4 , E. Artioli 5 , N. Hitschfeld‐Kahler 6, 7
Affiliation  

In this paper, we present a novel nodal integration scheme for meshfree Galerkin methods that draws on the mathematical framework of the virtual element method. We adopt linear maximum-entropy basis functions for the discretization of field variables, although the proposed scheme is applicable to any linear meshfree approximant. In our approach, the weak form integrals are nodally integrated using nodal representative cells that carry the nodal displacements and state variables such as strains and stresses. The nodal integration is performed using the virtual element decomposition, wherein the bilinear form is decomposed into a consistency part and a stability part that ensure consistency and stability of the method. The performance of the proposed nodal integration scheme is assessed through benchmark problems in linear and nonlinear analyses of solids for small displacements and small-strain kinematics. Numerical results are presented for linear elastostatics and linear elastodynamics, and viscoelasticity. We demonstrate that the proposed nodally integrated meshfree method is accurate, converges optimally, and is more reliable and robust than a standard cell-based Gauss integrated meshfree method.

中文翻译:

使用虚元分解的无网格伽辽金方法的节点积分方案

在本文中,我们提出了一种新的无网格伽辽金方法的节点积分方案,它利用了虚拟元方法的数学框架。我们采用线性最大熵基函数来离散化场变量,尽管所提出的方案适用于任何线性无网格逼近。在我们的方法中,弱形式积分使用承载节点位移和状态变量(如应变和应力)的节点代表单元进行节点积分。节点积分采用虚元分解,其中双线性形式分解为一致性部分和稳定性部分,保证了方法的一致性和稳定性。通过小位移和小应变运动学固体线性和非线性分析中的基准问题来评估所提出的节点集成方案的性能。给出了线性弹性静力学和线性弹性动力学以及粘弹性的数值结果。我们证明了所提出的节点集成无网格方法是准确的,收敛最佳,并且比基于标准单元的高斯集成无网格方法更可靠和稳健。
更新日期:2020-05-30
down
wechat
bug