Quadratically consistent one-point (QC1) quadrature for meshfree Galerkin methods

Qinglin Duan; Xikui Li; Hongwu ZhangBingbing WangXin Gao

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Quadratically consistent one-point (QC1) quadrature for meshfree Galerkin methods

机译：Quadratically consistent one-point (QC1) quadrature for meshfree Galerkin methods

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摘要

A robust and efficient integration method, named quadratically consistent one-point (QC1) scheme, which evaluates the Galerkin weak form only at the centers of background triangle elements (cells) is proposed for meshfree methods using quadratic basis. The strain at the evaluation points is approximated by corrected (smoothed) nodal derivatives which are determined by a discrete form of the divergence theorem between nodal shape functions and their derivatives in Taylor's expansion. We prove that such smoothed nodal derivatives also meet the differentiation of the approximation consistency (DAC). The same Taylor's expansion is applied to the weak form and the smoothed nodal derivatives are used to compute the stiffness matrix. The proposed QC1 scheme can pass both the linear and the quadratic patch tests exactly in a numerical sense. Several examples are provided to demonstrate its better numerical performance in terms of convergence, accuracy, efficiency and stability over other one-point integration methods in the meshfree literature, especially its superiority over the existing linearly consistent one-point (LC1) quadratures.

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来源
《Computer Methods in Applied Mechanics and Engineering》 |2012年第15期|256-272|共17页
作者
Qinglin Duan; Xikui Li; Hongwu ZhangBingbing WangXin Gao;
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作者单位

The State key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, Liaoning 1! 6024, PR China Department of Engineering Mechanics, Dalian University of Technology, Dalian, Liaoning U6024, PR China,Department;

The State key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, Liaoning 1! 6024, PR China Department of Engineering Mechanics, Dalian University of Technology, Dalian, Liaoning U6024, PR China;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种英语
中图分类自动化基础理论;
关键词
meshfree; integration; quadrature; SCNI; consistency; hourglass;

Quadratically consistent one-point (QC1) quadrature for meshfree Galerkin methods

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