Consistent element‐free Galerkin method. (7th April 2014)

• Record Type: Journal Article
• Authors: Duan, Qinglin; Gao, Xin; Wang, Bingbing; Li, Xikui; Zhang, Hongwu; Belytschko, Ted; Shao, Yulong
• Is Part Of: International journal for numerical methods in engineering. Volume 99:Number 2(2014)
• Page Start: 79
• Page End: 101
• Publication Date: 2014-04-07
• Subjects: Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.4661
• Languages: English
• ISSNs: 0029-5981

Abstract

<abstract abstract-type="main" id="nme4661-abs-0001"> <title>SUMMARY</title> <p id="nme4661-para-0001">An element‐free Galerkin (EFG) method with linear, quadratic and cubic approximations, which can exactly, in a numerical sense, pass the corresponding patch tests is proposed and is named as consistent EFG (CEFG) method. The development of this method is based on the Hu–Washizu three‐field variational principle. Numerical integration schemes with corrected nodal derivatives at quadrature points are proposed according to the satisfaction of the orthogonality condition between stress and strain difference. Thus, the method is variationally consistent. The consistency of the corrected nodal derivatives and the satisfaction of patch test conditions are theoretically proved and also numerically validated. Numerical results show that the proposed CEFG method greatly improves the numerical performance of the EFG method in terms of accuracy, convergence, efficiency and stability, especially the proposed cubic CEFG method, which shows exceptional accuracy and convergence. Copyright © 2014 John Wiley &amp; Sons, Ltd.</p> </abstract>