Download this article
Download this article For screen
For printing
Recent Issues

Volume 17, 1 issue

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 8 issues

Volume 7, 10 issues

Volume 6, 9 issues

Volume 5, 6 issues

Volume 4, 10 issues

Volume 3, 10 issues

Volume 2, 10 issues

Volume 1, 8 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1559-3959
Author Index
To Appear
 
Other MSP Journals
A Hermite interpolation element-free Galerkin method for elasticity problems

Xiao Ma, Bo Zhou, Yingjie Li and Shifeng Xue

Vol. 17 (2022), No. 1, 75–95
Abstract

We propose a Hermite interpolation element-free Galerkin method (HIEFGM) for elasticity problems by combining the Hermite approximation approach and an improved interpolation element-free Galerkin method (IIEFGM). The approximation function of the field quantity is constructed based on the moving least-squares method and the Hermite approximation approach. Employing the constitutive equation, geometric equation and Galerkin integral weak form, the discretization equation of the HIEFGM of elasticity problems is established. The proposed method considers the normal derivative of the displacements of boundary nodes in function approximation, so the accuracy of the IIEFGM is improved without increasing the number of nodes. Furthermore, the shape function has the property of a Kronecker delta function, which avoids the problems in dealing with the essential boundary condition. In numerical examples, the effects of the weight function, scaling factor, node density and node arrangement in accuracy and stability of the HIEFGM are discussed and the applicability of the HIEFGM is evaluated through comparing the present results with those of other available methods. The results suggest that the HIEFGM can effectively solve various elasticity problems with excellent accuracy and stability.

Keywords
meshless method, element-free Galerkin method, Hermite approximate approach, normal derivative, elasticity problem
Milestones
Received: 30 August 2021
Revised: 25 October 2021
Accepted: 3 November 2021
Published: 23 October 2022
Authors
Xiao Ma
College of Pipeline and Civil Engineering
China University of Petroleum (East China)
Qingdao
China
School of Mechanical and Automotive Engineering
Qingdao University of Technology
Qingdao
China
Bo Zhou
College of Pipeline and Civil Engineering
China University of Petroleum (East China)
Qingdao
China
Yingjie Li
CNPC Offshore Engineering Company Limited
Beijing
China
Shifeng Xue
College of Pipeline and Civil Engineering
China University of Petroleum (East China)
Qingdao
China