Isogeometric symmetric Galerkin boundary element method for three-dimensional elasticity problems

authored by: B. H. Nguyen, X. Zhuang, P. Wriggers, T. Rabczuk, M. E. Mear, H. D. Tran
Abstract: The isogeometric analysis (IGA) is applied for the weakly singular symmetric Galerkin boundary element method (SGBEM) to analyzelinear elastostatics problems in three-dimensional domains. The background of the proposed method is to use non-uniform rational B-splines (NURBS) as the basis functions for the approximation of both geometry and field variables (i.e. displacement and traction) of the governing integral equations. Same as weakly singular SGBEM, the basic ingredient of the method is a pair of weakly singular weak-form integral equations for the displacement and traction on the boundary of the domain. These integral equations are solved approximately using standard Galerkin approximation. In addition to the advantages that IGA owned, the proposed method exploits the common boundary representation of CAD model and boundary element method. Various numerical examples of both simple and complex geometries are examined to validate the accuracy and efficiency of the proposed method. Through the numerical examples, it is observed that the IGA–SGBEM produces highly accurate results.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Bauhaus-Universität Weimar
University of Texas at Austin
Vietnamese-German University (VGU)
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 323
Pages: 132-150
No. of pages: 19
ISSN: 0045-7825
Publication date: 19.05.2017
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanics of Materials, Mechanical Engineering, General Physics and Astronomy, Computer Science Applications
Electronic version(s): https://doi.org/10.1016/j.cma.2017.05.011 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{71cda67168f14bf1af0ec0101284dcb1,
title = "Isogeometric symmetric Galerkin boundary element method for three-dimensional elasticity problems",
abstract = "The isogeometric analysis (IGA) is applied for the weakly singular symmetric Galerkin boundary element method (SGBEM) to analyzelinear elastostatics problems in three-dimensional domains. The background of the proposed method is to use non-uniform rational B-splines (NURBS) as the basis functions for the approximation of both geometry and field variables (i.e. displacement and traction) of the governing integral equations. Same as weakly singular SGBEM, the basic ingredient of the method is a pair of weakly singular weak-form integral equations for the displacement and traction on the boundary of the domain. These integral equations are solved approximately using standard Galerkin approximation. In addition to the advantages that IGA owned, the proposed method exploits the common boundary representation of CAD model and boundary element method. Various numerical examples of both simple and complex geometries are examined to validate the accuracy and efficiency of the proposed method. Through the numerical examples, it is observed that the IGA–SGBEM produces highly accurate results.",
keywords = "CAD/CAE integration, IGA–SGBEM, Isogeometric analysis, Symmetric Galerkin BEM, Three-dimensional, Weakly singular",
author = "Nguyen, {B. H.} and X. Zhuang and P. Wriggers and T. Rabczuk and Mear, {M. E.} and Tran, {H. D.}",
year = "2017",
month = may,
day = "19",
doi = "10.1016/j.cma.2017.05.011",
language = "English",
volume = "323",
pages = "132--150",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
}