Abstract
The concept of isogeometric analysis, where functions that are used to describe geometry in CAD software are used to approximate the unknown fields in numerical simulations, has received great attention in recent years. The method has the potential to have profound impact on engineering design, since the task of meshing, which in some cases can add significant overhead, has been circumvented. Much of the research effort has been focused on finite element implementations of the isogeometric concept, but at present, little has been seen on the application to the Boundary Element Method. The current paper proposes an Isogeometric Boundary Element Method (BEM), which we term IGABEM, applied to two-dimensional elastostatic problems using Non-Uniform Rational B-Splines (NURBS). We find it is a natural fit with the isogeometric concept since both the NURBS approximation and BEM deal with quantities entirely on the boundary. The method is verified against analytical solutions where it is seen that superior accuracies are achieved over a conventional quadratic isoparametric BEM implementation.
| Original language | English |
|---|---|
| Pages (from-to) | 87-100 |
| Number of pages | 14 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 209-212 |
| DOIs | |
| Publication status | Published - 2012 Feb 1 |
| Externally published | Yes |
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Keywords
- Boundary Element Method
- Isogeometric analysis
- NURBS
ASJC Scopus subject areas
- Computer Science Applications
- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- Physics and Astronomy(all)
Cite this
A two-dimensional Isogeometric Boundary Element Method for elastostatic analysis. / Simpson, R. N.; Bordas, S. P A; Trevelyan, J.; Rabczuk, Timon.
In: Computer Methods in Applied Mechanics and Engineering, Vol. 209-212, 01.02.2012, p. 87-100.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A two-dimensional Isogeometric Boundary Element Method for elastostatic analysis
AU - Simpson, R. N.
AU - Bordas, S. P A
AU - Trevelyan, J.
AU - Rabczuk, Timon
PY - 2012/2/1
Y1 - 2012/2/1
N2 - The concept of isogeometric analysis, where functions that are used to describe geometry in CAD software are used to approximate the unknown fields in numerical simulations, has received great attention in recent years. The method has the potential to have profound impact on engineering design, since the task of meshing, which in some cases can add significant overhead, has been circumvented. Much of the research effort has been focused on finite element implementations of the isogeometric concept, but at present, little has been seen on the application to the Boundary Element Method. The current paper proposes an Isogeometric Boundary Element Method (BEM), which we term IGABEM, applied to two-dimensional elastostatic problems using Non-Uniform Rational B-Splines (NURBS). We find it is a natural fit with the isogeometric concept since both the NURBS approximation and BEM deal with quantities entirely on the boundary. The method is verified against analytical solutions where it is seen that superior accuracies are achieved over a conventional quadratic isoparametric BEM implementation.
AB - The concept of isogeometric analysis, where functions that are used to describe geometry in CAD software are used to approximate the unknown fields in numerical simulations, has received great attention in recent years. The method has the potential to have profound impact on engineering design, since the task of meshing, which in some cases can add significant overhead, has been circumvented. Much of the research effort has been focused on finite element implementations of the isogeometric concept, but at present, little has been seen on the application to the Boundary Element Method. The current paper proposes an Isogeometric Boundary Element Method (BEM), which we term IGABEM, applied to two-dimensional elastostatic problems using Non-Uniform Rational B-Splines (NURBS). We find it is a natural fit with the isogeometric concept since both the NURBS approximation and BEM deal with quantities entirely on the boundary. The method is verified against analytical solutions where it is seen that superior accuracies are achieved over a conventional quadratic isoparametric BEM implementation.
KW - Boundary Element Method
KW - Isogeometric analysis
KW - NURBS
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U2 - 10.1016/j.cma.2011.08.008
DO - 10.1016/j.cma.2011.08.008
M3 - Article
AN - SCOPUS:83455181910
VL - 209-212
SP - 87
EP - 100
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
ER -