Details
| Original language | English |
|---|---|
| Pages (from-to) | 1036-1043 |
| Number of pages | 8 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 199 |
| Issue number | 17-20 |
| Publication status | Published - 29 Nov 2010 |
| Externally published | Yes |
Abstract
Partition of unity based finite element methods (PUFEMs) have appealing capabilities for p-adaptivity and local refinement with minimal or even no remeshing of the problem domain. However, PUFEMs suffer from a number of problems that practically limit their application, namely the linear dependence (LD) problem, which leads to a singular global stiffness matrix, and the difficulty with which essential boundary conditions can be imposed due to the lack of the Kronecker delta property. In this paper we develop a new PU-based triangular element using a dual local approximation scheme by treating boundary and interior nodes separately. The present method is free from the LD problem and essential boundary conditions can be applied directly as in the FEM. The formulation uses triangular elements, however the essential idea is readily extendable to other types of meshed or meshless formulation based on a PU approximation. The computational cost of the present method is comparable to other PUFEM elements described in the literature. The proposed method can be simply understood as a PUFEM with composite shape functions possessing the delta property and appropriate compatibility.
Keywords
- Delta property, Dual local approximation, Interpolation, Linear dependence, Meshless, Partition of unity, PUFEM
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- General Physics and Astronomy
- Computer Science(all)
- Computer Science Applications
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In: Computer Methods in Applied Mechanics and Engineering, Vol. 199, No. 17-20, 29.11.2010, p. 1036-1043.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A new partition of unity finite element free from the linear dependence problem and possessing the delta property
AU - Cai, Yongchang
AU - Zhuang, Xiaoying
AU - Augarde, Charles
N1 - Funding information: The authors gratefully acknowledge the support of National Natural Science of China, NSFC ( 10972161 ). The second author is supported by a Dorothy Hodgkin Postgraduate Award from UK EPSRC at Durham University.
PY - 2010/11/29
Y1 - 2010/11/29
N2 - Partition of unity based finite element methods (PUFEMs) have appealing capabilities for p-adaptivity and local refinement with minimal or even no remeshing of the problem domain. However, PUFEMs suffer from a number of problems that practically limit their application, namely the linear dependence (LD) problem, which leads to a singular global stiffness matrix, and the difficulty with which essential boundary conditions can be imposed due to the lack of the Kronecker delta property. In this paper we develop a new PU-based triangular element using a dual local approximation scheme by treating boundary and interior nodes separately. The present method is free from the LD problem and essential boundary conditions can be applied directly as in the FEM. The formulation uses triangular elements, however the essential idea is readily extendable to other types of meshed or meshless formulation based on a PU approximation. The computational cost of the present method is comparable to other PUFEM elements described in the literature. The proposed method can be simply understood as a PUFEM with composite shape functions possessing the delta property and appropriate compatibility.
AB - Partition of unity based finite element methods (PUFEMs) have appealing capabilities for p-adaptivity and local refinement with minimal or even no remeshing of the problem domain. However, PUFEMs suffer from a number of problems that practically limit their application, namely the linear dependence (LD) problem, which leads to a singular global stiffness matrix, and the difficulty with which essential boundary conditions can be imposed due to the lack of the Kronecker delta property. In this paper we develop a new PU-based triangular element using a dual local approximation scheme by treating boundary and interior nodes separately. The present method is free from the LD problem and essential boundary conditions can be applied directly as in the FEM. The formulation uses triangular elements, however the essential idea is readily extendable to other types of meshed or meshless formulation based on a PU approximation. The computational cost of the present method is comparable to other PUFEM elements described in the literature. The proposed method can be simply understood as a PUFEM with composite shape functions possessing the delta property and appropriate compatibility.
KW - Delta property
KW - Dual local approximation
KW - Interpolation
KW - Linear dependence
KW - Meshless
KW - Partition of unity
KW - PUFEM
UR - http://www.scopus.com/inward/record.url?scp=78650678986&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2009.11.019
DO - 10.1016/j.cma.2009.11.019
M3 - Article
AN - SCOPUS:78650678986
VL - 199
SP - 1036
EP - 1043
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
IS - 17-20
ER -