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A new partition of unity finite element free from the linear dependence problem and possessing the delta property

Cai, Yongchang; Zhuang, Xiaoying; Augarde, Charles

A new partition of unity finite element free from the linear dependence problem and possessing the delta property Thumbnail


Authors

Yongchang Cai

Xiaoying Zhuang



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.

Citation

Cai, Y., Zhuang, X., & Augarde, C. (2010). A new partition of unity finite element free from the linear dependence problem and possessing the delta property. Computer Methods in Applied Mechanics and Engineering, 199(17-20), 1036-1043. https://doi.org/10.1016/j.cma.2009.11.019

Journal Article Type Article
Publication Date Jan 1, 2010
Deposit Date May 6, 2010
Publicly Available Date May 7, 2010
Journal Computer Methods in Applied Mechanics and Engineering
Print ISSN 0045-7825
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 199
Issue 17-20
Pages 1036-1043
DOI https://doi.org/10.1016/j.cma.2009.11.019
Keywords Partition of unity, PUFEM, Meshless,Linear dependence, Interpolation, Delta property, Dual local approximation.

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