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Volume 34, Issue 4
An Adaptive Hybrid Stress Transition Quadrilateral Finite Element Method for Linear Elasticity

Feiteng Huang, Xiaoping Xie & Chensong Zhang

DOI: 10.4208/jcm.1511-m4496

J. Comp. Math., 34 (2016), pp. 339-364.

Published online: 2016-08

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  • Abstract

In this paper, we discuss an adaptive hybrid stress finite element method on quadrilateral meshes for linear elasticity problems. To deal with hanging nodes arising in the adaptive mesh refinement, we propose new transition types of hybrid stress quadrilateral elements with 5 to 7 nodes. In particular, we derive a priori error estimation for the 5-node transition hybrid stress element to show that it is free from Poisson-locking, in the sense that the error bound in the a priori estimate is independent of the Lamé constant λ. We introduce, for quadrilateral meshes, refinement/coarsening algorithms, which do not require storing the refinement tree explicitly, and give an adaptive algorithm. Finally, we provide some numerical results.

  • Keywords

Hybrid stress element, Transition element, Adaptive method, Quadrilateral mesh, Poisson-locking, Plane elasticity.

  • AMS Subject Headings

65N12, 65N15, 65N30.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

hftenger@gmail.com (Feiteng Huang)

xpxie@scu.edu.cn (Xiaoping Xie)

zhangcs@lsec.cc.ac.cn (Chensong Zhang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-34-339, author = {Huang , FeitengXie , Xiaoping and Zhang , Chensong}, title = {An Adaptive Hybrid Stress Transition Quadrilateral Finite Element Method for Linear Elasticity}, journal = {Journal of Computational Mathematics}, year = {2016}, volume = {34}, number = {4}, pages = {339--364}, abstract = {

In this paper, we discuss an adaptive hybrid stress finite element method on quadrilateral meshes for linear elasticity problems. To deal with hanging nodes arising in the adaptive mesh refinement, we propose new transition types of hybrid stress quadrilateral elements with 5 to 7 nodes. In particular, we derive a priori error estimation for the 5-node transition hybrid stress element to show that it is free from Poisson-locking, in the sense that the error bound in the a priori estimate is independent of the Lamé constant λ. We introduce, for quadrilateral meshes, refinement/coarsening algorithms, which do not require storing the refinement tree explicitly, and give an adaptive algorithm. Finally, we provide some numerical results.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1511-m4496}, url = {http://global-sci.org/intro/article_detail/jcm/9800.html} }
TY - JOUR T1 - An Adaptive Hybrid Stress Transition Quadrilateral Finite Element Method for Linear Elasticity AU - Huang , Feiteng AU - Xie , Xiaoping AU - Zhang , Chensong JO - Journal of Computational Mathematics VL - 4 SP - 339 EP - 364 PY - 2016 DA - 2016/08 SN - 34 DO - http://doi.org/10.4208/jcm.1511-m4496 UR - https://global-sci.org/intro/article_detail/jcm/9800.html KW - Hybrid stress element, Transition element, Adaptive method, Quadrilateral mesh, Poisson-locking, Plane elasticity. AB -

In this paper, we discuss an adaptive hybrid stress finite element method on quadrilateral meshes for linear elasticity problems. To deal with hanging nodes arising in the adaptive mesh refinement, we propose new transition types of hybrid stress quadrilateral elements with 5 to 7 nodes. In particular, we derive a priori error estimation for the 5-node transition hybrid stress element to show that it is free from Poisson-locking, in the sense that the error bound in the a priori estimate is independent of the Lamé constant λ. We introduce, for quadrilateral meshes, refinement/coarsening algorithms, which do not require storing the refinement tree explicitly, and give an adaptive algorithm. Finally, we provide some numerical results.

Huang , FeitengXie , Xiaoping and Zhang , Chensong. (2016). An Adaptive Hybrid Stress Transition Quadrilateral Finite Element Method for Linear Elasticity. Journal of Computational Mathematics. 34 (4). 339-364. doi:10.4208/jcm.1511-m4496
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