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Volume 23, Issue 1
On Locking-Free Finite Element Schemes for Three-Dimensional Elasticity

He Qi, Lie-Heng Wang & Wei-Ying Zheng

J. Comp. Math., 23 (2005), pp. 101-112.

Published online: 2005-02

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  • Abstract

In the present paper, the authors discuss the locking phenomenon of the finite element method for three-dimensional elasticity as the Lamé constant $\lambda \rightarrow\infty$. Three kinds of finite elements are proposed and analyzed to approximate the three-dimensional elasticity with pure displacement boundary condition. Optimal order error estimates which are uniform with respect to $\lambda\in (0,+\infty)$ are obtained for three schemes. Furthermore, numerical results are presented to show that, our schemes are locking-free and and the trilinear conforming finite element scheme is locking.  

  • Keywords

Three-dimensional elasticity, Locking-free, Nonconforming finite element.

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-23-101, author = {He Qi, Lie-Heng Wang and Wei-Ying Zheng}, title = {On Locking-Free Finite Element Schemes for Three-Dimensional Elasticity}, journal = {Journal of Computational Mathematics}, year = {2005}, volume = {23}, number = {1}, pages = {101--112}, abstract = {

In the present paper, the authors discuss the locking phenomenon of the finite element method for three-dimensional elasticity as the Lamé constant $\lambda \rightarrow\infty$. Three kinds of finite elements are proposed and analyzed to approximate the three-dimensional elasticity with pure displacement boundary condition. Optimal order error estimates which are uniform with respect to $\lambda\in (0,+\infty)$ are obtained for three schemes. Furthermore, numerical results are presented to show that, our schemes are locking-free and and the trilinear conforming finite element scheme is locking.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8800.html} }
TY - JOUR T1 - On Locking-Free Finite Element Schemes for Three-Dimensional Elasticity AU - He Qi, Lie-Heng Wang & Wei-Ying Zheng JO - Journal of Computational Mathematics VL - 1 SP - 101 EP - 112 PY - 2005 DA - 2005/02 SN - 23 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8800.html KW - Three-dimensional elasticity, Locking-free, Nonconforming finite element. AB -

In the present paper, the authors discuss the locking phenomenon of the finite element method for three-dimensional elasticity as the Lamé constant $\lambda \rightarrow\infty$. Three kinds of finite elements are proposed and analyzed to approximate the three-dimensional elasticity with pure displacement boundary condition. Optimal order error estimates which are uniform with respect to $\lambda\in (0,+\infty)$ are obtained for three schemes. Furthermore, numerical results are presented to show that, our schemes are locking-free and and the trilinear conforming finite element scheme is locking.  

He Qi, Lie-Heng Wang and Wei-Ying Zheng. (2005). On Locking-Free Finite Element Schemes for Three-Dimensional Elasticity. Journal of Computational Mathematics. 23 (1). 101-112. doi:
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