Volume 16, Issue 4
Quadrilateral Finite Elements for Planar Linear Elasticity Problem with Large Lamé Constant

Xiao-liang Cheng, Hong-ci Huang & Jun Zou

DOI:

J. Comp. Math., 16 (1998), pp. 357-366

Published online: 1998-08

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  • Abstract

In this paper, we discuss the quadrilateral finite element approximation to the two-dimensional linear elasticity problem associated with a homogeneous isotropic elastic material. The optimal convergence of the finite element method is proved for both the $L^2$-norm and energy-norm, and in particular, the convergence is uniform with respect to the Lam\'{e} constant $\lambda$. Also the performance of the scheme does not deteriorate as the material becomes nearly incompressible. Numerical experiments are given which are consistent with our theory.

  • Keywords

Planar linear elasticity optimal error estimates large Lame constant locking phenomenon

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@Article{JCM-16-357, author = {}, title = {Quadrilateral Finite Elements for Planar Linear Elasticity Problem with Large Lamé Constant}, journal = {Journal of Computational Mathematics}, year = {1998}, volume = {16}, number = {4}, pages = {357--366}, abstract = { In this paper, we discuss the quadrilateral finite element approximation to the two-dimensional linear elasticity problem associated with a homogeneous isotropic elastic material. The optimal convergence of the finite element method is proved for both the $L^2$-norm and energy-norm, and in particular, the convergence is uniform with respect to the Lam\'{e} constant $\lambda$. Also the performance of the scheme does not deteriorate as the material becomes nearly incompressible. Numerical experiments are given which are consistent with our theory. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9166.html} }
TY - JOUR T1 - Quadrilateral Finite Elements for Planar Linear Elasticity Problem with Large Lamé Constant JO - Journal of Computational Mathematics VL - 4 SP - 357 EP - 366 PY - 1998 DA - 1998/08 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9166.html KW - Planar linear elasticity KW - optimal error estimates KW - large Lame constant KW - locking phenomenon AB - In this paper, we discuss the quadrilateral finite element approximation to the two-dimensional linear elasticity problem associated with a homogeneous isotropic elastic material. The optimal convergence of the finite element method is proved for both the $L^2$-norm and energy-norm, and in particular, the convergence is uniform with respect to the Lam\'{e} constant $\lambda$. Also the performance of the scheme does not deteriorate as the material becomes nearly incompressible. Numerical experiments are given which are consistent with our theory.
Xiao-liang Cheng, Hong-ci Huang & Jun Zou. (1970). Quadrilateral Finite Elements for Planar Linear Elasticity Problem with Large Lamé Constant. Journal of Computational Mathematics. 16 (4). 357-366. doi:
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