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Volume 8, Issue 3
Uniform Convergence Analysis of a Higher Order Hybrid Stress Quadrilateral Finite Element Method for Linear Elasticity Problems

Yanhong Bai, Yongke Wu & Xiaoping Xie

Adv. Appl. Math. Mech., 8 (2016), pp. 399-425.

Published online: 2018-05

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  • Abstract

This paper derives a higher order hybrid stress finite element method on quadrilateral meshes for linear plane elasticity problems. The method employs continuous piecewise bi-quadratic functions in local coordinates to approximate the displacement vector and a piecewise-independent 15-parameter mode to approximate the stress tensor. Error estimation shows that the method is free from Poisson-locking and has second-order accuracy in the energy norm. Numerical experiments confirm the theoretical results.

  • Keywords

Linear elasticity, hybrid stress finite element, Poisson-locking, second-order accuracy.

  • AMS Subject Headings

65N12, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-8-399, author = {Yanhong and Bai and and 19675 and and Yanhong Bai and Yongke and Wu and and 19676 and and Yongke Wu and Xiaoping and Xie and and 19677 and and Xiaoping Xie}, title = {Uniform Convergence Analysis of a Higher Order Hybrid Stress Quadrilateral Finite Element Method for Linear Elasticity Problems}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {3}, pages = {399--425}, abstract = {

This paper derives a higher order hybrid stress finite element method on quadrilateral meshes for linear plane elasticity problems. The method employs continuous piecewise bi-quadratic functions in local coordinates to approximate the displacement vector and a piecewise-independent 15-parameter mode to approximate the stress tensor. Error estimation shows that the method is free from Poisson-locking and has second-order accuracy in the energy norm. Numerical experiments confirm the theoretical results.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2014.m548}, url = {http://global-sci.org/intro/article_detail/aamm/12095.html} }
TY - JOUR T1 - Uniform Convergence Analysis of a Higher Order Hybrid Stress Quadrilateral Finite Element Method for Linear Elasticity Problems AU - Bai , Yanhong AU - Wu , Yongke AU - Xie , Xiaoping JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 399 EP - 425 PY - 2018 DA - 2018/05 SN - 8 DO - http://doi.org/10.4208/aamm.2014.m548 UR - https://global-sci.org/intro/article_detail/aamm/12095.html KW - Linear elasticity, hybrid stress finite element, Poisson-locking, second-order accuracy. AB -

This paper derives a higher order hybrid stress finite element method on quadrilateral meshes for linear plane elasticity problems. The method employs continuous piecewise bi-quadratic functions in local coordinates to approximate the displacement vector and a piecewise-independent 15-parameter mode to approximate the stress tensor. Error estimation shows that the method is free from Poisson-locking and has second-order accuracy in the energy norm. Numerical experiments confirm the theoretical results.

Yanhong Bai, Yongke Wu & Xiaoping Xie. (2020). Uniform Convergence Analysis of a Higher Order Hybrid Stress Quadrilateral Finite Element Method for Linear Elasticity Problems. Advances in Applied Mathematics and Mechanics. 8 (3). 399-425. doi:10.4208/aamm.2014.m548
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