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 = {}, 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 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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