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Uniform Convergence Analysis of a Higher Order Hybrid Stress Quadrilateral Finite Element Method for Linear Elasticity Problems

Part of: Partial differential equations, boundary value problems

Published online by Cambridge University Press:  27 January 2016

Yanhong Bai ,
Yongke Wu  and
Xiaoping Xie
Yanhong Bai
Affiliation:
School of Mathematics, Sichuan University, Chengdu 610064, China
Yongke Wu
Affiliation:
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China Institute of Structure Mechanical, China Academy of Engineering Physics, Mianyang 621900, China
Xiaoping Xie*
Affiliation:
School of Mathematics, Sichuan University, Chengdu 610064, China
*
*Corresponding author. Email: baiyanhong1982@126.com (Y. H. Bai), wuyongke1982@uestc.edu.cn (Y. K. Wu), xpxie@scu.edu.cn (X. P. Xie)
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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 elasticityhybrid stress finite elementPoisson-lockingsecond-order accuracy

MSC classification

Secondary: 65N12: Stability and convergence of numerical methods 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 3 , June 2016 , pp. 399 - 425
Copyright
Copyright © Global-Science Press 2016 

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