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

被引：19
|
作者：
Bai, Yanhong [1 ]
Wu, Yongke [2 ,3 ]
Xie, Xiaoping [1 ]
机构：
[1] Sichuan Univ, Sch Math, Chengdu 610064, Peoples R China
[2] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 611731, Peoples R China
[3] China Acad Engn Phys, Inst Struct Mech, Mianyang 621900, Peoples R China
来源：
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS | 2016年 / 8卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Linear elasticity; hybrid stress finite element; Poisson-locking; second-order accuracy; RATIONAL APPROACH; HIGH-PERFORMANCE; FORMULATION; STIFFNESS; MODES;
D O I：
10.4208/aamm.2014.m548
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：399 / 425
页数：27
相关论文
共 50 条
  • [21] UNIFORM CONVERGENCE OF FINITE-ELEMENT METHOD
    MCLAY, RW
    JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 1978, 45 (01): : 210 - 211
  • [22] THE ORDER OF CONVERGENCE IN THE FINITE ELEMENT METHOD
    Kim, Chang-Geun
    JOURNAL OF THE KOREAN SOCIETY OF MATHEMATICAL EDUCATION SERIES B-PURE AND APPLIED MATHEMATICS, 2005, 12 (02): : 153 - 159
  • [23] On the convergence of finite element method for second order elliptic interface problems
    Sinha, RK
    Deka, B
    NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2006, 27 (01) : 99 - 115
  • [24] HIGHER ORDER SENSITIVITY ANALYSIS FOR ELASTIC PROBLEMS USING THE MULTIDUAL FINITE ELEMENT METHOD
    Avila, David
    Montoya, Arturo
    Millwater, Harry
    PROCEEDINGS OF ASME 2023 INTERNATIONAL MECHANICAL ENGINEERING CONGRESS AND EXPOSITION, IMECE2023, VOL 13, 2023,
  • [25] The patch recovery for finite element approximation of elasticity problems under quadrilateral meshes
    Shi, Zhong-Ci
    Xu, Xuejun
    Zhang, Zhimin
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2008, 9 (01): : 163 - 182
  • [26] The lowest-order weak Galerkin finite element method for linear elasticity problems on convex polygonal grids
    Wang, Yue
    Gao, Fuzheng
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2024, 132
  • [27] A Stabilized Low Order Finite Element Method for Three Dimensional Elasticity Problems
    Jo, Gwanghyun
    Kwak, Do Y.
    NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2020, 13 (02): : 281 - 295
  • [28] A Conforming Discontinuous Galerkin Finite Element Method for Linear Elasticity Interface Problems
    Wang, Yue
    Gao, Fuzheng
    Cui, Jintao
    JOURNAL OF SCIENTIFIC COMPUTING, 2022, 92 (01)
  • [29] A Conforming Discontinuous Galerkin Finite Element Method for Linear Elasticity Interface Problems
    Yue Wang
    Fuzheng Gao
    Jintao Cui
    Journal of Scientific Computing, 2022, 92
  • [30] Generalized weak Galerkin finite element method for linear elasticity interface problems
    Wang, Yue
    Gao, Fuzheng
    NUMERICAL ALGORITHMS, 2024,
12345