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Jun Hu, Hongying Man, Shangyou Zhang (2013)
The simplest mixed finite element method for linear elasticity in the symmetric formulation on $n$-rectangular gridsarXiv: Numerical Analysis
D. Arnold, Gerard Awanou, R. Winther (2007)
Finite elements for symmetric tensors in three dimensionsMath. Comput., 77
(2012)
The Finite Element Method: Linear Static and Dynamic Finite Element Analysis
E. Reissner (1950)
On a Variational Theorem in ElasticityJournal of Mathematics and Physics, 29
T. Belytschko, Wing Liu, B. Moran (2000)
Nonlinear Finite Elements for Continua and Structures
Jay Gopalakrishnan, J. Guzmán (2011)
Symmetric Nonconforming Mixed Finite Elements for Linear ElasticitySIAM J. Numer. Anal., 49
I. Babuska, J. Oden, J. Lee (1977)
Mixed-hybrid finite element approximations of second-order elliptic boundary-value problemsComputer Methods in Applied Mechanics and Engineering, 11
(2011)
Variational Principles with Multi-variables and Finite Elements with Multi-variables
Astrid Sinwel (2009)
A New Family of Mixed Finite Elements for Elasticity: A Robust Computational Method for Mechanical Problems
W. Qiu, L. Demkowicz (2010)
Variable Order Mixed H-Finite Element Method for Linear Elasticity with Weakly Imposed Symmetry. Ii. Affine and Curvilinear Elements in 2DarXiv: Numerical Analysis
L. Herrmann (1967)
Finite-Element Bending Analysis for PlatesJournal of Engineering Mechanics-asce, 93
WZ Chien (1983)
Method of high-order lagrange multiplier and generalized variational principles of elasticity with more general forms of functionalsAppl. Math. Mech., 4
(2007)
Force, Work, Energy and Symplectic Mathematics
(1997)
Nonlinear ContinuumMechanics for Finite Element Analysis
(1996)
Exact Theory of Laminated Thick Plates and Shells
Dr.-Ing. Talaslidis (1979)
On the Convergence of a Mixed Finite Element Approximation for Cylindrical ShellsZamm-zeitschrift Fur Angewandte Mathematik Und Mechanik, 59
T. Pian (1964)
Derivation of element stiffness matrices by assumed stress distributionsAIAA Journal, 2
R. Taylor, Peter. Beresford, E. Wilson (1976)
A non-conforming element for stress analysisInternational Journal for Numerical Methods in Engineering, 10
S. Hoa, W. Feng (1998)
Hybrid Finite Element Method for Stress Analysis of Laminated Composites
Y. Cheung, Chen Wanji (1988)
Isoparametric hybrid hexahedral elements for three dimensional stress analysisInternational Journal for Numerical Methods in Engineering, 26
J. Oden, J. Reddy (1976)
On Mixed Finite Element ApproximationsSIAM Journal on Numerical Analysis, 13
D. Arnold, R. Winther (2002)
Mixed finite elements for elasticityNumerische Mathematik, 92
JT Oden JN Reddy (1975)
Mathematical theory of mixed finite element approximationsQuart. Appl. Math, 33
D. Arnold (1990)
Mixed finite element methods for elliptic problemsApplied Mechanics and Engineering, 82
S. Blau (2016)
Analysis Of The Finite Element Method
F. Brezzi (1974)
On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers, 8
RL Taylor (2000)
The Finite Element Method: Solid Mechanics
D.N. Arnold (2002)
Differential complexes and numerical stability. Preprint. arXiv:math/0212391
ZD Liu (2006)
Basis of Mixed Finite Element Methods and Its Application
M. Morley (1989)
A family of mixed finite elements for linear elasticityNumerische Mathematik, 55
C. Felippa (1989)
Parametrized multifield variational principles in elasticity: II. Hybrid functionals and the free formulationCommunications in Applied Numerical Methods, 5
W. Qiu (2010)
Variable order mixed $$h$$-finite element method for linear elasticity with weakly imposed symmetry. II. Affine and curvilinear elements in 2D. Mathematics 11
OC Zienkiewicz (1983)
Hybrid and Mixed Finite Element Methods
Jun-Jue Hu, Hongying Man, Jianye Wang, Shangyou Zhang (2016)
The simplest nonconforming mixed finite element method for linear elasticity in the symmetric formulation on n-rectangular gridsComput. Math. Appl., 71
S. Adams, Bernardo Cockburn (2005)
A Mixed Finite Element Method for Elasticity in Three DimensionsJournal of Scientific Computing, 25
Chien Wei-zang (1983)
Method of high-order lagrange multiplier and generalized variational principles of elasticity with more general forms of functionalsApplied Mathematics and Mechanics, 4
C. Felippa (1989)
Parametrized multifield variational principles in elasticity: I. Mixed functionalsCommunications in Applied Numerical Methods, 5
G. Gatica, Antonio Márquez, S. Meddahi (2008)
A new dual-mixed finite element method for the plane linear elasticity problem with pure traction boundary conditions☆Computer Methods in Applied Mechanics and Engineering, 197
J. Roberts, Jean-Marie Thomas (1987)
Mixed and hybrid finite element methods
R. Cook (1987)
A plane hybrid element with rotational d.o.f. and adjustable stiffnessInternational Journal for Numerical Methods in Engineering, 24
D. Arnold, R. Falk, R. Winther (2007)
Mixed finite element methods for linear elasticity with weakly imposed symmetryMath. Comput., 76
(1976)
A high preccision eight-node hexahedron element
W. Qiu, L. Demkowicz (2011)
Mixed variable order h-finite element method for linear elasticity with weakly imposed symmetry. Curvilinear elements in 2D, 11
D. Arnold (2002)
Differential complexes and numerical stabilityarXiv: Numerical Analysis
A. Sinwel (2009)
A new family of mixed finite elements for elasticity. [Ph.D. Thesis]
Abstract Without applying any stable element techniques in the mixed methods, two simple generalized mixed element (GME) formulations were derived by combining the minimum potential energy principle and Hellinger–Reissner (H–R) variational principle. The main features of the GME formulations are that the common \(C_{0}\)-continuous polynomial shape functions for displacement methods are used to express both displacement and stress variables, and the coefficient matrix of these formulations is not only automatically symmetric but also invertible. Hence, the numerical results of the generalized mixed methods based on the GME formulations are stable. Displacement as well as stress results can be obtained directly from the algebraic system for finite element analysis after introducing stress and displacement boundary conditions simultaneously. Numerical examples show that displacement and stress results retain the same accuracy. The results of the noncompatible generalized mixed method proposed herein are more accurate than those of the standard noncompatible displacement method. The noncompatible generalized mixed element is less sensitive to element geometric distortions.
"Acta Mechanica Sinica" – Springer Journals
Published: Apr 1, 2018
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