Access the full text.
Sign up today, get DeepDyve free for 14 days.
Xinwei Zhou, G. Cusatis (2015)
Tetrahedral Finite Element with Rotational Degrees of Freedom for Cosserat and Cauchy Continuum ProblemsJournal of Engineering Mechanics-asce, 141
(1961)
Fundamental equations of the theory of elastic media with rotationally interacting particles
R. Gauthier, W. Jahsman (1975)
A Quest for Micropolar Elastic ConstantsJournal of Applied Mechanics, 42
(2004)
Incompatible finite element for materials with strain gradient effects
J. Simo, M. Rifai (1990)
A CLASS OF MIXED ASSUMED STRAIN METHODS AND THE METHOD OF INCOMPATIBLE MODESInternational Journal for Numerical Methods in Engineering, 29
R. Mindlin (1965)
Stress functions for a Cosserat continuumInternational Journal of Solids and Structures, 1
Wenxiong Huang, Ke Xu (2015)
Characteristic lengths in Cosserat continuum modeling of granular materialsEngineering Computations, 32
R. Mindlin, N. Eshel (1968)
On first strain-gradient theories in linear elasticityInternational Journal of Solids and Structures, 4
J. Caseiro, R. Valente, A. Reali, J. Kiendl, F. Auricchio, R. Sousa (2014)
On the Assumed Natural Strain method to alleviate locking in solid-shell NURBS-based finite elementsComputational Mechanics, 53
Hongwu Zhang, Hui Wang, Guo-qing Liu (2005)
Quadrilateral isoparametric finite elements for plane elastic Cosserat bodiesActa Mechanica Sinica, 21
K. Sze, H. Fan (1996)
An economical assumed stress brick element and its implementationFinite Elements in Analysis and Design, 21
C. Truesdell, R. Toupin (1960)
The Classical Field Theories, 2
Pei Zhou, S. Cen, Junbin Huang, Chenfeng Li, Qun Zhang (2017)
An unsymmetric 8‐node hexahedral element with high distortion toleranceInternational Journal for Numerical Methods in Engineering, 109
Changsheng Wang, Xiangkui Zhang, P. Hu (2016)
A 4-node quasi-conforming quadrilateral element for couple stress theory immune to distorted meshComputers & Structures, 175
(1965)
Continuum theory of asymmetric elasticity: equilibrium of an isotropic body
R. Taylor, Peter. Beresford, E. Wilson (1976)
A non-conforming element for stress analysisInternational Journal for Numerical Methods in Engineering, 10
K. Sze, X. Liu, S. Lo (2004)
Hybrid‐stress six‐node prismatic elementsInternational Journal for Numerical Methods in Engineering, 61
T. Pian, K. Sumihara (1984)
Rational approach for assumed stress finite elementsInternational Journal for Numerical Methods in Engineering, 20
Sara Grbčić, A. Ibrahimbegovic, G. Jelenić (2018)
Variational formulation of micropolar elasticity using 3D hexahedral finite-element interpolation with incompatible modesComputers & Structures
Xupeng Ma, Wan-ji Chen (2013)
Refined 18-DOF triangular hybrid stress element for couple stress theoryFinite Elements in Analysis and Design, 75
A. Zervos (2008)
Finite elements for elasticity with microstructure and gradient elasticityInternational Journal for Numerical Methods in Engineering, 73
A. Eringen (1965)
LINEAR THEORY OF MICROPOLAR ELASTICITY, 15
O. Zienkiewicz, R. Taylor, J. Zhu (2005)
The Finite Element Method: Its Basis and Fundamentals
R. Taylor, J. Simo, O. Zienkiewicz, A. Chan (1986)
The patch test—a condition for assessing FEM convergenceInternational Journal for Numerical Methods in Engineering, 22
M. Godio, I. Stefanou, K. Sab, J. Sulem (2015)
Dynamic finite element formulation for Cosserat elastic platesInternational Journal for Numerical Methods in Engineering, 101
A. Soh, Chen Wanji (2004)
Finite element formulations of strain gradient theory for microstructures and the C0–1 patch testInternational Journal for Numerical Methods in Engineering, 61
K. Sze, A. Ghali (1992)
A TWO‐FIELD SOLID ELEMENT SUITING THIN‐MESH ANALYSIS BY ADMISSIBLE MATRIX FORMULATIONEngineering Computations, 9
R. Ansari, A. Shakouri, Majid Bazdid-Vahdati, A. Norouzzadeh, H. Rouhi (2017)
A Nonclassical Finite Element Approach for the Nonlinear Analysis of Micropolar PlatesJournal of Computational and Nonlinear Dynamics, 12
Hybrid and Mixed Finite Element Methods, 1
K. Bathe (1995)
Finite Element Procedures
R. Mindlin, H. Tiersten (1962)
Effects of couple-stresses in linear elasticityArchive for Rational Mechanics and Analysis, 11
Q. Xie, K. Sze, Y. Zhou, Y. Zhou (2014)
Modified and Trefftz unsymmetric finite element modelsInternational Journal of Mechanics and Materials in Design, 12
Chang-Koon Choi, Eun-Jin Lee (2004)
Nonconforming Variable-Node Axisymmetric Solid ElementJournal of Engineering Mechanics-asce, 130
S. Bauer, M. Schäfer, P. Grammenoudis, C. Tsakmakis (2010)
Three-dimensional finite elements for large deformation micropolar elasticityComputer Methods in Applied Mechanics and Engineering, 199
R. Lakes (1993)
Materials with structural hierarchyNature, 361
A. Eringen, P. Paslay (1962)
Nonlinear theory of continuous media
Yan Shang, Wengen Ouyang (2018)
4‐node unsymmetric quadrilateral membrane element with drilling DOFs insensitive to severe mesh‐distortionInternational Journal for Numerical Methods in Engineering, 113
W. Nowacki (1986)
Theory of Micropolar Elasticity
K. Sze, L. Yao, T. Pian (2002)
An eighteen-node hybrid-stress solid-shell element for homogeneous and laminated structuresFinite Elements in Analysis and Design, 38
E. Providas, M. Kattis (2002)
Finite element method in plane Cosserat elasticityComputers & Structures, 80
W. Koiter (1964)
Couple-Stress in the Theory of Elasticity, 67
Der-Uei Yang, F. Huang (2001)
Analysis of Poisson’s ratio for a micropolar elastic rectangular plate using the finite element methodEngineering Computations, 18
K. Sze, S. Zheng, S. Lo (2004)
A stabilized eighteen-node solid element for hyperelastic analysis of shellsFinite Elements in Analysis and Design, 40
T. Pian, P. Tong (1986)
Relations between incompatible displacement model and hybrid stress modelInternational Journal for Numerical Methods in Engineering, 22
Zhi Li, S. Cen, Cheng‐jin Wu, Yan Shang, Chenfeng Li (2018)
High‐performance geometric nonlinear analysis with the unsymmetric 4‐node, 8‐DOF plane element US‐ATFQ4International Journal for Numerical Methods in Engineering, 114
A. Bilotta, R. Casciaro (2002)
Assumed stress formulation of high order quadrilateral elements with an improved in-plane bending behaviourComputer Methods in Applied Mechanics and Engineering, 191
H. Neuber (1966)
On the general solution of linear-elastic problems in isotropic and anisotropic Cosserat continua
Poor bending response is a major shortcoming of lower-order elements due to excessive representation of shear stress/strain field. Advanced finite element (FE) formulations for classical elasticity enhance the bending response by either nullifying or filtering some of the symmetric shear stress/strain modes. Nevertheless, the stress/strain field in Cosserat elasticity is asymmetric; consequently any attempt to nullify or filter the anti-symmetric shear stress/strain modes may lead to failure in the constant couple-stress patch test where the anti-symmetric shear stress/strain field is linear. This paper aims at enhancing the bending response of lower-order elements for Cosserat elasticity problems.Design/methodology/approachA four-node quadrilateral and an eight-node hexahedron are formulated by hybrid-stress approach. The symmetric stress is assumed as those of Pian and Sumihara and Pian and Tong. The anti-symmetric stress components are first assumed to be completely linear in order to pass the constant couple-stress patch test. The linear modes are then constrained with respect to the prescribed body-couple via the equilibrium conditions.FindingsNumerical tests show that the hybrid elements can strictly pass the constant couple-stress patch test and are markedly more accurate than the conventional elements as well as the incompatible elements for bending problems in Cosserat elasticity.Originality/valueThis paper proposes a hybrid FE formulation to improve the bending response of four-node quadrilateral and eight-node hexahedral elements for Cosserat elasticity problems without compromising the constant couple-stress patch test.
Engineering Computations: International Journal for Computer-Aided Engineering and Software – Emerald Publishing
Published: Aug 15, 2019
Keywords: Cosserat; Finite element; Hybrid; Couple-stress; Anti-symmetric stress
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.