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Load versus displacement curves for three-story frame
Z. Zhou, S. Chan (1997)
SECOND-ORDER ANALYSIS OF SLENDER STEEL FRAMES UNDER DISTRIBUTED AXIAL AND MEMBER LOADSJournal of Structural Engineering-asce, 123
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Finite rotation analysis and consistent linearization using projectorsComputer Methods in Applied Mechanics and Engineering, 93
P. Khosravi, R. Ganesan, R. Sedaghati (2007)
Corotational non‐linear analysis of thin plates and shells using a new shell elementInternational Journal for Numerical Methods in Engineering, 69
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Large-deflection analysis of shell structure by using corotational total lagrangian formulationComputer Methods in Applied Mechanics and Engineering, 73
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An enhanced co‐rotational approach for large displacement analysis of platesInternational Journal for Numerical Methods in Engineering, 64
K. Bathe, E. Dvorkin, L. Ho (1983)
Our discrete-Kirchhoff and isoparametric shell elements for nonlinear analysis—An assessmentComputers & Structures, 16
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An excursion into large rotationsComputer Methods in Applied Mechanics and Engineering, 32
Y. Tang, Z. Zhou, S. Chan (2017)
A simplified co‐rotational method for quadrilateral shell elements in geometrically nonlinear analysisInternational Journal for Numerical Methods in Engineering, 112
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Collapse of thin shell structures—stress resultant plasticity modelling within a co-rotated ANDES finite element formulationInternational Journal for Numerical Methods in Engineering, 46
Siu-Lai Chan, Z. Zhou (1995)
SECOND-ORDER ELASTIC ANALYSIS OF FRAMES USING SINGLE IMPERFECT ELEMENT PER MEMBERJournal of Structural Engineering-asce, 121
M. Crisfield (1990)
A consistent co-rotational formulation for non-linear, three-dimensional, beam-elementsComputer Methods in Applied Mechanics and Engineering, 81
Y. Tang, Z. Zhou, Siu-Lai Chan (2015)
Nonlinear Beam-Column Element Under Consistent DeformationInternational Journal of Structural Stability and Dynamics, 15
K. Bathe, S. Bolourchi (1980)
A geometric and material nonlinear plate and shell elementComputers & Structures, 11
Zuo-lei Du, Yao-Peng Liu, Siu-Lai Chan (2017)
A second-order flexibility-based beam-column element with member imperfectionEngineering Structures, 143
Zhongxue Lia, Bassam Izzuddinb, Loc Vu-Quocb, Zihan Ronga, Xin Zhuoa (2017)
A 3-node co-rotational triangular elasto-plastic shell element using vectorial rotational variables
Y. Tang, Yao-Peng Liu, Siu-Lai Chan, Er-feng Du (2019)
An innovative co-rotational pointwise equilibrating polynomial element based on Timoshenko beam theory for second-order analysisThin-Walled Structures
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Hyeong-Min Jeon, Youngyu Lee, Phill-Seung Lee, K. Bathe (2015)
The MITC3+ shell element in geometric nonlinear analysisComputers & Structures, 146
Hsiao Kuo-Mo (1987)
Nonlinear analysis of general shell structures by flat triangular shell elementComputers & Structures, 25
R. Taylor, R.L.Taylor, O. Zienkiewicz (2013)
The Finite Element Method for Solid and Structural Mechanics
Yeong-Bin Yang, Hwa‐Thong Chiou (1987)
Rigid Body Motion Test for Nonlinear Analysis with Beam ElementsJournal of Engineering Mechanics-asce, 113
Lei Jiang, M. Chernuka, N. Pegg (1994)
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C. Rankin, F. Brogan (1986)
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K. Bathe (1995)
Finite Element Procedures
Z. Li, Tao Li, L. Vu-Quoc, B. Izzuddin, X. Zhuo, Q. Fang (2018)
A nine‐node corotational curved quadrilateral shell element for smooth, folded, and multishell structuresInternational Journal for Numerical Methods in Engineering, 116
K. Surana (1983)
Geometrically nonlinear formulation for the curved shell elementsInternational Journal for Numerical Methods in Engineering, 19
E. Dvorkin, K. Bathe (1984)
A continuum mechanics based four‐node shell element for general non‐linear analysisEngineering Computations, 1
P. Khosravi, R. Ganesan, R. Sedaghati (2008)
An efficient facet shell element for corotational nonlinear analysis of thin and moderately thick laminated composite structuresComputers & Structures, 86
Y. Tang, Z. Zhou, Siu-Lai Chan (2016)
Geometrically nonlinear analysis of shells by quadrilateral flat shell element with drill, shear, and warpingInternational Journal for Numerical Methods in Engineering, 108
A. Neuenhofer, F. Filippou (1997)
Evaluation of Nonlinear Frame Finite-Element ModelsJournal of Structural Engineering-asce, 123
A. Neuenhofer, F. Filippou (1998)
Geometrically Nonlinear Flexibility-Based Frame Finite ElementJournal of Structural Engineering-asce, 124
Siu-Lai Chan, Z. Zhou (1994)
Pointwise Equilibrating Polynomial Element for Nonlinear Analysis of FramesJournal of Structural Engineering-asce, 120
Jean-Marc Battini (2002)
Co-rotational beam elements in instability problems
J. Meek, H. Tan (1983)
LARGE DEFLECTION AND POST-BUCKLING ANALYSIS OF TWO AND THREE DIMENSIONAL ELASTIC SPATIAL FRAMES
Conventional co-rotational formulations for geometrically nonlinear analysis are based on the assumption that the finite element is only subjected to nodal loads and as a result, they are not accurate for the elements under distributed member loads. The magnitude and direction of member loads are treated as constant in the global coordinate system, but they are essentially varying in the local coordinate system for the element undergoing a large rigid body rotation, leading to the change of nodal moments at element ends. Thus, there is a need to improve the co-rotational formulations to allow for the effect. This paper proposes a new consistent co-rotational formulation for both Euler-Bernoulli and Timoshenko two-dimensional beam-column elements subjected to distributed member loads. It is found that the equivalent nodal moments are affected by the element geometric change and consequently contribute to a part of geometric stiffness matrix. From this study, the results of both eigenvalue buckling and second-order direct analyses will be significantly improved. Several examples are used to verify the proposed formulation with comparison of the traditional method, which demonstrate the accuracy and reliability of the proposed method in buckling analysis of frame structures under distributed member loads using a single element per member.
Advances in Structural Engineering – SAGE
Published: Jul 1, 2021
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