An alternative alpha finite element method with discrete shear gap technique for analysis of isotropic Mindlin-Reissner plates

N. Nguyen-Thanh; Timon Rabczuk; H. Nguyen-Xuan; S. Bordas

doi:10.1016/j.finel.2011.01.004

An alternative alpha finite element method with discrete shear gap technique for analysis of isotropic Mindlin-Reissner plates

N. Nguyen-Thanh, Timon Rabczuk, H. Nguyen-Xuan, S. Bordas

Research output: Contribution to journal › Article › peer-review

63 Citations (Scopus)

Abstract

An alternative alpha finite element method (AαFEM) coupled with a discrete shear gap technique for triangular elements is presented to significantly improve the accuracy of the standard triangular finite elements for static, free vibration and buckling analyses of MindlinReissner plates. In the AαFEM, the piecewise constant strain field of linear triangular elements is enhanced by additional strain terms with an adjustable parameter α which results in an effectively softer stiffness formulation compared to the linear triangular element. To avoid the transverse shear locking, the discrete shear gap technique (DSG) is utilized and a novel triangular element, the Aα-DSG3 is obtained. Several numerical examples show that the Aα-DSG3 achieves high reliability compared to other existing elements in the literature. Through selection of α, under or over estimation of the strain energy can be achieved.

Original language	English
Pages (from-to)	519-535
Number of pages	17
Journal	Finite Elements in Analysis and Design
Volume	47
Issue number	5
DOIs	https://doi.org/10.1016/j.finel.2011.01.004
Publication status	Published - 2011 May

Bibliographical note

Funding Information:
The author would like to thank the support of “Postgraduate Scholarship Regulation (ThuerGFVO)”. The third author would like to thank the support of the Vietnam National Foundation for Science and Technology Development (NAFOSTED). The support of the Royal Academy of Engineering and of the Leverhulme Trust for the Senior Research Fellowship of Professor Bordas is gratefully acknowledged (Title of the Grant: “Towards the next generation surgical simulators”).

Keywords

Discrete shear gap (DSG)
Finite element method
Plate bending
Smooth finite element method (SFEM)
Transverse shear locking

ASJC Scopus subject areas

Analysis
General Engineering
Computer Graphics and Computer-Aided Design
Applied Mathematics

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10.1016/j.finel.2011.01.004

Cite this

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title = "An alternative alpha finite element method with discrete shear gap technique for analysis of isotropic Mindlin-Reissner plates",

abstract = "An alternative alpha finite element method (AαFEM) coupled with a discrete shear gap technique for triangular elements is presented to significantly improve the accuracy of the standard triangular finite elements for static, free vibration and buckling analyses of MindlinReissner plates. In the AαFEM, the piecewise constant strain field of linear triangular elements is enhanced by additional strain terms with an adjustable parameter α which results in an effectively softer stiffness formulation compared to the linear triangular element. To avoid the transverse shear locking, the discrete shear gap technique (DSG) is utilized and a novel triangular element, the Aα-DSG3 is obtained. Several numerical examples show that the Aα-DSG3 achieves high reliability compared to other existing elements in the literature. Through selection of α, under or over estimation of the strain energy can be achieved.",

keywords = "Discrete shear gap (DSG), Finite element method, Plate bending, Smooth finite element method (SFEM), Transverse shear locking",

author = "N. Nguyen-Thanh and Timon Rabczuk and H. Nguyen-Xuan and S. Bordas",

note = "Funding Information: The author would like to thank the support of “Postgraduate Scholarship Regulation (ThuerGFVO)”. The third author would like to thank the support of the Vietnam National Foundation for Science and Technology Development (NAFOSTED). The support of the Royal Academy of Engineering and of the Leverhulme Trust for the Senior Research Fellowship of Professor Bordas is gratefully acknowledged (Title of the Grant: “Towards the next generation surgical simulators”).",

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AU - Rabczuk, Timon

AU - Nguyen-Xuan, H.

AU - Bordas, S.

N1 - Funding Information: The author would like to thank the support of “Postgraduate Scholarship Regulation (ThuerGFVO)”. The third author would like to thank the support of the Vietnam National Foundation for Science and Technology Development (NAFOSTED). The support of the Royal Academy of Engineering and of the Leverhulme Trust for the Senior Research Fellowship of Professor Bordas is gratefully acknowledged (Title of the Grant: “Towards the next generation surgical simulators”).

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N2 - An alternative alpha finite element method (AαFEM) coupled with a discrete shear gap technique for triangular elements is presented to significantly improve the accuracy of the standard triangular finite elements for static, free vibration and buckling analyses of MindlinReissner plates. In the AαFEM, the piecewise constant strain field of linear triangular elements is enhanced by additional strain terms with an adjustable parameter α which results in an effectively softer stiffness formulation compared to the linear triangular element. To avoid the transverse shear locking, the discrete shear gap technique (DSG) is utilized and a novel triangular element, the Aα-DSG3 is obtained. Several numerical examples show that the Aα-DSG3 achieves high reliability compared to other existing elements in the literature. Through selection of α, under or over estimation of the strain energy can be achieved.

AB - An alternative alpha finite element method (AαFEM) coupled with a discrete shear gap technique for triangular elements is presented to significantly improve the accuracy of the standard triangular finite elements for static, free vibration and buckling analyses of MindlinReissner plates. In the AαFEM, the piecewise constant strain field of linear triangular elements is enhanced by additional strain terms with an adjustable parameter α which results in an effectively softer stiffness formulation compared to the linear triangular element. To avoid the transverse shear locking, the discrete shear gap technique (DSG) is utilized and a novel triangular element, the Aα-DSG3 is obtained. Several numerical examples show that the Aα-DSG3 achieves high reliability compared to other existing elements in the literature. Through selection of α, under or over estimation of the strain energy can be achieved.

KW - Discrete shear gap (DSG)

KW - Finite element method

KW - Plate bending

KW - Smooth finite element method (SFEM)

KW - Transverse shear locking

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An alternative alpha finite element method with discrete shear gap technique for analysis of isotropic Mindlin-Reissner plates

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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