In this paper, the authors present Chebyshev finite element (CFE) method for the analysis of Reissner–Mindlin (RM) plates and shells. Chebyshev polynomials are a sequence of orthogonal polynomials that are defined recursively. The values of the polynomials belong to the interval and vanish at the Gauss points (GPs). Therefore, high-order shape functions, which satisfy the interpolation condition at the points, can be performed with Chebyshev polynomials. Full gauss quadrature rule was used for stiffness matrix, mass matrix and load vector calculations. Static and free vibration analyses of thick and thin plates and shells of different shapes subjected to different boundary conditions were conducted. Both regular and irregular meshes were considered. The results showed that by increasing the order of the shape functions, CFE automatically overcomes shear locking without the formation of spurious zero energy modes. Moreover, the results of CFE are in close agreement with the exact solutions even for coarse and irregular meshes.
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March 2019
Research-Article
Improvements in Shear Locking and Spurious Zero Energy Modes Using Chebyshev Finite Element Method
H. Dang-Trung,
H. Dang-Trung
Division of Computational
Mathematics and Engineering,
Institute for Computational Science,
Ton Duc Thang University,
Ho Chi Minh City 700000, Vietnam;
Faculty of Civil Engineering,
Ton Duc Thang University,
Ho Chi Minh City 700000, Vietnam;
Department of Mathematics,
University of Bergen,
Bergen 5020, Norway
e-mails: dangtrunghau@tdt.edu.vn; dtrhau@gmail.com
Mathematics and Engineering,
Institute for Computational Science,
Ton Duc Thang University,
Ho Chi Minh City 700000, Vietnam;
Faculty of Civil Engineering,
Ton Duc Thang University,
Ho Chi Minh City 700000, Vietnam;
Department of Mathematics,
University of Bergen,
Bergen 5020, Norway
e-mails: dangtrunghau@tdt.edu.vn; dtrhau@gmail.com
Search for other works by this author on:
Dane-Jong Yang,
Dane-Jong Yang
Department of Mechanical and
Computer-Aided Engineering,
Feng Chia University,
No. 100 Wenhwa Road,
Seatwen,
Taichung 40724, Taiwan
e-mail: mgyu49@yahoo.com.tw
Computer-Aided Engineering,
Feng Chia University,
No. 100 Wenhwa Road,
Seatwen,
Taichung 40724, Taiwan
e-mail: mgyu49@yahoo.com.tw
Search for other works by this author on:
Y. C. Liu
Y. C. Liu
Bachelor's Program in Precision System Design,
Feng Chia University,
No. 100 Wenhwa Road,
Seatwen,
Taichung 40724, Taiwan
e-mail: yucliu@fcu.edu.tw
Feng Chia University,
No. 100 Wenhwa Road,
Seatwen,
Taichung 40724, Taiwan
e-mail: yucliu@fcu.edu.tw
Search for other works by this author on:
H. Dang-Trung
Division of Computational
Mathematics and Engineering,
Institute for Computational Science,
Ton Duc Thang University,
Ho Chi Minh City 700000, Vietnam;
Faculty of Civil Engineering,
Ton Duc Thang University,
Ho Chi Minh City 700000, Vietnam;
Department of Mathematics,
University of Bergen,
Bergen 5020, Norway
e-mails: dangtrunghau@tdt.edu.vn; dtrhau@gmail.com
Mathematics and Engineering,
Institute for Computational Science,
Ton Duc Thang University,
Ho Chi Minh City 700000, Vietnam;
Faculty of Civil Engineering,
Ton Duc Thang University,
Ho Chi Minh City 700000, Vietnam;
Department of Mathematics,
University of Bergen,
Bergen 5020, Norway
e-mails: dangtrunghau@tdt.edu.vn; dtrhau@gmail.com
Dane-Jong Yang
Department of Mechanical and
Computer-Aided Engineering,
Feng Chia University,
No. 100 Wenhwa Road,
Seatwen,
Taichung 40724, Taiwan
e-mail: mgyu49@yahoo.com.tw
Computer-Aided Engineering,
Feng Chia University,
No. 100 Wenhwa Road,
Seatwen,
Taichung 40724, Taiwan
e-mail: mgyu49@yahoo.com.tw
Y. C. Liu
Bachelor's Program in Precision System Design,
Feng Chia University,
No. 100 Wenhwa Road,
Seatwen,
Taichung 40724, Taiwan
e-mail: yucliu@fcu.edu.tw
Feng Chia University,
No. 100 Wenhwa Road,
Seatwen,
Taichung 40724, Taiwan
e-mail: yucliu@fcu.edu.tw
Contributed by the Computers and Information Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received April 12, 2018; final manuscript received October 22, 2018; published online November 19, 2018. Assoc. Editor: John Michopoulos.
J. Comput. Inf. Sci. Eng. Mar 2019, 19(1): 011006 (16 pages)
Published Online: November 19, 2018
Article history
Received:
April 12, 2018
Revised:
October 22, 2018
Citation
Dang-Trung, H., Yang, D., and Liu, Y. C. (November 19, 2018). "Improvements in Shear Locking and Spurious Zero Energy Modes Using Chebyshev Finite Element Method." ASME. J. Comput. Inf. Sci. Eng. March 2019; 19(1): 011006. https://doi.org/10.1115/1.4041829
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