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Free Vibration Analysis of Functionally Graded Shells Using an Edge-Based Smoothed Finite Element Method

1,Quoc Hoa Pham 1, 2, 3,* and 1
1
Faculty of Mechanical Engineering, Le Quy Don Technical University, Ha Noi 100000, Vietnam
2
Center of Excellence for Automation and Precision Mechanical Engineering, Nguyen Tat Thanh University, Ho Chi Minh 700000, Vietnam
3
Modeling Evolutionary Algorithms Simulation and Artificial Intelligence, Faculty of Electrical & Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(5), 684; https://doi.org/10.3390/sym11050684
Received: 7 March 2019 / Revised: 2 May 2019 / Accepted: 7 May 2019 / Published: 17 May 2019
(This article belongs to the Special Issue Finite Elements and Symmetry)
PDF [1158 KB, uploaded 17 May 2019]

Abstract

: An edge-based smoothed finite element method (ES-FEM) combined withthe mixed interpolation of tensorial components technique for triangular shell element (MITC3), called ES-MITC3, for free vibration analysis of functionally graded shells is investigated in this work. In the formulation of the ES-MITC3, the stiffness matrices are obtained by using the strain-smoothing technique over the smoothing domains that are formed by two adjacent MITC3 triangular shell elements sharing an edge. The strain-smoothing technique can improve significantly the accuracy and convergence of the original MITC3. The material properties of functionally graded shells are assumed to vary through the thickness direction by a power–rule distribution of volume fractions of the constituents.The numerical examples demonstrated that the present ES-MITC3method is free of shear locking and achieves the high accuracy compared to the reference solutions in the literature.
Keywords: FGMshells; edge-based smoothed finite element method (ES-FEM);mixed interpolation of tensorial components (MITC) FGMshells; edge-based smoothed finite element method (ES-FEM);mixed interpolation of tensorial components (MITC)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Pham, T.D.; Phan, V.D.; Nguyen, H.N.; Do, V.T. Free Vibration Analysis of Functionally Graded Shells Using an Edge-Based Smoothed Finite Element Method. Symmetry 2019, 11, 684.

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