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research-article

Improvements in the Shear Locking and Spurious Zero Energy Modes by using Chebyshev Finite Element Method

[+] Author and Article Information
Hau Dang-Trung

Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam; Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam; Department of Mathematics, University of Bergen, 5020 Bergen, Norway
dangtrunghau@tdt.edu.vn; dtrhau@gmail.com

Dane Jong Yang

Department of Mechanical and Computer-Aided Engineering, Feng Chia University, No. 100 Wenhwa Rd., Seatwen, Taichung, Taiwan 40724, R.O.C.
mgyu49@yahoo.com.tw

Yu-Cheng Liu

Bachelor Program in Precision System Design, Feng Chia University, No. 100 Wenhwa Rd., Seatwen, Taichung, Taiwan 40724, R.O.C.
yucliu@fcu.edu.tw

1Corresponding author.

ASME doi:10.1115/1.4041829 History: Received April 12, 2018; Revised October 22, 2018

Abstract

In this paper, the authors present a finite element method based on Chebyshev polynomials (CFE) for the analysis of Reissner-Mindlin 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. 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 with several different shapes subjected to different boundary conditions were carried out. Both regular and irregular meshes were considered. The obtained 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 solution even for coarse and irregular meshes.

Copyright (c) 2018 by ASME
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