An edge-based smoothed three-node mindlin plate element (ES-MIN3) for static and free vibration analyses of plates

2014 ◽  
Vol 18 (4) ◽  
pp. 1072-1082 ◽  
Author(s):  
T. Nguyen-Thoi ◽  
T. Bui-Xuan ◽  
P. Phung-Van ◽  
S. Nguyen-Hoang ◽  
H. Nguyen-Xuan
Keyword(s):  
Free Vibration ◽  
Mindlin Plate ◽  
Plate Element ◽  
Edge Based

An Extended Cell-Based Smoothed Three-Node Mindlin Plate Element (XCS-MIN3) for Free Vibration Analysis of Cracked FGM Plates

2017 ◽  
Vol 14 (02) ◽  
pp. 1750011 ◽  
Author(s):  
T. Nguyen-Thoi ◽  
T. Rabczuk ◽  
V. Ho-Huu ◽  
L. Le-Anh ◽  
H. Dang-Trung ◽  
...  
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Mindlin Plate ◽  
Plate Element ◽  
Softening Effect ◽  
Strain Smoothing ◽  
Graded Material ◽  
A Cell

A cell-based smoothed three-node Mindlin plate element (CS-MIN3) was recently proposed and proven to be robust for static and free vibration analyses of Mindlin plates. The method improves significantly the accuracy of the solution due to softening effect of the cell-based strain smoothing technique. In addition, it is very flexible to apply for arbitrary complicated geometric domains due to using only three-node triangular elements which can be easily generated automatically. However so far, the CS-MIN3 has been only developed for isotropic material and for analyzing intact structures without possessing internal cracks. The paper hence tries to extend the CS-MIN3 by integrating itself with functionally graded material (FGM) and enriched functions of the extended finite element method (XFEM) to give a so-called extended cell-based smoothed three-node Mindlin plate (XCS-MIN3) for free vibration analysis of cracked FGM plates. Three numerical examples with different conditions are solved and compared with previous published results to illustrate the accuracy and reliability of the XCS-MIN3 for free vibration analysis of cracked FGM plates.

Smoothing Technique Based Beta FEM (βFEM) for Static and Free Vibration Analyses of Reissner–Mindlin Plates

2019 ◽  
Vol 17 (02) ◽  
pp. 1845006 ◽  
Author(s):  
F. Wu ◽  
W. Zeng ◽  
L. Y. Yao ◽  
M. Hu ◽  
Y. J. Chen ◽  
...  
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Steel Plate ◽  
Free Vibration Analysis ◽  
Mindlin Plate ◽  
Shear Locking ◽  
Smoothing Technique ◽  
Smoothed Finite Element Method ◽  
Edge Based ◽  
Good Agreement

Recently, the edge-based and node-based smoothed finite element method (ES-FEM and NS-FEM) has been proposed for Reissner–Mindlin plate problems. In this work, in order to utilize the numerical advantages of both ES-FEM and NS-FEM for static and vibration analysis, a hybrid smoothing technique based beta FEM ([Formula: see text]FEM) is presented for Reissner–Mindlin plate problems. A tunable parameter [Formula: see text] is introduced to tune the proportion of smoothing domains calculated by ES-FEM or NS-FEM, which controlled the accuracy of the results. Numerical illustrations in both static and free vibration analysis are conducted. The shear locking free property, converge property and dynamic stability are carefully examined via several well-known benchmark examples. Moreover, an experimental test is carefully designed and conducted for validations, in which the mode values and shape of a rectangular steel plate is tested. Numerical examples demonstrate the advantages of [Formula: see text]FEM, in comparison with the standard FEM, ES-FEM and NS-FEM using the same meshes. The numerical and experimental results are in good agreement with each other and the [Formula: see text]FEM achieves the best accuracy among all the methods for the static or free vibration analysis of plates.

Edge-Based Smoothed Three-Node Mindlin Plate Element

2016 ◽  
Vol 142 (9) ◽  
pp. 04016055 ◽  
Author(s):  
Wei Li ◽  
Xiangyu You ◽  
Yingbin Chai ◽  
Tianyun Li
Keyword(s):  
Mindlin Plate ◽  
Plate Element ◽  
Edge Based

A cell-based smoothed three-node Mindlin plate element (CS-MIN3) for static and free vibration analyses of plates

2012 ◽  
Vol 51 (1) ◽  
pp. 65-81 ◽  
Author(s):  
T. Nguyen-Thoi ◽  
P. Phung-Van ◽  
H. Luong-Van ◽  
H. Nguyen-Van ◽  
H. Nguyen-Xuan
Keyword(s):  
Free Vibration ◽  
Mindlin Plate ◽  
Plate Element ◽  
A Cell

Free vibration analysis of rectangular and annular Mindlin plates with undamaged and damaged boundaries by the spectral collocation method

2011 ◽  
Vol 18 (11) ◽  
pp. 1722-1736 ◽  
Author(s):  
Ma’en S Sari ◽  
Eric A Butcher
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Collocation Method ◽  
Vibration Analysis ◽  
Natural Vibration ◽  
Numerical Technique ◽  
Free Vibration Analysis ◽  
Mindlin Plate ◽  
Grid Points ◽  
Matrix Vector

The objective of this paper is the development of a new numerical technique for the free vibration analysis of isotropic rectangular and annular Mindlin plates with damaged boundaries. For this purpose, the Chebyshev collocation method is applied to obtain the natural frequencies of Mindlin plates with damaged clamped boundary conditions, where the governing equations and boundary conditions are discretized by the presented method and put into matrix vector form. The damaged boundaries are represented by distributed translational and torsional springs. In the present study the boundary conditions are coupled with the governing equation to obtain the eigenvalue problem. Convergence studies are carried out to determine the sufficient number of grid points used. First, the results obtained for the undamaged plates are verified with previous results in the literature. Subsequently, the results obtained for the damaged Mindlin plate indicate the behavior of the natural vibration frequencies with respect to the severity of the damaged boundary. This analysis can lead to an efficient technique for structural health monitoring of structures in which joint or boundary damage plays a significant role in the dynamic characteristics. The results obtained from the Chebychev collocation solutions are seen to be in excellent agreement with those presented in the literature.

Static analysis of corrugated panels using homogenization models and a cell-based smoothed mindlin plate element (CS-MIN3)

2018 ◽  
Vol 13 (2) ◽  
pp. 251-272 ◽  
Author(s):  
Nhan Nguyen-Minh ◽  
Nha Tran-Van ◽  
Thang Bui-Xuan ◽  
Trung Nguyen-Thoi
Keyword(s):  
Static Analysis ◽  
Mindlin Plate ◽  
Plate Element ◽  
A Cell

Coupled Analysis of Structural–Acoustic Problems Using the Cell-Based Smoothed Three-Node Mindlin Plate Element

2016 ◽  
Vol 13 (02) ◽  
pp. 1640007 ◽  
Author(s):  
Z. X. Gong ◽  
Y. B. Chai ◽  
W. Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Solid Mechanics ◽  
Mindlin Plate ◽  
Coupled Analysis ◽  
Plate Element ◽  
Fem Model ◽  
The Face ◽  
Smoothed Finite Element Method ◽  
Element Method

The cell-based smoothed finite element method (CS-FEM) using the original three-node Mindlin plate element (MIN3) has recently established competitive advantages for analysis of solid mechanics problems. The three-node configuration of the MIN3 is achieved from the initial, complete quadratic deflection via ‘continuous’ shear edge constraints. In this paper, the proposed CS-FEM-MIN3 is firstly combined with the face-based smoothed finite element method (FS-FEM) to extend the range of application to analyze acoustic fluid–structure interaction problems. As both the CS-FEM and FS-FEM are based on the linear equations, the coupled method is only effective for linear problems. The cell-based smoothed operations are implemented over the two-dimensional (2D) structure domain discretized by triangular elements, while the face-based operations are implemented over the three-dimensional (3D) fluid domain discretized by tetrahedral elements. The gradient smoothing technique can properly soften the stiffness which is overly stiff in the standard FEM model. As a result, the solution accuracy of the coupled system can be significantly improved. Several superior properties of the coupled CS-FEM-MIN3/FS-FEM model are illustrated through a number of numerical examples.

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