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

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.

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

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

Static and Free Vibration Analysis of Stiffened Flat Shells by a Cell-Based Smoothed Discrete Shear Gap Method (CS-FEM-DSG3) Using Three-Node Triangular Elements

2018 ◽  
Vol 15 (06) ◽  
pp. 1850056 ◽  
Author(s):  
T. Nguyen-Thoi ◽  
T. Bui-Xuan ◽  
G. R. Liu ◽  
T. Vo-Duy
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Beam Element ◽  
Triangular Element ◽  
Plate Element ◽  
Smoothing Technique ◽  
A Cell ◽  
Triangular Elements ◽  
Discrete Shear Gap

A cell-based smoothed discrete shear gap method (CS-FEM-DSG3) using three-node triangular element was recently proposed for static, free vibration and buckling analyses of stiffened Mindlin plates. The CS-FEM-DSG3 element is a significant improvement of the original DSG3 element by using smoothing technique to soften the stiffness of the DSG3 element while it has still inherited the locking-free feature of the former. In this paper, the CS-FEM-DSG3 is further extended for the static and free vibration analyses of stiffened flat shells by combining the original plate element CS-FEM-DSG3 with Allman’s plane stress element and a linearly isotropic two-node stiffened beam element. The compatibility of displacement field of stiffeners and shell is applied at the contact positions. Numerical results of the proposed element are compared with those of some existing methods to demonstrate the accuracy and reliability of the proposed method.

A Cell-Based Smoothed Finite Element Method for Free Vibration Analysis of a Rotating Plate

2019 ◽  
Vol 16 (05) ◽  
pp. 1840003 ◽  
Author(s):  
C. F. Du ◽  
D. G. Zhang ◽  
G. R. Liu
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Free Vibration Analysis ◽  
Mindlin Plate ◽  
Smoothed Finite Element Method ◽  
A Cell ◽  
Mindlin Plate Theory ◽  
Rotating Plate

A cell-based smoothed finite element method (CS-FEM) is formulated for nonlinear free vibration analysis of a plate attached to a rigid rotating hub. The first-order shear deformation theory which is known as Mindlin plate theory is used to model the plate. In the process of formulating the system stiffness matrix, the discrete shear gap (DSG) method is used to construct the strains to overcome the shear locking issue. The effectiveness of the CS-FEM is first demonstrated in some static cases and then extended for free vibration analysis of a rotating plate considering the nonlinear effects arising from the coupling of vibration of the flexible structure with the undergoing large rotational motions. The nonlinear coupling dynamic equations of the system are derived via employing Lagrange’s equations of the second kind. The effects of different parameters including thickness ratio, aspect ratio, hub radius ratio and rotation speed on dimensionless natural frequencies are investigated. The dimensionless natural frequencies of CS-FEM are compared with those other existing method including the FEM and the assumed modes method (AMM). It is found that the CS-FEM based on Mindlin plate theory provides more accurate and “softer” solution compared with those of other methods even if using coarse meshes. In addition, the frequency loci veering phenomena associated with the mode shape interaction are examined in detail.

Analyses of Stiffened Plates Resting on Viscoelastic Foundation Subjected to a Moving Load by a Cell-Based Smoothed Triangular Plate Element

2017 ◽  
Vol 17 (01) ◽  
pp. 1750011 ◽  
Author(s):  
H. Dang-Trung ◽  
H. Luong-Van ◽  
T. Nguyen-Thoi ◽  
K. K. Ang
Keyword(s):  
Moving Load ◽  
Shear Deformation Theory ◽  
Dynamic Responses ◽  
Mindlin Plate ◽  
Stiffened Plates ◽  
Viscoelastic Foundation ◽  
Plate Element ◽  
Stiffened Plate ◽  
Numerical Examples ◽  
A Cell

A cell-based smoothed three-node Mindlin plate element (CS-MIN3) based on the first-order shear deformation theory (FSDT) was recently proposed for static and dynamic analyses of Mindlin plates. The CS-MIN3 overcomes shear-locking phenomena and has a faster convergence compared with the original MIN3. In addition, the CS-MIN3 uses only three-node triangular elements that can be easily generated automatically for arbitrary complicated geometric domains. This paper extends the CS-MIN3 by integrating itself with the Timoshenko beam element to give a new stiffened plate element for static, free vibration and dynamic responses of stiffened plates resting on viscoelastic foundation subjected to a moving load. The viscoelastic foundation is modeled by discrete springs and dampers, and the displacement compatible condition between the plate and the stiffener is imposed. Some benchmark numerical examples were performed to illustrate the good agreement of the CS-MIN3 results with those by other methods in the literature to illustrate its accuracy and reliability. In addition, some new numerical examples that consider the effects of stiffeners on the behaviors of plate resting on viscoelastic foundation are conducted. The results demonstrate the expected properties in which the deflection of the stiffened plate resting on viscoelastic foundation can be reduced significantly.

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.

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