Development of the Cell-based Smoothed Discrete Shear Gap Plate Element (CS-FEM-DSG3) using Three-Node Triangles

2015 ◽  
Vol 12 (04) ◽  
pp. 1540015 ◽  
Author(s):  
T. Nguyen-Thoi ◽  
M. H. Nguyen-Thoi ◽  
T. Vo-Duy ◽  
N. Nguyen-Minh
Keyword(s):  
Static Analysis ◽  
Free Vibration Analysis ◽  
Composite Plates ◽  
Functionally Graded ◽  
Triangular Element ◽  
Plate Element ◽  
Strain Smoothing ◽  
Discrete Shear Gap ◽  
Transverse Shear Locking ◽  
Coarse Meshes

The paper presents the formulation and recent development of the cell-based smoothed discrete shear gap plate element (CS-FEM-DSG3) using three-node triangles. In the CS-FEM-DSG3, each triangular element will be divided into three sub-triangles, and in each sub-triangle, the original plate element DSG3 is used to compute the strains and to avoid the transverse shear locking. Then the cell-based strain smoothing technique (CS-FEM) is used to smooth the strains on these three sub-triangles. The numerical examples illustrate four superior properties of the CS-FEM-DSG3 including: (1) being a strong competitor to many existing three-node triangular plate elements in the static analysis; (2) giving high accurate solutions for problems with skew geometries in the static analysis; (3) giving high accurate solutions in free vibration analysis; (4) providing accurate values of high frequencies of plates by using only coarse meshes. Due to its superior and simple properties, the CS-FEM-DSG3 has been now developed for various analyses such as: flat shells, stiffened plates, functionally graded plates, composite plates, piezoelectricity composite plates, cracked plate and plates resting on the viscoelastic foundation subjected to moving loads, etc.

Static and Free Vibration Analyses of Functionally Graded Carbon Nanotube Reinforced Composite Plates using CS-DSG3

2019 ◽  
Vol 17 (03) ◽  
pp. 1850133 ◽  
Author(s):  
T. Truong-Thi ◽  
T. Vo-Duy ◽  
V. Ho-Huu ◽  
T. Nguyen-Thoi
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Free Vibration ◽  
Numerical Solutions ◽  
Composite Plates ◽  
Functionally Graded ◽  
Triangular Element ◽  
Reinforced Composite ◽  
Strain Smoothing ◽  
Discrete Shear Gap

This study presents an extension of the cell-based smoothed discrete shear gap method (CS-DSG3) using three-node triangular elements for the static and free vibration analyses of carbon nanotube reinforced composite (CNTRC) plates. The single-walled carbon nanotubes (SWCNTs) are assumed to be uniformly distributed (UD) and functionally graded (FG) distributed along the thickness direction. The material properties of carbon nanotube-reinforced composite plates are estimated according to the rule of mixture. The governing equations are developed based on the first-order shear deformation plate theory (FSDT). In the CS-DSG3, each triangular element will be divided into three sub-triangles, and in each sub-triangle, the stabilized discrete shear gap method is used to compute the strains and to avoid the transverse shear locking. Then the strain smoothing technique on the whole triangular element is used to smooth the strains on these three sub-triangles. Effects of several parameters, such as the different distribution of carbon nanotubes (CNTs), nanotube volume fraction, boundary condition and width-to-thickness ratio of plates are investigated. In addition, the effect of various orientation angles of CNTs is also examined in detail. The accuracy and reliability of the proposed method are verified by comparing its numerical solutions with those of other available results in the literature.

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.

scholarly journals A new finite element for free vibration analysis of stiffened composite plates

2007 ◽  
Vol 29 (4) ◽  
pp. 529-538 ◽  
Author(s):  
Tran Ich Thinh ◽  
Ngo Nhu Khoa
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Plate Theory ◽  
Free Vibration Analysis ◽  
Composite Plates ◽  
Laminated Plates ◽  
Triangular Element ◽  
Plate Element ◽  
Stiffened Plate

A new 6-noded stiffened triangular plate element for the analysis of stiffened composite plates based on Mindlins deformation plate theory has been developed. The stiffened plate element is a combination of basic triangular element and bar component. The element can accommodate any number of arbitrarily oriented stiffeners and obviates the use of mesh lines along the stiffeners. Free vibration analyses of stiffened laminated plates have been carried out with this element and the results are compared with those published. The finite element results show very good matching with the experimental ones.

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.

scholarly journals An edge-based smoothed finite element for buckling analysis of functionally graded material variable-thickness plates

2021 ◽  
Author(s):  
Tran Trung Thanh ◽  
Tran Van Ke ◽  
Pham Quoc Hoa ◽  
Tran The Van ◽  
Nguyen Thoi Trung
Keyword(s):  
Finite Element ◽  
Variable Thickness ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Triangular Element ◽  
Stiffness Matrices ◽  
Strain Smoothing ◽  
Graded Material ◽  
Smoothed Finite Element Method ◽  
Edge Based

The paper aims to extend the ES-MITC3 element, which is an integration of the edge-based smoothed finite element method (ES-FEM) with the mixed interpolation of tensorial components technique for the three-node triangular element (MITC3 element), for the buckling analysis of the FGM variable-thickness plates subjected to mechanical loads. The proposed ES-MITC3 element is performed to eliminate the shear locking phenomenon and to enhance the accuracy of the existing MITC3 element. In the ES-MITC3 element, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains formed by two adjacent MITC3 triangular elements sharing the same edge. The numerical results demonstrated that the proposed method is reliable and more accurate than some other published solutions in the literature. The influences of some geometric parameters, material properties on the stability of FGM variable-thickness plates are examined in detail.

A NEW TRIANGULAR ELEMENT BASED ON HIGHER ORDER SHEAR DEFORMATION THEORY FOR FLEXURAL VIBRATION OF COMPOSITE PLATES

2002 ◽  
Vol 02 (02) ◽  
pp. 163-184 ◽  
Author(s):  
A. CHAKRABARTI ◽  
A. H. SHEIKH
Keyword(s):  
Shear Deformation ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Plate Theory ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Composite Plates ◽  
Higher Order ◽  
Triangular Element

A triangular element based on Reddy's higher order shear deformation theory is developed for free vibration analysis of composite plates. In the Reddy's plate theory, the transverse shear stress varies in a parabolic manner across the plate thickness and vanishes at the top and bottom surfaces of the plate. Moreover, it does not involve any additional unknowns. Thus the plate theory is quite simple and elegant. Unfortunately, such an attractive plate theory cannot be exploited as expected in finite element analysis, primarily due to the difficulties in satisfying the inter-element continuity requirement. This has inspired us to develop the present element, which has three corner nodes and three mid-side nodes with the same number of degrees of freedom. To demonstrate the performance of the element, numerical examples of isotropic and composite plates under different situations are solved. The results are compared with the analytical solutions and other published results, which show the accuracy and range of applicability of the proposed element in the problem of vibration analysis.

Analytical investigation on nonlinear dynamic behavior and free vibration analysis of laminated nanocomposite plates

2019 ◽  
Vol 233 (19-20) ◽  
pp. 6866-6878 ◽  
Author(s):  
Nguyen Dinh Khoa ◽  
Pham Dinh Nguyen
Keyword(s):  
Carbon Nanotubes ◽  
Dynamic Behavior ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Geometrical Nonlinearity ◽  
Free Vibration Analysis ◽  
Composite Plates ◽  
Analytical Investigation ◽  
Functionally Graded ◽  
Geometrical Parameters

This work presents the results of the dynamic behavior and natural frequencies of laminated polymer plates that are reinforced by carbon nanotubes. The laminated nanocomposite plates have two components: carbon nanotubes reinforced in different polymer matrices. The nonlinear equations are obtained by Reddy's third-order laminated plate theory with von Kármán's geometrical nonlinearity and solved by both Runge–Kutta and Galerkin methods. Detailed studies for the influences of carbon nanotubes' different types of reinforcements and weight fractions, geometrical parameters, Winkler and Pasternak foundations on the deflection–time curves, and natural frequencies of laminated functionally graded carbon nanotube-reinforced composite plates are examined.

An Edge-Based Smoothed Discrete Shear Gap Method for Static and Free Vibration Analyses of FG-CNTRC Plates

2019 ◽  
Vol 16 (04) ◽  
pp. 1850102 ◽  
Author(s):  
T. Nguyen-Quoc ◽  
S. Nguyen-Hoai ◽  
D. Mai-Duc
Keyword(s):  
Free Vibration ◽  
Material Properties ◽  
Volume Fraction ◽  
Plate Theory ◽  
Functionally Graded ◽  
Correction Factors ◽  
Reinforced Composite ◽  
Strain Smoothing ◽  
Edge Based ◽  
Discrete Shear Gap

In this paper, an edge-based smoothed stabilized discrete shear gap method (ES-DSG) is integrated with the C0-type high-order shear deformation plate theory (C0-HSDT) for free vibration and static analyses of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates. The material properties of FG-CNTRC are assumed to be graded through the thickness direction according to several distributions of the volume fraction of carbon nanotubes (CNTs). The stiffness formulation of the ES-DSG based on C0-HSDT is performed by using the strain smoothing technique over the smoothing domains associated with edges of elements. This hence does not require shear correction factors. The accuracy and reliability of the proposed method are confirmed in several numerical examples.

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

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 684 ◽  
Author(s):  
Tien Dat Pham ◽  
Quoc Hoa Pham ◽  
Van Duc Phan ◽  
Hoang Nam Nguyen ◽  
Van Thom Do
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Smoothing Technique ◽  
Strain Smoothing ◽  
Smoothed Finite Element Method ◽  
Edge Based

An edge-based smoothed finite element method (ES-FEM) combined with the 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.

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