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.

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.

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.

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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