Damping analysis of composite plates with zig-zag triangular element

AIAA Journal ◽  
2002 ◽  
Vol 40 ◽  
pp. 1211-1219
Author(s):  
D. G. Lee ◽  
J. B. Kosmatka
Keyword(s):  
Composite Plates ◽  
Triangular Element

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.

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.

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 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.

Higher Order Global-Local Theory Coupled Bending and Extension for Laminated Composite Plates and Refined Element Methods

2006 ◽  
Author(s):  
Wanji Chen ◽  
Zhen Wu
Keyword(s):  
Transverse Shear ◽  
Composite Plates ◽  
Higher Order ◽  
Laminated Plates ◽  
Triangular Element ◽  
Local Theory ◽  
Weak Continuity ◽  
Shear Stresses ◽  
Thickness Direction ◽  
Transverse Shear Stresses

In this paper an augmented higher order global-local theories are presented to analyze the laminated plate problems coupled bending and extension. The in-plane displacement field is composed of a mth-order (9 > m > 3) polynomial of global coordinate z in the thickness direction and 1,2-3 order power series of local coordinate ζk in the thickness direction of each layer and a nth-order (5 > n >= 0) polynomial of global coordinate z in the thickness direction of transverse deflection. The transverse shear stresses can satisfy continuity at interfaces, and the number of unknowns is independent of the layer numbers of the laminate. Based on this theory, a refined three-node triangular element satisfying the requirement of C1 weak-continuity is presented. Numerical results show that present theory can be used to predict accurately in-plane stresses and transverse shear stresses from direct use of the relations of stresses and strains without any postprocessing method. However, to accurately obtain transverse normal stresses, the local equilibrium equation approach in one element is employed herein. It is effective when the number of layers of laminated plates is more than five and up to fourteen, and it can solve the problems for coupling bending and extension. It is also shown that the present refined triangular element possesses higher accuracy.

Damping Analysis of Composite Plates with Zig-Zag Triangular Element

AIAA Journal ◽  
2002 ◽  
Vol 40 (6) ◽  
pp. 1211-1219 ◽  
Author(s):  
D. G. Lee ◽  
J. B. Kosmatka
Keyword(s):  
Composite Plates ◽  
Triangular Element

Free Flexural Vibration of Composite Plates in Different Situations Using a High Precision Triangular Element

2004 ◽  
Vol 10 (3) ◽  
pp. 371-386 ◽  
Author(s):  
A. H. Sheikh ◽  
S. Haldar ◽  
D. Sengupta
Keyword(s):  
High Precision ◽  
Mass Matrix ◽  
Free Vibration Analysis ◽  
Flexural Vibration ◽  
Composite Plates ◽  
Triangular Element ◽  
Transverse Displacement ◽  
Lumped Mass ◽  
Concentrated Mass ◽  
Independent Field

A high precision, thick-plate element developed by D. Sengupta has been applied to the free vibration analysis of laminated composite plates with necessary addition and modification. The effect of shear deformation has been incorporated in the formulation, taking the transverse displacement and rotations of the normal as independent field variables. These are approximated with polynomials of different orders, which has made the element free from locking in shear. The element contains internal nodes. The degrees of freedom of these nodes have been eliminated through condensation in its final form. To facilitate the condensation, an efficient mass lumping scheme has been recommended to form the mass matrix having zero mass for the internal nodes. Recommendation has also been made for the inclusion of the rotary inertia in the lumped mass matrix. Numerical examples of plates having different shapes, boundary conditions, thickness ratios, fiber orientations and number of layers have been solved. Examples of plates having internal cutout and concentrated mass have also been studied. The results obtained in all cases have been compared with those obtained from other sources to show the accuracy and range of applicability of the element.

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