• Proceedings of the Korean Society For Composite Materials Conference
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• 2001.05a
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• pp.5-8
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• 2001

A three node flat triangular element incorporating Layerwise Zig-Zag Theory(HZZT) is developed suitable for analyzing damped laminated composite structures. Using an interdependent kinematic relation, the higher order shear rotations are replaced by in-plane displacements, a transverse displacement and section rotations, which result in three translations and two rotations. Natural frequencies and modal loss factors of cantilevered laminated plates with embedded damping layers are calculated with the zig-zag triangular element and compared to the experimental results and MSC/NASTRAN results using a layered combination of plate and solid elements.

• Journal of Advanced Marine Engineering and Technology
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• v.26 no.3
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• pp.344-352
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• 2002

In the analysis of the 3 dimensional plate structures by the finite element method, the triangular elements are generally used for the global stiffness matrix of the analyzed system. But the triangular elements of the plates have some problems in the process of formulation and in the precision of analysis. The formulation of the finite element method to analyze 3 dimensional plate structures using quadrilateral elements is presented in this paper. The degree of freedom off nodal point is 6, that is, the displacements in the direction off-y-z is and the rotations about x-y-z axis and then the degree of freedom off element is 24. For the comparison of the analysis using triangular elements and quadrilateral elements, the rectangular plates subjected to the uniform load and a concentrated load on the centroid of the plate, for which the theoretical solutions have been obtained, are analyzed. The calculated deflections of the rectangular plates using the finite element method by the triangular elements and the quadrilateral elements are also compared with the deflections of the plates calculated by theoretical solutions. The defections of the rectangular plates calculated by the finite element method using the quadrilateral elements are closer to the theoretical solutions than the defections calculated by the finite element method using the triangular elements. The deflection of the centroid of plate, calculated by the finite element method, converges to that of theoretical solution as the number of elements is increased. This convergence is much more rapid for the case of using the quakrilateral elements than fir the case of using triangular elements.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.1
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• pp.29-37
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• 2007

This study deals with displacement analysis of anisotropic folded structures with triangular elements and quadrilateral elements. When folded plates are analyzed, triangular elements as well as quadrilateral elements are needed for conveniences of modelling. However, using triangular elements is not a simple problem. A simple formulation is presented which allows a quadrilateral element to degenerate into a triangular element. Therefore it can easily be used for computational simplicity and avoided complexities on mixed use of triangular element and quadrilateral element. In this paper, a high-order shear deformation theory using only Lagrangian interpolation functions and drilling degrees of freedom for folded plates are utilized for more accurate analysis. Especially, various results of anisotropic laminated and folded composite structures with triangular element and quadrilateral element show the structural behavior characteristics of them.

• Structural Engineering and Mechanics
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• v.60 no.5
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• pp.795-807
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• 2016

This study tries to examine the effect of different parameters on stress analysis of infinite plates with central quasi-triangular cutout using particle swarm optimization (PSO) algorithm and also an attempt has been made to introduce general optimum parameters in order to achieve the minimum amount of stress concentration around this type of cutout on isotropic and orthotropic plates. Basis of the presented method is expansion of analytical method conducted by Lekhnitskii for circular and elliptical cutouts. Design variables in this study include fiber angle, load angle, curvature radius of the corner of the cutout, rotation angle of the cutout and at last material of the plate. Also, diagrams of convergence and duration time of the desired problem are compared with Simulated Annealing algorithm. Conducted comparison is indicative of appropriateness of this method in optimization of the plates. Finite element numerical solution is employed to examine the results of present analytical solution. Overlap of the results of the two methods confirms the validity of the presented solution. Results show that by selecting the aforementioned parameters properly, less amounts of stress can be achieved around the cutout leading to an increase in load-bearing capacity of the structure.

• Structural Engineering and Mechanics
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• v.12 no.2
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• pp.189-200
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• 2001

This paper presents an experimental modal analysis of perforated rectangular plates in air or in contact with water. The penetration of holes in the plates had a triangular pattern with P/D (pitch to diameter) 2.125, 2.500, 3.000 and 3.750. The plate was clamped along the plate edges by a number of bolts and nuts. The natural frequencies of the perforated plates in air were obtained by the analytical method based on the relation between the reference kinetic and maximum potential energies and compared with the experimental results. Good agreement between the results was found for the natural frequencies of the perforated plates in air. Additionally, it was empirically found that the natural frequencies of the perforated plate in air increase with an increase of P/D, on the other hand, the natural frequencies of the perforated plate in contact with water decrease with an increase of P/D.

• Journal of the Korean Society of Safety
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• v.18 no.1
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• pp.19-27
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• 2003

This paper presented an experimental modal analysis of clamped perforated rectangular plates submerged in water. The penetration of holes in the plates had a triangular pattern with P/D (pitch to diameter) 1.750, 2.125, 2.500, 3.000 and 3.750. The natural frequencies of the perforated plates in air were obtained by the Rayleigh-Ritz method and compared with the experimental results. Good agreement was obtained between the analytical solution and experimental result. The experimental results in water showed that the mode shapes are not sensitive to the depth of submergence. The natural frequencies were shown to decrease drastically once the perforated plates come in contact with water. However, the natural frequencies decrease with the depth of submergence until a certain depth is reached, and become the asymptotic values beyond this depth of submergence. The depth of submergence did not affect the damping ratio greatly.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.5
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• pp.849-863
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• 1992

A very simple and computationally efficient numerical method is developed for the free vibration of isotropic and orthotropic composite triangular plates. A set of two-dimensional simple series functions is used as an admissible displacement functions in the Rayleigh-Ritz method to obtain the natural frequencies, nodal patterns and mode shapes for the plates. From the prescribed starting function satisfying only the geometric boundary conditions, the higher terms in the series functions are constructed with adding order of polynominal. Natural frequencies, nodal patterns and mode shapes are obtained for right triangular plates with three different support conditions. The obtained numerical results are presented, and the isotropic and some orthotropic cases are verified with other numerical methods in the liternature.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11a
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• pp.345.1-345
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• 2002

This paper dealt with an experimental study on the hydroelastic vibration of clamped perforated rectangular plates submerged in water. The penetration of holes in the plates had a triangular pattern with P/D (pitch to diameter) 1.750, 2.125, 2.500, 3.000 and 3.750. The natural frequencies of the perforated plates in air were obtained by the analytical method based on the relation between the reference kinetic and maximum potential energies and compared with the experimental results. (omitted)

• Structural Engineering and Mechanics
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• v.43 no.2
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• pp.253-271
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• 2012

To analyze the bending and transverse shear effects of laminated composite plates, a thirteen nodes triangular element will be presented. The suggested formulations consider a parabolic variation of the transverse shear strains through the thickness. As a result, there is no need to use shear correction coefficients in computing the shear stresses. The proposed element can model both thin and thick plates without any problems, such as shear locking and spurious modes. Moreover, the effectiveness of $w_{,n}$, as an independent degree of freedom, is concluded by the present study. To perform the accuracy tests, several examples will be solved. Numerical results for the orthotropic materials with different boundary conditions, shapes, number of layers, thickness ratios and fiber orientations will be presented. The suggested element calculates the deflections and stresses more accurate than those available in the literature.

• Computational Structural Engineering
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• v.5 no.2
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• pp.105-118
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• 1992

Static performance was compared for the triangular plate elements through some numerical experiments. Four Kirchhoff elements and six Mindlin elements were selected for the comparison. Numerical tests were executed for the problems of rectangular plates with regular and distorted meshes, rhombic plates, circular plates and cantilever plates. Among the Kirchhoff 9 DOF elements, the discrete Kirchhoff theory element was the best. Element distortion and the aspect ratio were shown to have negligible effects on the displacement behaviour. The Specht's element resulted in better results than the Bergan's but it was sensitive to the aspect ratio. The element based on the hybrid stress method also resulted in good results but it assumed to be less reliable. Among the linear Mindlin elements, the discrete shear triangle was the best in view of reliability, accuracy and convergence. Since the thin plate behaviour of it was as good as the DKT element, it can be used effectively in the finite element code regardless of the thickness. As a quadratic Mindlin element, the MITC7 element resulted in best results in almost all cases considered. The results were at least as good as those of doubly refined meshes of linear elements.