• Structural Engineering and Mechanics
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• v.40 no.1
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• pp.121-148
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• 2011

Closed form solutions for equilibrium and flexibility matrices of the Mindlin-Reissner theory based eight-node rectangular plate bending element (MRP8) using Integrated Force Method (IFM) are presented in this paper. Though these closed form solutions of equilibrium and flexibility matrices are applicable to plate bending problems with square/rectangular boundaries, they reduce the computational time significantly and give more exact solutions. Presented closed form solutions are validated by solving large number of standard square/rectangular plate bending benchmark problems for deflections and moments and the results are compared with those of similar displacement-based eight-node quadrilateral plate bending elements available in the literature. The results are also compared with the exact solutions.

• Journal of the Korean Society of Safety
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• v.7 no.2
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• pp.30-41
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• 1992

Analysis of Dynamic Characterisocs of Rectangular Plate by Finite Element Method. Dynamic characteristics of a rectangular plate with opening in it is studied by finite element method. To investigate these characteristics 12 degrees of freedom membrane finite element in used. The rectangular membrane finite elements are defined by specifying geometry, internal displacement functions and strain-displacement relations. Then, the governing equation for the finite element is derived by energy method. To derive the mass matrix and stiffness matrix of the element, expressions for strain and kineic energy in terms of the node displacement are generated. In constructing the overall structure matrix, the matrix of each elements are superposed and partitioned by applying the given boundary condition to obtain a nonslngular matrix. To find the natural freguencies and viration modes, the eigen values and the corresponding eigen vectors are computed by the computer using well known Jacobi power method. In order to verify the capability of the membrane finite element, a flat rectangular plate is analyzed first, and the result is compared with well known analytical results to show the good agreement. A rectangular plate with opening in It is analyzed with the same finite element. The results are presented in this paper. Unfortunately, the literature study could not provide with some results to compare, but the results reveal that the output of this research is phlslcally reasonable. And the results of this research are useful not only in practice but also for the future experimental research in comparison purpose.

• Structural Engineering and Mechanics
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• v.55 no.3
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• pp.583-603
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• 2015

There are so many applications of perforated pates with various penetration patterns. If they are penetrated regularly, it can be represented by solid plate with equivalent material properties, which has a benefit of finite element modelling and reducing computation time for the analysis. Because the equivalent material properties suggested already are not proper to be applicable for the dynamic analysis, it is necessary to extract the equivalent material properties for the dynamic analysis. Therefore, in this study, the equivalent modulus of elasticity are obtained for the perforated plate with a triangular penetration pattern by comparing the natural frequencies of the perforated plate with those of solid plate, which are represented with respect to the ligament efficacy. Using the equivalent material properties suggested, the modal analyses of the partially perforated rectangular plate with a triangular penetration pattern are performed and its applicability is shown by comparing natural frequencies of perforated and homogeneous solid plates from finite element method and analytical method.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11b
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• pp.85-89
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• 2005

For the analysis of a vibrating two dimensional structure such as the simply supported rectangular plate, Spectral Finite Element Method (SFEM) has been studied. Under the condition that two parallel edges are simply supported at least and the other two edges can be arbitrary, Spectral Finite Element has been developed. Using this element SFEM is applied to the vibrating rectangular plate which all edges are simply supported, and obtain the frequency response function in frequency domain and the dynamic response in time domain. To evaluate these results normal mode method and finite element method (FEM) are also accomplished and compared. It is seen that SFEM is more powerful analysis tool than FEM in high frequency range.

• Structural Engineering and Mechanics
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• v.36 no.6
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• pp.669-678
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• 2010

In general means, the stress concentration problem of elastic plate with a rectangular hole can be investigated by numerical methods, and only approximative results are derived. This paper deduces an analytical study of the stress concentration due to a rectangular hole in an elastic plate under bending loads. Base on classical elasticity theory and FEM applying the U-transformation technique, the uncoupled governing equations with 3-DOF are established, and the analytical displacement solutions of the finite element equations are derived in series form or double integral form. Therefore, the stress concentration factor can then be discussed easily and conveniently. For the plate subjected to unidirectional bending loads, the non-conforming plate bending element with four nodes and 12-DOF is taken as examples to demonstrate the application of the proposed method. The inner force distribution is obtained. The solutions are adequate for the condition when the hole is far away from the edges and the thin plate subjected to any transverse loadings.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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• pp.907-910
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• 2005

This paper has the object of investigating natural frequencies of tapered thick plate, tapered ratio, thick plate's opening size by means of finite element method and providing kinetic design data for mat of building structures. Free vibration analysis that tapered thick plate in this paper. Finite element analysis of rectangular plate is done by use of rectangular finite element with 8-nodes. In order to analysis plate which is varioued of plate thickness. the thickness is varied with 5, 10, 15, 20 and the tapered ratio is applied as 0.0, 0.25, 0.5, 0.75, 1.0 respectively. This paper is analyzed varying thickness by taper ratio.

• Geomechanics and Engineering
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• v.6 no.4
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• pp.341-358
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• 2014

Uplift response of rectangular anchor plates has been investigated in physical model tests and numerical simulation using Plaxis. The behavior of rectangular plates during uplift test was studied by experimental data and finite element analyses in cohesionless soil. Validation of the analysis model was also carried out with 200 mm and 300 mm diameter of rectangular plates in sand. Agreement between the uplift responses from the physical model tests and finite element modeling using PLAXIS 2D, based on 200 mm and 300 mm computed maximum displacements were excellent for rectangular anchor plates. Numerical analysis using rectangular anchor plates was conducted based on hardening soil model (HSM). The research has showed that the finite element results gives higher than the experimental findings in dense and loose packing of cohesionless soil.

• Journal of Power System Engineering
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• v.11 no.1
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• pp.92-97
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• 2007

It is important to compute the structural analysis of plate structures in structural design. In this paper, the author uses the finite element-transfer stiffness coefficient method (FE-TSCM) for the structural analysis of plate structures. The FE-TSCM is based on the concept of the successive transmission of the transfer stiffness coefficient method and the modeling technique of the finite element method (FEM). The algorithm for in-plane structural analysis of a rectangular plate structure is formulated by using the FE-TSCM. In order to confirm the validity of the FE-TSCM for structural analysis of plate structures, two numerical examples for the in-plane structural analysis of a plate with triangular elements and the bending structural analysis of a plate with rectangular elements are computed. The results of the FE-TSCM are compared with those of the FEM on a personal computer.

• Journal of the korean Society of Automotive Engineers
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• v.8 no.2
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• pp.51-64
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• 1986

There has been considerable interest over the last twenty years in the subject of the elastic properties of the cord-rubber laminate. This has been due to the rather intensive study of the composites materials characteristics brought about by the increased use of rigid composites materials characteristics brought about by the increased use of rigid composites in many structural applications. The object of this study is to obtain the natural frequencies and modes of the simply supported cord-rubber laminate plates prior to the study on the analysis of the dynamic properties of the pneumatic tire. To obtain these natural frequencies and modes, the 12 degrees of freedom orthotropic rectangular plate finite elements are developed. By using classical lamination theory, the stress-strain relations are represented. The governing equation for the finite element is derived by energy method. To find the natural frequencies and modes, he eigenvalues and corresponding eigenvectors are computed by the well known Jacobi power method. In order to verify the capability of this present finite element, the results of the specially orthotropic plate and the angle-ply laminate plate are compared with the analytical solution. The analytical and numberical results are in good agreement. The following problems of the simply supported plate are analyzed by the present finite element. a) the natural frequencies and mode shapes of the cord-rubber laminate plate for various aspect ratio. b) The natural frequencies and mode shapes of the orthotropic plate with the rectangular hole in its center.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.4 s.97
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• pp.388-394
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• 2005

This paper has the object of investigating natural frequencies of tapered thick plate on Pasternak foundation by means of finite element method and providing kinetic design data for mat of building structures. Vibration analysis for tapered thick plate subjected to in-plane stress is presented in this paper. Finite element analysis of rectangular plate is done by use of rectangular finite element with 8-nodes. Analysis conditions of tapered thick plate are as follows each. The ratio of in-plane stress to critical load is varied with $0.2\sigma_{cr}$, $0.4\sigma_{cr}$, $0.6\sigma_{cr}$. The Winkler parameter is 0, 10, 100, 1000, the shear foundation parameter is 0, 10 and the taper ratio is 0.0, 0.2, 0.4, 0.6, 0.8.