• Structural Engineering and Mechanics
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• v.7 no.3
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• pp.289-302
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• 1999

An approximate method for analyzing the bending problems of irregular-shaped plates is proposed. In this paper irregular-shaped plates are such plates as plate with opening, circular plate, semi-circular plate, elliptic plate, triangular plate, skew plate, rhombic plate, trapezoidal plate or the other polygonal plates which are not uniform rectangular plates. It is shown that these irregular-shaped plates can be considered finally as a kind of rectangular plates with non-uniform thickness. An opening in a plate can be considered as an extremely thin part of the plate, and a non-rectangular plate can be translated into a circumscribed rectangular plate whose additional parts are extremely thin or thick according to the boundary conditions of the original plate. Therefore any irregular-shaped plate can be replaced by the equivalent rectangular plate with non-uniform thickness. For various types of irregular-shaped plates the convergency and accuracy of numerical solution by proposed method are investigated.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.1177-1182
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• 2006

This paper is concerned with the vibration analysis of a simply-supported rectangular plate with a circular cutout. Even though there have be en many methods developed for the free vibration of the rectangular plate with a rectangular cutout., very few research has been carried out for the rectangular plate with a circular cutout. In this paper, a new methodology called independent coordinate coupling method, which was developed to save the computational effort for the free vibration analysis of rectangular plate with a rectangular cutout, is applied to the case of circular cutout. The independent coordinate coupling method employs the global coordinate system for the plate and the local coordinate system for the cutout. In the case of the rectangular plate with a circular cutout, the global coordinate system is the Cartesian co ordinate system and the local coordinate system is the polar coordinate system. By imposing the compatibility condition, the relationship between the global coordinates and the local coordinates is derived. This equation is then used for the calculation of the mass and stiffness matrices resulting in eigenvalue problem. The numerical results show the efficacy of the proposed method.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.6 s.111
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• pp.643-650
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• 2006

This paper is concerned with the vibration analysis of a simply-supported rectangular plate with a circular cutout. Even though there have been many methods developed for the free vibration of the rectangular plate with a rectangular cutout, very few research has been carried out for the rectangular plate with a circular cutout. In this paper, a new methodology called independent coordinate coupling method, which was developed to save the computational effort for the free vibration analysis of rectangular plate with a rectangular cutout, is applied to the case of circular cutout. The independent coordinate coupling method employs the global coordinate system for the plate and the local coordinate system for the cutout. In the case of the rectangular plate with a circular cutout, the global coordinate system is the Cartesian coordinate system and the local coordinate system is the polar coordinate system. By imposing the compatibility condition, the relationship between the global coordinates and the local coordinates is derived. This equation is then used for the calculation of the mass and stiffness matrices resulting in eigenvalue problem. The numerical results show the efficacy of the proposed method.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.3
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• pp.172-177
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• 2003

This paper investigates the effect of reinforced plate on the deflection of the rectangular plate, when the rectangular plate is reinforced with rectangular rigid body at the centroid of the plate. For two boundary conditions such as simple supported and clamped boundary This study derives deflection formula of reinforced plates with three kinds of the aspect ratio of a rectangular plate with respect to the elastic modulus ratio and the length ratio of rigid body using the least square method. The results are as follows: 1. As the elastic modulus ratio r$_{e}$$\geq$ 1000, the maximum deflection with respect to the length ratio r$_{1}$ converges into constant value. 2. Deflection formula with respect to the length ratio r$_{1}$ is derived as the third order polynomial.l.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.9
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• pp.881-887
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• 2007

This paper is concerned with the vibration analysis of a rectangular plate with multiple rectangular holes. Even though there have been many methods developed for the addressed problem, they suffer from computational time. In this paper, we applied the Independent Coordinate Coupling Method(ICCM) to the addressed problem, which was developed to compute natural vibration characteristics of the rectangular plate with a rectangular hole and proven to be computationally effective. The ICCM is based on Rayleigh-Ritz method but utilizes independent coordinates for each hole domain. By matching the deflection conditions for each hole imposed on the expressions, we can easily derive the reduced mass and stiffness matrices. The resulting equation is then used for the calculation of the eigenvalue problem. The numerical results show the efficacy of the Independent Coordinate Coupling Method.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.05a
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• pp.869-872
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• 2002

This paper deals with the effect of reinforced plate on the deflection of the rectangular plate, when the rectangular plate is reinforced with rectangular rigid body at the centroid of the plate. For Two boundary conditions such as simple supported and clamped boundary, this study derives deflection formula of reinforced plates with respect to the stiffness ratio and the length ratio of rigid body using the least square method. The results are as follows: 1. As $r_e$ $\geq$ 1000, the maximum deflection with respect to $r_e$ converges into constant value. 2. Deflection formula with respect to $r_e$ is derived as the fifth order polynomial.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.11
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• pp.1086-1092
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• 2007

This paper is concerned with the vibration analysis of a rectangular plate with multiple circular holes. On the contrary to the case of rectangular plate with multiple rectangular holes, it is very difficult to perform qualitative analysis on natural vibration characteristics because of geometrical inconsistency. In this paper, we applied the Independent Coordinate Coupling Method(ICCM) to the addressed problem, which was developed to compute natural vibration characteristics of the rectangular plate with a circular hole and proven to be computationally effective. The ICCM is based on Rayleigh-Ritz method but utilizes independent coordinates for each hole domain. By matching the deflection conditions for each hole imposed on the expressions, we can easily derive the reduced mass and stiffness matrices. The resulting equation is then used for the calculation of the eigenvalue problem. The numerical results show the efficacy of the Independent Coordinate Coupling Method.

• The Journal of the Acoustical Society of Korea
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• v.18 no.7
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• pp.39-44
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• 1999

An analysis of the frequency parameters and vibrational modes is described for a rectangular plate. Double Fourier sine series is used as a modal displacement functions of a rectangular plate and applied to the free vibration analysis of a rectangular plate under various boundary conditions. The frequency parameters obtained by the double Fourier sine series method are compared with those obtained by the theory of finite element method and Ritz method. Frequency parameters are presented for the various aspect ratios for plate. The first four modal shapes for the rectangular plate under various boundary conditions are accurately described.

• 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.

• International Journal of Aeronautical and Space Sciences
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• v.18 no.3
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• pp.450-466
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• 2017

This paper defines the modified effective membrane stiffness, bending stiffness considering the directionally dependent mechanical properties and mode shape function of a composite lattice rectangular plate, which is assumed to be a Kirchhoff-Love plate. It subsequently presents an approximate method of conducting a buckling analysis of the composite lattice rectangular plate with various boundary conditions under uniform compression using the Ritz method. This method considers the coupled buckling mode as well as the global and local buckling modes. The validity of the present method is verified by comparing the results of the finite element analysis. In addition, this paper performs a parametric analysis to investigate the effects of the design parameters on the critical load and buckling mode shape of the composite lattice rectangular plate based on the present method. The results allow a database to be obtained on the buckling characteristics of composite lattice rectangular plates. Consequently, it is concluded that the present method which facilitates the calculation of the critical load and buckling mode shape according to the design parameters as well as the parametric analysis are very useful not only because of their structural design but also because of the buckling analysis of composite lattice structures.