• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.3 s.120
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• pp.220-225
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• 2007

Free vibration analysis using the method of NDIF (non-dimensional dynamic influence function), which was developed by the author, is extended to arbitrarily shaped polygonal plates with free edges. Local Cartesian coordinate systems are employed to apply the free boundary condition to nodes distributed along the edges of the plate of interest. Furthermore, a new way for applying the free boundary condition to nodes located at corners of the plate is for the first time introduced by considering the phenomenon of stress concentration at the corners. Two case studies show that the proposed method is valid and accurate when the eigenvalues by the proposed method are compared to those by FEM(ANSYS).

• Journal of the Society of Naval Architects of Korea
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• v.47 no.4
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• pp.508-516
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• 2010

This study aims at investigating the effect of the chamfer on the liquid sloshing in the three-dimensional (3D) rectangular tank. In order to simulate the 3D incompressible viscous two-phase flow in the 3D tank with partially filled liquid, the present study has adopted the volume of fluid (VOF) method based on the finitevolume method which has been well verified by comparing with the results of the relevant previous researches. The effects of the chamfering top corners of the tank on the liquid sloshing characteristics have been investigated. The angle of the chamfering top corners (${\theta}$) has been changed in the range of $0^{\circ}{\leq}{\theta}{\leq}60^{\circ}$(${\Delta}{\theta}=15^{\circ}$) to observe the free surface behavior, and the effect on wall impact load. Generally, as the angle of the chamfering top corners increases, the impact pressure on the upper knuckle point decreases. However it seemed that a critical angle of the chamfering top corners exists to reveal the lowest impact pressure on the wall.

• Proceedings of the KSME Conference
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• 2000.11b
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• pp.447-452
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• 2000

In this study, the design of Free-Fall Simulator was carried out using concept of vertical wind tunnel. Free-Fall Simulator is not an experimental equipment but a training equipment. Therefore Free-Fall Simulator needs a large training section compared with test section of wind tunnel and has critical limit of height. These limits bring about the difficulty of design for a return passage. Due to small area ratio, the downstream flow of training section with high speed is not decelerated adequately to the fan section. High-speed flow leads to great losses in the small area ratio diffuser and corner. So design of diffusers and corners located between training section and fan section has a great effect on the Free-Fall Simulator performance. This study used an estimation method of subsonic wind tunnel performance. It considered each section of Free-Fall Simulator as an independent section. Therefore loss of one section didn't affect loss of other sections. Because losses of corner with vane and $1^{st}$ diffuser are most parts of overall Free-Fall Simulator, this study focused on the design of these sections.

• 한국신재생에너지학회:학술대회논문집
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• 2005.06a
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• pp.534-537
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• 2005

Free Vibration Analysis using Non-dimensional Dynamic Influence Function (NDIF) is extended to arbitrarily shaped plates including polygonal plates. Since the corners of polygonal plates have indefinite normal directions and additional boundary conditions related to a twisting moment at a corner along with moment and shear force zero conditions, it is not easy to apply the NDIF method to polygonal plates wi th the free boundary condition. Moreover, owing to the fact that the local polar coordinate system, which has been introduced for free plates with smoothly varying edges, cannot be employed for the straight edges of the polygonal plates, a new coordinate system is required for the polygonal plates. These problems are solved by developing the new method of modifying a corner into a circular arc and setting the normal direction at the corner to an average value of normal direct ions of two edges adjacent to the corner. Some case studies for plates with various shapes show that the proposed method gives credible natural frequencies and mode shapes for various polygons that agree well with those by an exact method or FEM (ANSYS).

• Steel and Composite Structures
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• v.28 no.6
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• pp.655-670
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• 2018

A coupled method, that combines the Ritz method and the finite element (FE) method, is proposed to solve the vibration problem of rectangular thin and thick plates with general boundary conditions. The eigenvalue partial differential equation(s) of the plate is (are) first reduced to a set of eigenvalue ordinary differential equations by the application of the Ritz method. The resulting eigenvalue differential equations are then reduced to an eigenvalue algebraic equation system using the finite element method. The natural boundary conditions of the plate problem including the free edge and free corner boundary conditions are also implemented in a simple and accurate manner. Various boundary conditions including simply supported, clamped and free boundary conditions are considered. Comparisons with existing numerical and analytical solutions show that the proposed mixed method can produce highly accurate results for the problems considered using a small number of Ritz terms and finite elements. The proposed mixed Ritz-FE formulation is also compared with the mixed FE-Ritz formulation which has been recently proposed by the present author and his co-author. It is found that the proposed mixed Ritz-FE formulation is more efficient than the mixed FE-Ritz formulation for free vibration analysis of rectangular plates with Levy-type boundary conditions.

• 한국전산유체공학회:학술대회논문집
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• 1998.05a
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• pp.55-60
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• 1998

An elliptic grid generation scheme using Laplace's equations guarantees the resulting grids to be crossing-free as a result of maximum principle in its analytic form. Numerical results, however, often show the grid lines overlapping each other or crossing the boundaries, especially for very sharp convex corners. The cause of this problem is investigated, and it is found that this problem can be handled by properly modifying the coefficients of transformed Laplace's equations in the computational domain.

• Journal of computational fluids engineering
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• v.13 no.4
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• pp.13-23
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• 2008

This paper is an extension of previous study[1] on a development of a divergence-free element method using a hermite interpolated stream function. Divergence-free velocity bases defined on rectangles derived herein produce pointwise divergence-free flow fields. Hence the explicit imposition of continuity constraint is not necessary and the Galerkin finite element formulation for velocities does not involve the pressure. The divergence-free element of the previous study employed hermite (serendipity) cubic for interpolation of stream function, and it has been noted a possible discontinuity in variables along element interfaces. This deficiency can be removed by use of a hermite bicubic interpolated stream function, which requires four degrees-of-freedom at each element corners. Those degrees-of-freedom are the unknown variable, its x- and y-derivatives and its cross derivative. Detailed derivations are presented for both solenoidal and irrotational basis functions from the hermite bicubic interpolated stream function. Numerical tests are performed on the lid-driven cavity flow, and results are compared with those from hermite serendipity cubics and a stabilized finite element method by Illinca et al[2].

• Journal of the Earthquake Engineering Society of Korea
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• v.3 no.1
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• pp.9-20
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• 1999

An accurate method is presented for flexural vibrations of rhombic plates having all combinations of clamped and free edge conditions. The prime focus here is that the analysis explicitly considers the bending stress singularities that occur in the two opposite, clamped-free corners having obtuse angles of the rhombic plates. Accurate non-dimensional frequencies and normalized contours of the vibratory transverse displacement are presented for rhombic plates having a large enough obtuse angle of 165$^{\circ}$, so that a significant influence of clamped-free corner stress singularities may be understood.

• 한국전산유체공학회:학술대회논문집
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• 2008.03a
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• pp.33-41
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• 2008

This paper is an extension of previous study[9] on a development of a divergence-free element method using a hermite interpolated stream function. Divergence-free velocity bases defined on rectangles derived herein produce pointwise divergence-free flow fields. Hence the explicit imposition of continuity constraint is not necessary and the Galerkin finite element formulation for velocities does not involve the pressure. The divergence-free element of the previous study employed hermite serendipity cubic for interpolation of stream function, and it has been noted a possible discontinuity in variables along element interfaces. This deficiency can be removed by use of a hermite bicubic interpolated stream function, which requires at each element corners four degrees-of-freedom such as the unknown variable, its x- and y-derivatives and its cross derivative. Detailed derivations are presented for both solenoidal and irrotational bases from the hermite bicubic interpolated stream function. Numerical tests are performed on the lid-driven cavity flow, and results are compared with those from hermite serendipity cubics and a stabilized finite element method by Illinca et al[7].

• 한국전산유체공학회:학술대회논문집
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• 2008.10a
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• pp.33-41
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• 2008

This paper is an extension of previous study[9] on a development of a divergence-free element method using a hermite interpolated stream function. Divergence-free velocity bases defined on rectangles derived herein produce pointwise divergence-free flow fields. Hence the explicit imposition of continuity constraint is not necessary and the Galerkin finite element formulation for velocities does not involve the pressure. The divergence-free element of the previous study employed hermite serendipity cubic for interpolation of stream function, and it has been noted a possible discontinuity in variables along element interfaces. This deficiency can be removed by use of a hermite bicubic interpolated stream function, which requires at each element corners four degrees-of-freedom such as the unknown variable, its x- and y-derivatives and its cross derivative. Detailed derivations are presented for both solenoidal and irrotational bases from the hermite bicubic interpolated stream function. Numerical tests are performed on the lid-driven cavity flow, and results are compared with those from hermite serendipity cubics and a stabilized finite element method by Illinca et al[7].