• Steel and Composite Structures
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• v.47 no.1
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• pp.71-77
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• 2023

This paper presents a study on the wave propagation of functionally graded material (FGM) sandwich nanoplates with soft core resting on a Winkler foundation. The structure is modelled by classical theory. Motion equations are derived by the assumption of nonlocal Eringen theory and energy method. Then, the equations are solved using an exact method for finding phase velocity responses. The effects of Winkler foundation, nonlocal parameters, thickness and mode number on the dispersion of elastic waves are shown. With the increase of spring constant, the speed of wave propagation increases and reaches a uniform state at a higher wave number.

• Journal of ILASS-Korea
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• v.10 no.4
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• pp.32-46
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• 2005

The breakup characteristics of liquid sheets formed by the impinging and swirl type injectors were studied as increasing the Weber number (or injection condition) and the ambient gas pressure to 4.0.MPa. In the case of impinging type injector. we compared the changes of breakup lengths between laminar and turbulent sheets. which are formed by the impingement of laminar and turbulent jets. respectively. The results showed that both sheets expand as increasing the injection velocity irrespective of the ambient gas density when the gas based Weber number is low. When the Weber number is high, however, the breakup of turbulent sheet depends on the hydraulic force of jets as well as the aerodynamic force of ambient gas which determines the breakup of laminar sheet. Using the experimental results. we could suggest empirical models on the breakup lengths of laminar and turbulent sheets. In the case of swirl type injector. as $We_l$, and ambient gas density increased, the disturbances on the annular liquid sheet surface were amplified by the increase of the aerodynamic forces. and thus the liquid sheet disintegrated near from the injector exit. Finally, the measured breakup length of swirl type injector according to the ambient gas density and $We_l$, was compared with the result by the linear instability theory. We found that the corrected breakup length relation derived from linear instability theory considering the attenuation of sheet thickness agrees well with our experimental results.

• Membrane and Water Treatment
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• v.6 no.6
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• pp.513-524
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• 2015

In this study, the effects of the angles of spacer filaments and the different feed Reynolds number on the fluid flow behavior have been investigated. Three-dimensional computational fluid dynamics (CFD) study is carried out for fluid flow through rectangular channels within different angles ($30^{\circ}$, $40^{\circ}$, $50^{\circ}$, $60^{\circ}$, $70^{\circ}$, $80^{\circ}$, $90^{\circ}$, $100^{\circ}$, $110^{\circ}$, $120^{\circ}$, respectively) between two filaments of spacer for membrane modules. The results show that the feed Reynolds number and the angles of spacer filaments have an important influence on pressure drop. While the feed Reynolds number is fixed, the optimal angle of spacer should be between $80^{\circ}$ to $90^{\circ}$, because the pressure drop is not only relatively small, but also high flow rate region expanded significantly with the increase of the angles between $80^{\circ}$ to $90^{\circ}$.The Contours of velocities and change of the average shear stress with the different angle of spacer filaments confirm the conclusion.

• Bulletin of the Korean Mathematical Society
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• v.20 no.2
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• pp.81-85
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• 1983

It is the purpose of this paper to give some remarks on finite fields. We shall show that the little theorem of Fermat, Euler's criterion for quadratic residue mod p, and other few theorems in the number theory can be derived from the theorems in theory of finite field K=GF(p), where p is a prime. The forms of some irreducible ploynomials over K-GF(p) will be given explicitly.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.1277-1280
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• 1993

In this short note we show that a number of conclusions unacceptable to our intuitions or commonsense knowledge can be drawn from Zadeh's possiliblity theory.

• Journal of the Korean Institute of Educational Facilities
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• v.18 no.6
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• pp.33-43
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• 2011

The Korean academics of classical learning, Seowon which from the middle of Joseon Dynasty was complexly reflected in "the illustration of Taiji(太極圖說)" Five-Elements school(陰陽五行說), "Zhou Yi(周易)" and a theory on spherical heaven and square ground(天圓地方) which based on orientalism. Also the theory of Xiangshu Xue(象數學) was a significant factor to decide the size(number of facade module) of Seowon architecture. So, in this study, how the oriental thought was adopted and reflected in existing 21 Seowon in South Korea. The size of Seowon architecture was adopted a theory of combination with heaven, earth and human(天地人三合論) that based on the theory of Xiangshu Xue on "the illustration of Taiji" and "Zhou Yi". "Zhou Yi" was the central thought of Confucian culture in Joseon Dynasty, with which Seowon space was divided into two, ancestral rites space and lecture space. It coincides with balance of yin(陰) and yang(陽), Five-Elements(五行) and four seasons(四季節). In lecture space, lecture hall is relevant with the water(水) and winter, and front tower structure or outer three-door is the fire(火) and summer. Also, central garden means the soil(土) and center. Thus, the size and spatial composition was planned with the philosophy, "the illustration of Taiji", Five-Elements school and a theory on spherical heaven and square ground. Yin and yang has an idea of the heaven and earth, and Five-Elements has an idea of direction and season with which spatial composition of Seowon could be set. And the numeral meaning on the theory of Xiangshu Xue established an ideal background for spatial composition of Seowon architecture.

• Computers and Concrete
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• v.25 no.3
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• pp.225-244
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• 2020

The influence of boundary conditions on the bending and free vibration behavior of functionally graded sandwich plates resting on a two-parameter elastic foundation is examined using an original novel high order shear theory. The Hamilton's principle is used herein to derive the equations of motion. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. This theory includes indeterminate integral variables and contains only four unknowns in which any shear correction factor not used, with even less than the conventional theory of first shear strain (FSDT). Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five, six or more in the case of other shear deformation theories. Galerkin's approach is utilized for FGM sandwich plates with six different boundary conditions. The accuracy of the proposed solution is checked by comparing it with other closed form solutions available in the literature.

• Steel and Composite Structures
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• v.39 no.1
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• pp.51-64
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• 2021

This paper presents a high-order shear and normal deformation theory for the bending of FGM plates. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five or more in the case of other shear and normal deformation theories. Based on the novel shear and normal deformation theory, the position of neutral surface is determined and the governing equilibrium equations based on neutral surface are derived. There is no stretching-bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. Navier-type analytical solution is obtained for functionally graded plate subjected to transverse load for simply supported boundary conditions. The accuracy of the present theory is verified by comparing the obtained results with other quasi-3D higher-order theories reported in the literature. Other numerical examples are also presented to show the influences of the volume fraction distribution, geometrical parameters and power law index on the bending responses of the FGM plates are studied.

• Steel and Composite Structures
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• v.17 no.1
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• pp.69-81
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• 2014

The novelty of this paper is the use of trigonometric four variable plate theory for free vibration analysis of laminated rectangular plate supporting a localized patch mass. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The Hamilton's Principle, using trigonometric shear deformation theory, is applied to simply support rectangular plates. Numerical examples are presented to show the effects of geometrical parameters such as aspect ratio of the plate, size and location of the patch mass on natural frequencies of laminated composite plates. It can be concluded that the proposed theory is accurate and simple in solving the free vibration behavior of laminated rectangular plate supporting a localized patch mass.

• Steel and Composite Structures
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• v.24 no.5
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• pp.569-578
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• 2017

In this research work, a simple and accurate hyperbolic plate theory for the buckling analysis of functionally graded sandwich plates is presented. The main interest of this theory is that, in addition to incorporating the thickness stretching effect (${\varepsilon}_z{\not=}0$), the displacement field is composed only of 5 unknowns as the first order shear deformation theory (FSDT), instead of 6 like in the well-known "higher order shear and normal deformation theories". Thus, the number of unknowns and governing equations for the present theory is reduced, significantly facilitating engineering analysis. Governing equations are obtained by employing the principle of minimum total potential energy. Comparison studies are performed to verify the validity of present results. A numerical investigation has been conducted considering and neglecting the thickness stretching effects on the buckling of sandwich plates with functionally graded skins. It can be concluded that the present theory is not only accurate but also simple in predicting the buckling response of sandwich plates with functionally graded skins.