• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.461-469
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• 1995

Some bounds for anisotropic torsional rigidity with one plane of elastic symmetry perpendicular to the axis of the beam are derived by making use of the isoperimetric inequalities, complementary variational principles, and the maximum principle. Upper and lower bounds are obtained by applying the isoperimetric inequalities. While the upper bound investigated by the variational principles and maximum principle. The analysis is patterned after the work of Payne and Weinbeger [J. Math. Anal. Appl. 2(1961). pp. 210-216].

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.751-761
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• 2000

Symmetry properties of positive solutions for semilinear elliptic problems in n are considered. We give a symmetry result for the problem in the feneral case, and then derive various results for certain classes of demilinear elliptic equations. We employ the moving plane method based on the maximum principle on unbounded domains to obtain the result on symmetry.

• Steel and Composite Structures
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• v.11 no.5
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• pp.359-374
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• 2011

In this paper, the influence of fibre orientation and aspect ratio on stability analysis of simply supported skew plates subjected to in plane loading is studied by using a four noded hybrid plate finite element. The formulation of the element is based on Hellinger-Reissner variational principle. The element is developed by combining a hybrid plane stress element and a hybrid plate element. Some numerical problems are solved and the effects of skew angle, aspect ratio, fibre orientation and loading type on the critical buckling loads are highlighted.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.836-839
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• 2005

The in-plane vibration response of a clamped circular plate should be predicted in many applications. Up to now, papers on the in-plane vibration of rectangular plate are published. However, analytical derivation on the in-plane vibration of the clamped circular plate is not carried out. Therefore, the in-plane vibration of the clamped circular plate is the concern of this paper. In order to derive the equations of motion for the clamped circular plate in the cylindrical coordinate, the kinetic energy and potential energy for the in-plane behavior are obtained by us ing the stress-strain-displacement expressions. Application of Hamilton's principle leads to two sets of differential equations. These displacement equations were highly coupled. It is possible to obtain a simpler set of equations by introducing Helmholtz decomposition. Substituting them into the coupled differential equations, we obtain the uncoupled equations of motion. In order to solve them, we assume that the solutions are harmonic. Then, they lead to the wave equations. Using the separation of variable, we obtain the general solutions for the equations. Based on the solutions, the displacements for r and $\theta$ direction are assumed. Finally we obtain the frequency equation for the clamped circular plate by the application of boundary conditions. The derived equation is compared with the finite element analysis for validation by using the some numerical examples.

• Structural Engineering and Mechanics
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• v.42 no.4
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• pp.589-608
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• 2012

In this study, the effect of in-plane deformations on the dynamic behavior of laminated plates is investigated. For this purpose, the displacement-time and strain-time histories obtained from the large deflection analysis of laminated plates are compared for the cases with and without including in-plane deformations. For the first one, in-plane stiffness and inertia effects are considered when formulating the dynamic response of the laminated composite plate subjected to the blast loading. Then, the problem is solved without considering the in-plane deformations. The geometric nonlinearity effects are taken into account by using the von Karman large deflection theory of thin plates and transverse shear stresses are ignored for both cases. The equations of motion for the plate are derived by the use of the virtual work principle. Approximate solution functions are assumed for the space domain and substituted into the equations of motion. Then, the Galerkin method is used to obtain the nonlinear algebraic differential equations in the time domain. The effects of the magnitude of the blast load, the thickness of the plate and boundary conditions on the in-plane deformations are investigated.

• Journal of the Semiconductor & Display Technology
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• v.2 no.4
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• pp.23-26
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• 2003

The general users find difficulties in using ellipsometers. Thus, the object of this study is to construct an ellipsometer with simple operation principle. We developed an ellipsometer which does not require alignment and calibration before measuring sample. A basis structure model after rotating a compensator spectroscopic ellipsometry, the fixed incidence angle at $70^{\circ}$. This ellipsometer does not demand calibration, because the plane of incidence is not changed due to the novel sample holder structure. The results for various standard samples were compared with those from conventional RCSE to test the performance of this instrument. Also repeated measurements were performed to test the precision of the calibration coefficient in a plane of incidence fixed.

• Journal of information and communication convergence engineering
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• v.9 no.1
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• pp.105-109
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• 2011

In this paper, we study the dominating-free sest which is defined as follows: k points called servers and n points called clients in the plane are given. For a point p in the plane is said to be dominated by a client c if for every server s, the distance between s and p is greater than the distance between s and c. The dominating-free set is the set of points in the plane which aren't dominated by any client. We present an O(nklogk+$n^2k$) time algorithm for computing the dominating-free set under the $L_1$-metric. Specially, we present an O(nlogn) time algorithm for the problem when k=2. The algorithm uses some variables and 1-dimensional arrays as its principle data structures, so it is easy to implement and runs fast.

• Journal of the Korean earth science society
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• v.32 no.1
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• pp.73-83
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• 2011

A new method was developed to better understand the principle of Coriolis force. We also investigated the understanding of 5 10th grade students and analyzed their responses. Since no clear explanation about the nature of a rotating disk is provided in school textbooks, it tends to be misunderstood as the earth surface revolving on its axis pointing to the North Pole. This study was carried out focusing on the fact that a rotating disk is the tangential plane at arbitrary latitude. Results showed that there are changes in students' conceptions on the principle of Coriolis force with a new understanding of the rotating disk. In conclusion, a new method used in this study helped students better understand the link between Coriolis force and rotating disk. The method would be helpful to clarify the principle of Coriolis force in school science.

• Communications of Mathematical Education
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• v.21 no.4
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• pp.663-676
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• 2007

In this paper we study tetrahedron's properties related with intersection of segments and planes using the principle of the lever. We analyze proof method using the principle of the lever, and describe how to prove intersection of segments and planes using the principle of the lever in tetrahedron.

• Wind and Structures
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• v.25 no.5
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• pp.415-432
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• 2017

The nonlinear aerodynamic instability of a tensioned plane orthotropic membrane structure is theoretically investigated in this paper. The interaction governing equation of wind-structure coupling is established by the Von $K\acute{a}rm\acute{a}n's$ large amplitude theory and the D'Alembert's principle. The aerodynamic force is determined by the potential flow theory of fluid mechanics and the thin airfoil theory of aerodynamics. Then the interaction governing equation is transformed into a second order nonlinear differential equation with constant coefficients by the Bubnov-Galerkin method. The critical wind velocity is obtained by judging the stability of the second order nonlinear differential equation. From the analysis of examples, we can conclude that it's of great significance to consider the orthotropy and geometrical nonlinearity to prevent the aerodynamic instability of plane membrane structures; we should comprehensively consider the effects of various factors on the design of plane membrane structures; and the formula of critical wind velocity obtained in this paper provides a more accurate theoretical solution for the aerodynamic stability of the plane membrane structures than the previous studies.