• 한국정밀공학회지
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• 제12권6호
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• pp.80-86
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• 1995

A method of eliminating the branch problem in driving crank center point plane for 3 position synthesis of 4 bar mechanism is introduced. By studying various transformation characteristics from the circle point plane into the center poi t plane, the curves in the center point plane transformed from the filemon line in circle point plane are analytically obtained, which will seperate the whole center point plane into many sub-areas for the selec- tion of the center point of the driving crank. And a simple method to identify which of the sub-areas will cause the branch problem is also presented. The method will allow the selection of the center point of driving crank without the branch problem.

• 한국CDE학회논문집
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• 제6권1호
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• pp.31-39
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• 2001

Presented in this paper are algorithms to compute the positions of vertices and equations of edges of the Voronoi diagram of a circle set. The circles are located in a Euclidean plane, the radii of the circles are not necessarily equal and the circles are not necessarily disjoint. The algorithms correctly and efficiently work when the correct topology of the Voronoi diagram was given. Given three circle generators, the position of the Voronoi vertex is computed by treating the plane as a complex plane, the Z-plane, and transforming it into another complex plane, the W-plane, via the Mobius transformation. Then, the problem is formulated as a simple point location problem in regions defined by two lines and two circles in the W-plane. And the center of the inverse-transformed circle in Z-plane from the line in the W-plane becomes the position of the Voronoi vertex. After the correct topology is constructed with the geometry of the vertices, the equations of edge are computed in a rational quadratic Bezier curve farm.

• Journal of information and communication convergence engineering
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• 제10권1호
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• pp.1-4
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• 2012

Given separated points divided by a line, called a wall, in a plane, we aim to make a gate in the wall to connect the separated points to each other. In this setting, the problem is to find a location for the gate that minimizes the average distance between the points. The problem is a variant of the well-known facility location problem, which is extensively studied in the fields of operations research, location theory, theoretical computer science, and so on. In this paper, we consider the $L^1$-distance of the points in the plane. The points are projected onto the wall and so the problem is transformed to a proximity problem of points on a line. Then it is shown that the transformed problem is related to the weighted median problem of points on the line. Therefore, we obtain an O(n log n)-time algorithm to solve our problem.

• Interaction and multiscale mechanics
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• 제3권3호
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• pp.213-234
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• 2010

A multiscale method is presented for analysis of thin slab structures in which the microstructures can not be reduced to two-dimensional plane stress models and thus three dimensional treatment of microstructures is necessary. This method is based on the classical asymptotic expansion multiscale approach but with consideration of the special geometric characteristics of the slab structures. This is achieved via a special form of multiscale asymptotic expansion of displacement field. The expanded three dimensional displacement field only exhibits in-plane periodicity and the thickness dimension is in the global scale. Consequently by employing the multiscale asymptotic expansion approach the global macroscopic structural problem and the local microscopic unit cell problem are rationally set up. It is noted that the unit cell is subjected to the in-plane periodic boundary conditions as well as the traction free conditions on the out of plane surfaces of the unit cell. The variational formulation and finite element implementation of the unit cell problem are discussed in details. Thereafter the in-plane material response is systematically characterized via homogenization analysis of the proposed special unit cell problem for different microstructures and the reasoning of the present method is justified. Moreover the present multiscale analysis procedure is illustrated through a plane stress beam example.

• Structural Engineering and Mechanics
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• 제58권4호
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• pp.731-743
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• 2016

Plastic behaviors, based on the von Mises yield criterion, of circular discs containing a purely elastic, circular inclusion under uniform temperature loading are studied with the finite element analysis. Temperature-dependent mechanical properties are considered for the matrix material only. In addition to analyzing the plane stress and plane strain disc, a 3D thin disc and cylinder are also analyzed to compare the plane problems. We determined the elastic irreversible temperature and global plastic collapse temperature by the finite element calculations for the plane and 3D problem. In addition to the global plastic collapse, for the elastically hard case, the plane stress problem and 3D thin disc may exhibit a local plastic collapse, i.e. significant pile up along the thickness direction, near the inclusion-matrix interface. The pileup cannot be correctly modeled by the plane stress analysis. Furthermore, due to numerical difficulties originated from large deformation, only the lower bound of global plastic collapse temperature of the plane stress problem can be identified. Without considerations of temperature-dependent mechanical properties, the von Mises stress in the matrix would be largely overestimated.

• Structural Engineering and Mechanics
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• 제64권4호
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• pp.505-513
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• 2017

In this paper, a receding contact problem for an elastic layer resting on a half plane is considered. The layer is pressed by two rectangular stamps placed symmetrically. It is assumed that the contact surfaces are frictionless and only compressive traction can be transmitted through the contact surfaces. In addition the effect of body forces is neglected. Firstly, the problem is solved analytically based on theory of elasticity. In this solution, the problem is reduced into a system of singular integral equations in which half contact length and contact pressures are unknowns using boundary conditions and integral transform techniques. This system is solved numerically using Gauss-Jacobi integral formulation. Secondly, two dimensional finite element analysis of the problem is carried out using ANSYS. The dimensionless quantities for the contact length and the contact pressures are calculated under various stamp size, stamp position and material properties using both solutions. The analytic results are verified by comparison with finite element results.

• East Asian mathematical journal
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• 제26권4호
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• pp.553-579
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• 2010

Geometric education emphasize reasoning ability and spatial sense through development of logical thinking and intuitions in space. Researches about space understanding go along with investigations of space perception ability which is composed of space relationship, space visualization, space direction etc. Especially space visualization is one of the factors which try conclusion with geometric problem solving. But studies about space visualization are limited to middle school geometric education, studies in elementary level haven't been done until now. Namely, discussions about elementary students' space visualization process and ability in plane or space figures is deficient in relation to geometric problem solving. This paper examines these aspects, especially in relation to plane and space problem solving in elementary levels. Firstly we propose the analysis frame to investigate a visualization process for plane problem solving and a visualization ability for space problem solving. Nextly we select 13 elementary students, and observe closely how a visualization process is progress and how a visualization ability is played role in geometric problem solving. Together with these analyses, we propose concrete examples of visualization ability which make a road to geometric problem solving. Through these analysis, this paper aims at deriving various discussions about visualization in geometric problem solving of the elementary mathematics.

• Journal of Mechanical Science and Technology
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• 제15권1호
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• pp.61-65
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• 2001

Using the theory of linear piezoelectricity, the problem of two layered strip with a piezoelectric ceramic bonded to an elastic material containing a finite interface crack is considered. The out-of-plane mechanical and in-plane electrical loadings are simultaneously applied to the strip. Fourier transforms are used to reduce the problem to a pair of dual integral equations, which is then expressed in terms of a Fredholm integral equation of the second kind. The stress intensity factor is determined, and numerical analyses for several materials are performed and discussed.

• 호남수학학술지
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• 제41권4호
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• pp.823-835
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• 2019

A solution for Nevanlinna-Pick interpolation problem with low complexity is constructed via non-recursive method. More precisely, a stable rational function satifying the given interpolation data in the complex right half plane is found by solving a homogeneous interpolation problem related to a minial interpolation problem for the given data in the right half plane together with its mirror-image data.

• 대한수학회논문집
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• 제9권2호
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• pp.327-329
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• 1994

The Dirichlet problem (DP) on the upper half plane {z = x ＋ iy : y > 0} is to find a real-valued harmonic function u(x, y) satisfying u(x, 0) = g(x) almost everywhere for some reasonably nice function g defined on the real line, which is called the data on the boundary for (DP).(omitted)