• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.10a
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• pp.1045-1048
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• 2002

Micromachines are extremely novel artifacts with a variety of special characteristics. Utilizing their tiny dimensions ranging roughly from 10 to $1O^3$ micro-meters, the micromachines can perform tasks in a revolutionary manner that would be impossible for conventional artifacts. Micromachines are in general related to various coupled physical phenomena. They are required to be evaluated and designed considering the coupled phenomena. This paper describes finite element analysis (FEA) simulation of practical behaviors for the micro actuator. Especially, electric field modeling in micro actuators has been generally restricted to in-plane two-dimensional finite element analysis because of the complexity of the micro actuator geometry. However, in this thesis, the actual three-dimensional geometry of the micro actuator is considered. The starting torque obtained from the in-plane two-dimensional analytical solutions were compared with that of the actual three-dimensional FE analysis results. The starting torque is proportional to $V^2$, and that the two-dimensional analytical solutions are larger than the three-dimensional FE ones. It is found that the evaluation of micro actuator has to be considered electrical leakage phenomenon.

• Proceedings of the KIEE Conference
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• 2006.07c
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• pp.1494-1495
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• 2006

A complete finite element analysis method for discharge onset process, which is governed and coupled by charge transport equation and electric field equation, was presented. The charge transport equation of first order was transformed into a second-order one by utilizing the artificial diffusion scheme. The two second-order equations were analyzed by the finite element formulation which is well-developed for second-order ones. The Fowler-Nordheim injection boundary condition was adopted for charge transport equation. After verifying the numerical results by comparing to the analytic solutions using parallel plane electrodes with one carrier system, we extended the result to blade-plane electrodes in 2D xy geometry with three carriers system. Radius of the sharp tip was taken to be 50 ${\mu}m$. When this sharp geometry was solved by utilizing the space discretizing methods, the very sharp tip was found to cause a singularity in electric field and space charge distribution around the tip. To avoid these numerical difficulties in the FEM, finer meshes, a higher order shape function, and artificial diffusion scheme were employed.

• Journal of Educational Research in Mathematics
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• v.26 no.4
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• pp.715-730
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• 2016

The purpose of this study is to analyze Descartes's point of view on the mathematical connection of algebra and geometry which help comprehend the traditional frame with a new perspective in order to access to unsolved problems and provide useful pedagogical implications in school mathematics. To achieve the goal, researchers have historically reviewed the fundamental principle and development method's feature of analytic geometry, which stands on the basis of mathematical connection between algebra and geometry. In addition we have considered the significance of geometric solving of equations in terms of analytic geometry by analyzing related preceding researches and modern trends of mathematics education curriculum. These efforts could allow us to have discussed on some opportunities to get insight about mathematical connection of algebra and geometry via geometric approaches for solving equations using the intersection of curves represented on coordinates plane. Furthermore, we could finally provide the method and its pedagogical implications for interpreting geometric approaches to cubic equations utilizing intersection of conic sections in the process of inquiring, solving and reflecting stages.

• School Mathematics
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• v.9 no.4
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• pp.523-533
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• 2007

This article focused the meaning of Pythagoras' and Euclid's proof about the Pythagorean theorem in a historical and mathematical perspective. Pythagoras' proof using similarity is based on the arithmetic assumption about commensurability. However, Euclid proved the Pythagorean theorem again only using the concept of dissection-rearrangement that is purely geometric so that it does not need commensurability. Pythagoras' and Euclid's different approaches to geometry have to do with Birkhoff's axiom system and Hilbert's axiom system in the school geometry Birkhoff proposed the new axioms for plane geometry accepting real number that is strictly defined. Thus Birkhoff's metrical approach can be defined as a Pythagorean approach that developed geometry based on number. On the other hand, Hilbert succeeded Euclid who had pursued pure geometry that did not depend on number. The difference between the proof using similarity and dissection-rearrangement is related to the unsolved problem in the geometry curriculum that is conflict of Euclid's conventional synthetical approach and modern mathematical approach to geometry.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.3
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• pp.230-237
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• 2004

Lane Sensing techniques based on vision sensors are regarded promising because they require little infrastructure on the highway except clear lane markers. However, they require more intelligent processing algorithms in vehicles to generate the previewed roadway from the vision images. In this paper, a lane sensing algorithm using vision sensors is developed to improve the sensing robustness. The parallel stereo-camera is utilized to regenerate the 3-dimensional road geometry. The lane geometry models are derived such that their parameters represent the road curvature, lateral offset and heading angle, respectively. The parameters of the lane geometry models are estimated by the Kalman filter and utilized to reconstruct the lane geometry in the global coordinate. The inverse perspective mapping from the image plane to the global coordinate considers roll and pitch motions of a vehicle so that the mapping error is minimized during acceleration, braking or steering. The proposed sensing system has been built and implemented on a 1/10-scale model car.

• Journal of Educational Research in Mathematics
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• v.20 no.4
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• pp.529-546
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• 2010

This study aims to analyze and criticize the definition of the similarity concept in mathematical texts by investigating mathematical history. At first, we analyzed the definition of Pythagoras, the definition of Euclid's ${\ll}$Elements${\gg}$, the definition of Clairaut's ${\ll}$Elements of geometry${\gg}$, the postulate of Brkhoff's postulates for plane geometry, the definition of Birkhoff & Beatly의 ${\ll}$Basic Geometry${\gg}$. the definition of SMSG ${\ll}$Geometry${\gg}$. and the definition of the similarity concept in current mathematics texts. Then we criticized the definition of the similarity concept in current mathematics texts based on mathematical history. We critically discussed three issues and gave three suggestions.

• Bulletin of the Korean Chemical Society
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• v.34 no.12
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• pp.3615-3620
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• 2013

Two novel copper(II) bromide complexes with pyridine containing Schiff base ligands, $Cu(pmed)Br_2$ and $Cu(pmed)Br_2$ where pmed = N'-((pyridin-2-yl)methylene)ethane-1,2-diamine (pmed) and dpmed = N,N-diethyl-N'-((pyridin-2-yl)methylene)ethane-1,2-diamine (dpmed) were synthesized and characterized using X-ray single crystal structure analysis, optical and magnetic susceptibility measurements. Crystal structural analysis of $Cu(pmed)Br_2$ showed that the copper(II) ion has a distorted square-pyramidal geometry with the trigonality index of ${\tau}=0.35$ and two intermolecular hydrogen bonds, which result in the formation of two dimensional networks in the ab plane. On the other hand, $Cu(pmed)Br_2$ displayed a near square-pyramidal geometry with the value of ${\tau}=0.06$. In both compounds, the NNN Schiff base and one Br atom occupy the basal plane, whereas the fifth apical position is occupied by the other Br atom at a greater Cu-Br apical distance. The reported complexes show $g_{\mid}$ > $g_{\perp}$ > 2.0023 with a $d_{x2-y2}$ ground state and a penta-coordinated square pyramidal geometry. Variable temperature magnetic susceptibility measurements showed that the developed copper(II) complexes follow the Curie-Weiss law, that is there are no magnetic interactions between the copper(II) ions since the Cu--Cu distance is too far for magnetic contact.

• Fire Science and Engineering
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• v.25 no.4
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• pp.74-81
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• 2011

The numerical analyses for three different shafts in geometry of high buildings were carried out by using computational fluid dynamics model (FDS ver.5.3) for the calculation of the pressure difference and the location of the neutral plane and the visualization of stack effect. At 10 seconds of stack effect, the pressure difference of stack effect in the elevator shaft (79.3 Pa) almost corresponded to the theoretical value (78 Pa). At 300 seconds of stack effect, all the neutral planes of three cases were located about 49 m above floor, where was 5 m higher than the theoretical value. The maximum pressure difference between upper and lower position of shaft decreased with increasing of the geometrical complexity of shaft. This study showed that there was the difference of the stack effects among the geometries of shafts with the visualization of stack effect.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.577-582
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• 2007

A variational formulation for plane elasticity problems is derived based on an isogeometric approach. The isogeometric analysis is an emerging methodology such that the basis functions in analysis domain arc generated directly from NURBS (Non-Uniform Rational B-Splines) geometry. Thus. the solution space can be represented in terms of the same functions to represent the geometry. The coefficients of basis functions or the control variables play the role of degrees-of-freedom. Furthermore, due to h-. p-, and k-refinement schemes, the high order geometric features can be described exactly and easily without tedious re-meshing process. The isogeometric sensitivity analysis method enables us to analyze arbitrarily shaped structures without re-meshing. Also, it provides a precise construction method of finite element model to exactly represent geometry using B-spline base functions in CAD geometric modeling. To obtain precise shape sensitivity, the normal and curvature of boundary should be taken into account in the shape sensitivity expressions. However, in conventional finite element methods, the normal information is inaccurate and the curvature is generally missing due to the use of linear interpolation functions. A continuum-based adjoint sensitivity analysis method using the isogeometric approach is derived for the plane elasticity problems. The conventional shape optimization using the finite element method has some difficulties in the parameterization of boundary. In isogeometric analysis, however, the geometric properties arc already embedded in the B-spline shape functions and control points. The perturbation of control points in isogeometric analysis automatically results in shape changes. Using the conventional finite clement method, the inter-element continuity of the design space is not guaranteed so that the normal vector and curvature arc not accurate enough. On tile other hand, in isogeometric analysis, these values arc continuous over the whole design space so that accurate shape sensitivity can be obtained. Through numerical examples, the developed isogeometric sensitivity analysis method is verified to show excellent agreement with finite difference sensitivity.

• Transactions of the Korean Society of Mechanical Engineers
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• v.13 no.3
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• pp.433-442
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• 1989

Owing to the development of CNC machine tools and automatic programing software, the milling process with ball-end mill has become the most widely used process where three-dimensional precision machining is important. In this study, the ball-end milling process has been analyzed and a cutting force model has been developed to predict the cutting force acting on the ball-end mill on given machining conditions. The development of the model is based on the analysis of geometry of a ball-end mill an the oblique cutting process. The cutting edges of ball-end mills are considered as a series of infinitesimal elements and the geometry of the cutting edge element each cutting edge element is straight. The oblique cutting process in the small cutting edge element has been analyzed as orthogonal cutting process in the plane containing the cutting velocity vector and chip-flow vector. Hence, with the orthogonal cutting data obtained from orthogonal turning test, the cutting forces can be predicted through the model. The predicted cutting forces has shown a fairly good agreement with the test results in various plane cutting conditions.