• Coupled systems mechanics
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• v.3 no.1
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• pp.89-110
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• 2014

In this work we provide the theoretical formulation, discrete approximation and solution algorithm for instability problems combing geometric instability at large displacements and material instability due to softening under combined thermo-mechanical extreme loads. While the proposed approach and its implementation are sufficiently general to apply to vast majority of structural mechanics models, more detailed developments are provided for truss-bar model. Several numerical simulations are presented in order to illustrate a very satisfying performance of the proposed methodology.

• Journal of the Korean Mathematical Society
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• v.33 no.1
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• pp.137-144
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• 1996

One of the fundamental problems in Riemannian geometry is "How the geometric invariants of Riemannian manifolds influenced by the curvature restriction \ulcorner".ner".uot;.

• The Mathematical Education
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• v.47 no.2
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• pp.197-219
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• 2008

Unlike ordinary situations, deifinitions play a very important role in mathematics education in schools. Mathematical concepts have been mainly acquired by given definitions. However, according to didactical intentions, mathematics education in schools has employed mathematical concepts and definitions with less strict forms than those in pure mathematics. This research mainly discusses definitions used in geometry (promising) course in primary schools to cope with possibilities of creating misconception due to this didactical transformation. After analyzing problems with potential misconceptions, a survey was conducted $\underline{with}$ 80 primary school teachers in Jeju to investigate their recognitions in meaning of mathematical concepts in geometry and attitudes toward teaching. Most of the respondents answered they taught their students while they knew well about mathematical definitions in geometry but the respondents sometimes confused mathematical concepts of polygons and circles. Also, they were aware of problems in current mathematics textbooks which have explained figures in small topics (classes). Here, several suggestions are proposed as follows from analyzing teachers' recognitions and researches in mathematical viewpoints of definitions (promising) in geometric figures which have been adopted by current mathematics textbooks in primary schools from the seventh educational curriculum. First, when primary school students in their detailed operational stage studying figures, they tend to experience $\underline{a}$ collision between concept images acquired from activities to find out promising and concept images formed through promising. Therefore, a teaching method is required to lessen possibility of misconceptions. That is, there should be a communication method between defining conceptual definitions and Images. Second, we need to consider how geometric figures and their elements in primary school textbooks are connected with fundamental terminologies laying the foundation for geometrical definitions and more logical approaches should be adopted. Third, the consistency with studying geometric figures should be considered. Fourth, sorting activities about problems in coined words related to figures and way and time of their introductions should be emphasized. In primary schools mathematics curriculum, geometry has played a crucial role in increasing mathematical ways of thoughts. Hence, being introduced by parts from viewpoints of relational understanding should be emphasized more in textbooks and teachers should teach students after restructuring this. Mathematics teachers should help their students not only learn conceptual definitions of geometric figures in their courses well but also advance to rigid mathematical definitions. Therefore, that's why mathematics teachers should know meanings of concepts clearly and accurately.

• ETRI Journal
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• v.35 no.6
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• pp.1084-1093
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• 2013

problem of pedestrian localization using mobile nodes containing impulse radio ultra wideband (IR-UWB) is considered. IEEE 802.15.4a-based IR-UWB can achieve accurate ranging. However, the coverage is as short as 30 m, owing to the restricted transmit power. This factor may cause a poor geometric relationship among the mobile nodes and anchor nodes in certain environments. To localize a group of pedestrians accurately, an enhanced cooperative localization method is proposed. We describe a sequential algorithm and define problems that may occur in the implementation of the algorithm. To solve these problems, a batch algorithm is proposed. The batch algorithm can be carried out after performing the sequential algorithm to linearize the nonlinear range equation. When a sequential algorithm cannot be performed due to a poor geometric relationship among nodes, a batch algorithm can be carried out directly. Herein, Monte Carlo simulations are presented to illustrate the proposed method and verify its performance.

• The KSFM Journal of Fluid Machinery
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• v.14 no.2
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• pp.17-24
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• 2011

Temperature gradient focusing (TGF) of analytes via Joule heating is achieved when electric field is applied along a microchannel of varying width. The effect of varying width of the microchannel for the focusing performance of the device was numerically studied. The governing equations were implemented into a quasi-1D numerical model along a microchannel. The validity of the numerical model was verified by a comparison between numerical and experimental results. The distributions of temperature, velocity, and concentration along a microchannel were predicted by the numerical results. The narrower middle width and wider outside width of the channel having the fixed length contribute to improve the focusing performance of the device. However, too narrow middle width of the channel generates a higher temperature which can cause the problems including sample denaturation and buffer solution boiling. Therefore, the channel geometry should be optimized to prevent these problems. The optimal widths of the microchannel for the improvement on TGF were proposed and this model can be easily applied to lab-on-a-chip (LOC) applications where focusing is required based on its simple design.

• The Journal of Engineering Geology
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• v.1 no.1
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• pp.137-145
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• 1991

Groundwater flow in fractured rocks generates many challenging problems to scientist and engineers in the projects related to oil and geothermal reservoirs, subsurface contaminations and underground openings. To circumvent these problems, the numerical simulation of groundwater system is used as an established tool in these days. Discrete modelling approach emphasizes geometric parameters, aperture and transport properties of fracture. On the other hand, continuum modelling approach uses the parameters formulated in a way of average hydraulic property. In recent years, the results of field observations from underground opening indicate that groundwater in rock mass flows in a channel form. The channel flow is postulated as the result of the combined effects of geometric pattern and aperture variation.

• 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.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.6
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• pp.449-453
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• 2001

In this paper, we propose an algorithm to design the adaptive structure of wavelet neural network with F-projection and geometric growing criterion. Geometric growing criterion consists of estimated error criterion considering local error and angle criterion which attempts to assign a wavelet function that is nearly orthogonal to all other existing wavelet functions. These criteria provide a methodology that a network designer can construct wavelet neural network according to one's intention. We apply the proposed constructing algorithm of the adaptive structure of wavelet neural network to approximation problems of 1-D and 2-D function, and evaluate the effectiveness of the proposed algorithm.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.10 no.1
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• pp.27-36
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• 1990

Two beam/column elements in order to analyze the geometric nonlinear plane framed structures including the effects of transverse shear deformation and bending stretching coupling are developed. In the case of the first element (finite segment method), tangent stiffness matrix are derived by directly integrating the equilibrium equations whereas in the case of the second element (finite element method) elastic and geometric stiffness matrices are calculated by using the hermitian polynomials including shear deformation effect as the shape function. Both elements possess the usual six degree of freedoms. Numerical results are presented for the selected test problems which demonstrate that both elements represent reliable and highly accurate tools.

• Journal of the Korea Society of Computer and Information
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• v.9 no.4 s.32
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• pp.133-139
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• 2004

In this paper. we propose a medical image processing method for detection of periodontal disease by geometric analysis on dental digital radiography. This paper proposes the method of an automatic image alignment and detection of minute changes, to overcome defects in the conventional subtraction radiography by image processing technique, that is necessary for getting subtraction image and ROI(Region Of Interest) focused on a selection method using the geometric features in target images. Therefore, we use these methods because they give accuracy, consistency and objective information or data to results. In result, easily and visually we can identify minute differences in the affected parts whether they have problems or not, and using application system.